Amelia Carolina Sparavigna

The Roman Towns and the geometry -Examples of Varatio

Keywords: Centuriaton, Orientaton of Roman colonies, Varare, Varato Torino

The Roman Towns and the geometry -Examples of Varatio

Amelia Carolina Sparavigna

The planning of the Roman colonies was realized by the ancient land surveyors by means of a method which is known as limitatio or ceoturiatio. It is characterized by a layout in the form of a square or rectangular grids, created by parallel and perpendicular roads and canals, which subdivided the setlement into iosulae, which were the house-blocks in the towns or the agricultural plots in the countryside. In some cases these plots were allocated to Roman army veterans [START_REF] Haverield | Ancient town -planning[END_REF]. The main axes of the grids were called decumaous maximus and cardi maximus. The parallel roads to them were the decumaoi and the cardioes. Of course, the choice of the place of a town or colony was dictated by the local environment and the presence of rivers and roads.

To subdivide and label the plots of the land, the surveyor (grimatcus) identied a central viewpoint, known as the umbilicus agri or umbilicus sili. Taking positon there and assuming the same orientaton of the decumanus, the gromatcus deined the territory with the following names: ultra, the land he saw in front of him; citra, the land behind him; dextera, the land to his right; sioistra, the land to his lef [START_REF] Barthel | Römische Limitaton in der Provinz Africa[END_REF][START_REF]dextram appellauerunt quae septentrioni subiaceret, sinistram quae ad meridianum terrae esset, ab oriente ad occasum, quod eo sol et luna spectaret, sicut quidam architect delubra in occidentem recte spectare scripserunt. Aruspices altera linea ad septentrionem a meridiano diuiserunt terram, et a media ultra antca[END_REF]. According to the Latn writer Frontnus [START_REF]dextram appellauerunt quae septentrioni subiaceret, sinistram quae ad meridianum terrae esset, ab oriente ad occasum, quod eo sol et luna spectaret, sicut quidam architect delubra in occidentem recte spectare scripserunt. Aruspices altera linea ad septentrionem a meridiano diuiserunt terram, et a media ultra antca[END_REF], who was referring Varro, the Romans inherited the manner to subdivide the land from the Etruscan Doctrine.

We read in [START_REF]dextram appellauerunt quae septentrioni subiaceret, sinistram quae ad meridianum terrae esset, ab oriente ad occasum, quod eo sol et luna spectaret, sicut quidam architect delubra in occidentem recte spectare scripserunt. Aruspices altera linea ad septentrionem a meridiano diuiserunt terram, et a media ultra antca[END_REF] that the decumaous runs from irieos to iccasus, that is from the sunrise to the sunset. Of course, this is a natural manner to identfy the plots of the land by a simple orientaton from east to west and from north to south, in order to have a conventonal method to label them. However, afer Frontnuss words, some scholars, such as Barthel [START_REF] Barthel | Römische Limitaton in der Provinz Africa[END_REF], argued for an orientaton of the decumanus towards the point of the horizon were the sun was rising, secuodum cielum, but other scholars maintained that the orientaton was just dictated by the local environment or by the main roads of the area, as stressed by Le Gall and Castagnoli [START_REF] Castagnoli | Le ricerche sui rest della centuriazione[END_REF][START_REF] Gall | Les romains et l'orientaton solaire[END_REF].

In any case, to have the regular grids of the limitaton matching the local environments, secuodum oaturam, the Roman surveyors had to rotate the grids. The surveyors had some methods that we can include under the term of varati. We can ind the varati in the literature of the Gromatci, given in [START_REF] Libertni | Gromatci Veteres -Gli Antchi Agrimensori -Traduzione in italiano con comment, igure, schemi e illustrazioni a cura di Giacinto Libertni e con presentazione di Gianluca Soricelli[END_REF][START_REF] Campbell | The Writngs of the Roman Land Surveyors. Introducton, Text, Translaton and Commentary[END_REF].

A remarkable work on the Roman land surveying is [START_REF] Roth Congés | Modalités pratques d'implantaton des cadastres romains : quelques aspects (Quintarios Claudere. Perpendere. Cultellare.Varare : la constructon des cadastres sur une diagonale et ses traces dans le Corpus agrimensorum[END_REF]. The author, Anne Roth-Congès, explains the methods used by the Romans and the Euclidean geometry involved in them. Let us note that Roth-Congès uses the verb varare, from which varati is coming. This verb can be translated in the acton of measuring by means of triangulaton [9]. The method is based on the vara, a sort of pertca. The noun indicates in general "any of various branched structures or implements". It is a term derived from feminine of vārus, "bent outwards with converging extremites, bow-legged," of uncertain origin [9]. According to [START_REF] Roth Congés | Modalités pratques d'implantaton des cadastres romains : quelques aspects (Quintarios Claudere. Perpendere. Cultellare.Varare : la constructon des cadastres sur une diagonale et ses traces dans le Corpus agrimensorum[END_REF][START_REF] Peterson | Design and Performance of the Varatoscope[END_REF], the term varati, also writen uarati, refers in general to the process of oblique surveying. It has two approaches: the varati fumiois, by means of which the distance of an inaccessible point could be calculated by the constructon of right angled triangles, and the varati io agris divisis, that the surveyors could made by means of lines "along the hypotenuse of right angled triangles deined in a rectangular coordinate system" [START_REF] Peterson | Design and Performance of the Varatoscope[END_REF]. This second varati is the one which is statstcally analyzed in [START_REF] Peterson | Design and Performance of the Varatoscope[END_REF]. As stressed by John Peterson, when introducing his analysis, the variety of observed oblique relatonships, that is (1:1, 1:2, 2:3, 3:4 …), is limited.

Besides the study of varati concerning the Hadrianss Wall and the Weterau Limes [START_REF] Peterson | Design and Performance of the Varatoscope[END_REF], we can ind the varati considered for the orientaton of the Roman towns in Spain [START_REF] Orila | Las estructuras ortogonales de nueva planta en época romana[END_REF][START_REF] Rodríguez-Antón | The Uarato and Its Possible Use in Roman Urban Planning to Obtain Astronomical Orientatons[END_REF]. In [START_REF] Sparavigna | The Geometry in the Urban Layout of the Roman Como and Verona: The Same Soluton to Diferent Problems[END_REF], we have analyzed two Roman towns in Italy, Como and Verona. Here we show some example of varati applied to the layout of Roman towns. The axis of reference for the varati was the east-west line. It is quite easy to determine this directon by a gnomon, a pole ixed on a plane surface, its shadow and a circle. In the following discussion, we search for the hypotenuse of rectangular triangles as a segment of the east-west axis. We will try to ind the cathet as multples of the sizes of the townss iosulae.

Como and Verona

The cases of Como and Verona had been discussed in [START_REF] Sparavigna | The Geometry in the Urban Layout of the Roman Como and Verona: The Same Soluton to Diferent Problems[END_REF]. These two towns are showing the same geometry used for a quite diferent natural environment. For what concerns Como, is was founded by Julius Caesar in 59 BC, with the name of Nivum Cimum. In the case of Verona, its territory became Roman about 300 BC. Verona became a Roman colony in 89 BC, and it was classiied as a muoicipium in 49 BC.

As we can see from the Figure 1, the terrain of the two towns is quite diferent. But, as shown in [START_REF] Sparavigna | The Geometry in the Urban Layout of the Roman Como and Verona: The Same Soluton to Diferent Problems[END_REF], the layout is the same. So let us consider the geometry of this layout. We assume that the iosulae of the centuriaton were squares. Let us note that, during the centuries, the iosulae had been deformed and therefore it is difcult to see today the original Roman layout perfectly maintained in the town. In the Figures 2 we can see the rectangular triangles which could have been determined by the varati. The hypotenuses are coincident to the east-west directon. The cathet seem to correspond to 3 and 4 iosulae respectvely [START_REF] Sparavigna | The Geometry in the Urban Layout of the Roman Como and Verona: The Same Soluton to Diferent Problems[END_REF]. So we have that the rectangular triangle is that of the fundamental Pythagorean triple 3,4 and 5. In the Figure 3, a corresponding ideal scheme is given. The two cathet give the directons of the decumaous and the cardi. The angle that the decumanus and the hypotenuse form is given by α=arctan( 3/4)=36.87°.

Therefore the azimuth from true North of the decumaous is 53,13°. These two towns have been proposed as oriented to solstces [START_REF] Sparavigna | Roman Towns Oriented to Sunrise and Sunset on Solstces[END_REF][START_REF] Morandot | Quel solstzio che disegnò il volto di Como[END_REF][START_REF] Gaspani | Verona. Origini storiche e astronomiche[END_REF]. As shown in [START_REF] Sparavigna | The Geometry in the Urban Layout of the Roman Como and Verona: The Same Soluton to Diferent Problems[END_REF], we can see that, within an error of one degree, the directon of the sunrise on solstces is close to the directon of the decumanus given in the Figure 3 (ideal case). The same happens for the decumani of Como and Verona. The fact that the towns were planned according to the varato 3:4 seems well posed. But that this varato was chosen to have the towns aligned to sunrise on solstces could be simply a coincidence.

Torino (Julia Augusta Taurinorum). About the foundaton and the orientaton of Torino, we discussed in [START_REF] Sparavigna | Discussione di alcuni artcoli sulla fondazione di Augusta Taurinorum[END_REF][START_REF] Sparavigna | The Orientaton of Julia Augusta Taurinorum (Torino)[END_REF][START_REF] Sparavigna | Julia Augusta Taurinorum, an archaeoastronomical reload[END_REF]. Torino was probably found in 28/27 a.C. as the cilioia Julia Augusta Taurioirum. The Roman town was placed close to the confuence of Dora and Po rivers, at the foot of the hills (see Figure 4). The geometry of Torino is based on the rectangular triangles 1:2. This geometry had been suggested by Gaetano Barbella in 2008 [START_REF] Barbella | [END_REF]. Triangles are shown in the Figure 5. In the image, the Decumaous and the Cardi are also shown such as the positon of the four gates. In the case of Julia Concordia, the iosulae are not squares. However, the decumanus has the same azimuth (within a degree) of Torino. Therefore the triangle is 1:2. Here in the Figure 6 we have the map and the triangle. The case of this town is very interestng, because of the rectangular iosulae. The fortied camp, which at the tme was the westernmost military fort of Rome in the Po Valley, survived the war and gradually evolved into a town. The importance of Pavia grew with the extension of the Via Aemilia from Ariminum (Rimini) to the Po River (187 BC), which it crossed at Placenta (Piacenza).

In the Figure 7 we can see the terrain of Pavia. The rectangular triangle is 2:7, as shown in the Figure 8. Piacenza. Piacenza and Cremona were founded as Roman military colonies in May 218 BC. The towns were planned in order to be constructed afer the successful war with the Gauls, that ended in 219 BC. In 218 BC, afer declaring war on Carthage, the Senate decided to accelerate the colonizaton. The layout that we see today is probably based on a second deducton of 190 BC [23]. In the Figure 9 we can see its triangle. Other cases Let us menton the case of Bologna. The geometry of the Roman Bologna is given in [START_REF] Incert | The Urban fabric of Bologna: orientaton problems[END_REF] by Manuela Incert. The rectangular triangle is 2:9. It is evident therefore, from [START_REF] Barbella | [END_REF] and [START_REF] Incert | The Urban fabric of Bologna: orientaton problems[END_REF], that the problem of the geometry on which the layout of the Roman towns had been founded, is a known problem, addressed in literature. The only way to contnue the study is that of collectng, besides the maps of the towns, also the literature on their planning.

To conclude, let me menton book [START_REF] Kaiser | Roman Urban Street Networks: Streets and the Organizaton of Space in Four Cites[END_REF]; this can be the origin of further analyses on street networks. As told in [START_REF] Boeing | Urban Spatal Order: Street Network Orientaton, Coniguraton, and Entropy[END_REF], [START_REF] Kaiser | Roman Urban Street Networks: Streets and the Organizaton of Space in Four Cites[END_REF] is telling that the "Roman Empire used standardized street grids to efciently lay out new towns and colonies during rapid imperial expansion". Therefore, the study of the geometry could be interestng to determine the standardizaton of the urban layout.

Figure 1 :

 1 Figure 1: Thanks to Acme Mapper, htps://mapper.acme.com, we can appreciate very well the terrain of Como (lef panel) and Verona (right panel). The core of the Roman Verona is in the bend of the Adige river.

Figure 2 :

 2 Figure 2: Como (on the lef) and its rectangular triangle 3,4 and 5 shown on a epsg.io map. The same rectangular triangle on the right for Verona (© MapTiler © OpenStreetMap contributors).

Figure 4 :

 4 Figure 4: Thanks to Acme Mapper, htps://mapper.acme.com, we can appreciate the positon of Julia Augusta Taurinorum, the red square, and the terrain surrounding it.

Figure 5 .

 5 Figure 5. By means of Acme Mapper and © OpenStreetMap contributors, we can see the layout of Torino. OpenStreetMap (CC BY-SA). In the image, the Decumaous and the Cardi are also given.

Figure 6 .

 6 Figure 6. Map of Julia Concordia by Bertolini D., Notzie degli scavi di antchità,1880.

Figure 7 :

 7 Figure 7: Pavia in the Acme Mapper, htps://mapper.acme.com.

Figure 8 :

 8 Figure 8: Pavia. The rectangular triangle is 2:7. Courtesy © MapTiler © OpenStreetMap contributors.

Figure 9 :

 9 Figure 9: Piacenza The rectangular triangle is 5:6. Courtesy © OpenStreetMap contributors.

Zenodo.[START_REF] Sparavigna | The Orientaton of Julia Augusta Taurinorum (Torino)[END_REF] August 2019 -DOI 10.5281/zenodo.3370498


Stuart Hallifax
email: stuart.hallifax@liris.cnrs.fr

Jean Moulin Lyon

Audrey Serna
email: audrey.serna@liris.cnrs.fr

Jean-Charles Marty
email: jean-charles.marty@liris.cnrs.fr

Guillaume Lavoué
email: guillaume.lavoue@liris.cnrs.fr

Elise Lavoué
email: elise.lavoue@liris.cnrs.fr

Factors to Consider for Tailored Gamification

Keywords: •Human-centered computing → Empirical studies in HCI, User models, •Applied computing → Computer games, Gamification, User motivation, User Types, Tailoring, Crowdsourcing

Gamification is widely used to foster user motivation. Recent studies show that users can be more or less receptive to different game elements, based on their personality or player profile. Consequently, recent work on tailored gamification tries to identify links between user types and motivating game elements. However findings are very heterogeneous due to different contexts, different typologies to characterize users, and different implementations of game elements. Our work seeks to obtain more generalizable findings in order to identify the main factors that will support design choices when tailoring gamification to users' profiles and provide designers with concrete recommendations for designing tailored gamification systems. For this purpose, we ran a crowdsourced study with 300 participants to identify the motivational impact of game elements. Our study differs from previous work in three ways: first, it is independent from a specific user activity and domain; second, it considers three user typologies; and third, it clearly distinguishes motivational strategies and their implementation using multiple different game elements. Our results reveal that (1) different implementations of a same motivational strategy have different impacts on motivation, (2) dominant user type is not sufficient to differentiate users according to their preferences for game elements, (3) Hexad is the most appropriate user typology for tailored gamification and (4) the motivational impact of certain game elements varies with the user activity or the domain of gamified systems.

INTRODUCTION

Since the early 2000s, gamification has been increasingly used to enhance user motivation [START_REF] Ferro | Towards personalised, gamified systems: an investigation into game design, personality and player typologies[END_REF][START_REF] Looyestyn | Does gamification increase engagement with online programs? A systematic review[END_REF][START_REF] Baptiste Monterrat | Motivation for learning: Adaptive gamification for web-based learning environments[END_REF][START_REF] Robinson | A preliminary taxonomy of gamification elements for varying anticipated commitment[END_REF][START_REF] Yee | Motivations for play in online games[END_REF]. Gamification, defined as "the use of design elements characteristic of games in non game contexts" [START_REF] Deterding | From game design elements to gamefulness: defining gamification[END_REF], is used nowadays in many domains, from education [START_REF] Denny | Empirical Support for a Causal Relationship Between Gamification and Learning Outcomes[END_REF][START_REF] Landers | Enhancing instructional outcomes with gamification: An empirical test of the Technology-Enhanced Training Effectiveness Model[END_REF][START_REF] Lavoué | Adaptive Gamification for Learning Environments[END_REF], to health [START_REF] Jia | Personality-targeted Gamification: A Survey Study on Personality Traits and Motivational Affordances[END_REF][START_REF] Lehto | Persuasive features in web-based alcohol and smoking interventions: a systematic review of the literature[END_REF], and the workplace [START_REF] Eickhoff | Quality through flow and immersion: gamifying crowdsourced relevance assessments[END_REF][START_REF] Flatla | Calibration games: making calibration tasks enjoyable by adding motivating game elements[END_REF][START_REF] Oprescu | I PLAY AT WORK-ten principles for transforming work processes through gamification[END_REF]]. These "design elements" are named differently, often using the terms "pervasive strategies", "motivational strategies", "game mechanics", or "game elements".

Several studies in this field show that users can be more or less receptive to different game elements [START_REF] Busch | Personalization in serious and persuasive games and gamified interactions[END_REF][START_REF] Kaptein | Adaptive persuasive systems: a study of tailored persuasive text messages to reduce snacking[END_REF][START_REF] Monterrat | A player model for adaptive gamification in learning environments[END_REF][START_REF] Baptiste Monterrat | Adaptation of Gaming Features for Motivating Learners[END_REF][START_REF] Orji | Tailoring persuasive health games to gamer type[END_REF]. These studies suggest that user personality and preferences have a great influence on the effect that game elements have on user motivation. Appropriate game elements can lead to higher levels of user motivation, whereas inappropriate game elements can demotivate users. Recent work on tailored gamification [START_REF] Ferro | Towards personalised, gamified systems: an investigation into game design, personality and player typologies[END_REF][START_REF] Jia | Personality-targeted Gamification: A Survey Study on Personality Traits and Motivational Affordances[END_REF][START_REF] Mora | Effect of personalized gameful design on student engagement[END_REF][START_REF] Orji | Improving the Efficacy of Games for Change Using Personalization Models[END_REF] has provided valuable results that identify links between user types and relevant or motivating game elements. However, these results are very heterogeneous due to three reasons. First, the studies are generally carried out in different and particular domains (usually in health or education). Second, they rely on specific and different user typologies or personality models, mainly BrainHex [START_REF] Lennart | BrainHex: preliminary results from a neurobiological gamer typology survey[END_REF], Hexad [START_REF] Tondello | The Gamification User Types Hexad Scale[END_REF], or Big Five [START_REF] Lewis | The development of markers for the Big-Five factor structure[END_REF]. Third, they do not consider the same game elements or study different levels of abstraction of motivational strategies.

Thus, the motivational impact of game elements considered in these studies is difficult to isolate and the results are hard to reuse when designing tailored gamification. The goal of our work is to obtain more generalizable findings on factors to consider to support gameful design choices for tailored gamification. For this purpose, we conducted a new study on the motivational impact of game elements according to user types. Our study differs from existing works in three ways: first, our study is context-independent meaning that the scenarios that illustrate the game elements are not related to a specific user activity or domain; second, we characterize users using two different user typologies (BrainHex, Hexad) and a personality trait model (Big Five); third, we make a clear distinction between the high-level motivational strategies and their implementation in the form of game elements.

Our study was conducted using a crowdsourcing platform and reached 616 participants. They were then filtered down to a set of 300 high-quality and consistent participants. The motivational impact of game elements was evaluated using a pairwise comparison protocol involving 66 comparisons between pairs of game elements illustrated by storyboards. Our results show that: [START_REF] Anderson | Steering user behavior with badges[END_REF] game elements from a same motivational strategy have significantly different impacts on user motivation, [START_REF] Attali | Gamification in assessment: Do points affect test performance[END_REF] the dominant user type is not sufficient to differentiate users according to their preferences for game elements (3) out of the user models tested, Hexad is most appropriate for tailored gamification, and (4) the motivational impact of certain game elements varies with the user activity and the domain of gamified systems. Finally, we provide designers with concrete recommendations for tailored gamification.

RELATED WORK

Gamification design and user motivation

Meaningful design advocates that game elements should make sense to users, creating explicit connections to the activity [START_REF] Deterding | The lens of intrinsic skill atoms: A method for gameful design[END_REF][START_REF] Hallifax | A Design Space For Meaningful Structural Gamification[END_REF][START_REF] Nicholson | A user-centered theoretical framework for meaningful gamification[END_REF]. To do so, global design processes generally recommend to take the following steps: define the main objective, understand users' motivation for the activity, identify the game mechanics and analyze the effect of gamification [START_REF] Kumar | Gamification at work: Designing engaging business software[END_REF][START_REF] Marache | Process of gamification[END_REF][START_REF] Werbach | For the win: How game thinking can revolutionize your business[END_REF].

To broaden these guidelines, several studies have been conducted to measure the impact of game elements on user motivation in different domains, mainly health [START_REF] Jia | Personality-targeted Gamification: A Survey Study on Personality Traits and Motivational Affordances[END_REF][START_REF] Orji | Towards Personality-driven Persuasive Health Games and Gamified Systems[END_REF][START_REF] Orji | Personalizing Persuasive Strategies in Gameful Systems to Gamification User Types[END_REF][START_REF] Orji | Modeling the efficacy of persuasive strategies for different gamer types in serious games for health[END_REF][START_REF] Tondello | The Gamification User Types Hexad Scale[END_REF] and education [START_REF] Denny | Empirical Support for a Causal Relationship Between Gamification and Learning Outcomes[END_REF][START_REF] Lavoué | Adaptive Gamification for Learning Environments[END_REF][START_REF] Baptiste Monterrat | Adaptation of Gaming Features for Motivating Learners[END_REF][START_REF] Mora | Effect of personalized gameful design on student engagement[END_REF]. They are usually based on a small set of game elements in specific contexts and do not reach a consensus on the impact on user motivation [START_REF] Seaborn | Gamification in theory and action: A survey[END_REF]. For instance, in the context of online communities users who used badges were significantly more engaged [START_REF] Hamari | Do badges increase user activity? A field experiment on the effects of gamification[END_REF]. Another study showed that the integration of a leaderboard and badges induced a lower level of motivation and lower final exam scores [START_REF] Michael | Assessing the effects of gamification in the classroom: A longitudinal study on intrinsic motivation, social comparison, satisfaction, effort, and academic performance[END_REF]. However, leaderboards have also been shown to be interesting for supporting goal setting [START_REF] Landers | Gamification of task performance with leaderboards: A goal setting experiment[END_REF]. These contradictory results suggest that the observed impact of game elements may be influenced by the user activity (e.g. exchanging with peers, taking exams or goal setting) and/or the domain (e.g. online community, education). Hence these specific results are hard to reuse when designing gamification. Only one study [START_REF] Tondello | Elements of Gameful Design Emerging from User Preferences[END_REF] was conducted independently from a context, but considering only component elements and not specific game elements.

Theoretical foundations of gamification research mainly rely on the Self-Determination Theory (SDT [START_REF] Ryan | Self-determination theory and the facilitation of intrinsic motivation, social development, and well-being[END_REF]) that argues that human beings are intrinsically motivated to engage in activities that satisfy three basic psychological needs: competence (sense of efficacy), autonomy (volition and personal agency), and relatedness (social interaction). SDT also argues that Humans strive to fulfill these three needs in order to enhance wellbeing. Meaningful gamification should spontaneously provoke the satisfaction of these three user needs [START_REF] Rigby | Glued to games: How video games draw us in and hold us spellbound (New directions in media)[END_REF], especially the sense of competence [START_REF] Deterding | The lens of intrinsic skill atoms: A method for gameful design[END_REF]. This theoretical framework suggests that user motivation when using gamified environments may be enhanced by game elements independently from any context. For instance, we could suppose that the need for relatedness can be fulfilled with any kind of social interaction. However, existing studies do not allow us to identify general recommendations for gamification design as they were all conducted in specific contexts.

No ground studies have been conducted on the influence of the user activity and domain on the motivational impact of game elements. We address this question by considering contextindependent game elements, and comparing our results with previous studies in specific contexts. Our study aims to provide general recommendations for game elements that can be used in any context, and identify those whose motivational impact varies with the context.

User typologies for tailored gamification

Several studies focus on player types to differentiate the motivational impact of game elements. They rely on different typologies, such as BrainHex [START_REF] Lennart | BrainHex: preliminary results from a neurobiological gamer typology survey[END_REF] and Hexad [START_REF] Marczewski | Even Ninja Monkeys like to play[END_REF].

The BrainHex player typology [START_REF] Lennart | BrainHex: preliminary results from a neurobiological gamer typology survey[END_REF] was originally developed specifically as a "gamer" typology. However, research has applied it indiscriminately in both game and gamification studies [START_REF] Busch | a. Using Player Type Models for Personalized Game Design-An Empirical Investigation[END_REF][START_REF] Lavoué | Adaptive Gamification for Learning Environments[END_REF][START_REF] Baptiste Monterrat | Adaptation of Gaming Features for Motivating Learners[END_REF][START_REF] Orji | Improving the Efficacy of Games for Change Using Personalization Models[END_REF][START_REF] Orji | Tailoring persuasive health games to gamer type[END_REF][START_REF] Orji | Modeling the efficacy of persuasive strategies for different gamer types in serious games for health[END_REF]. It proposes seven player types : Seeker, Survivor, Daredevil, Mastermind, Conqueror, Socialiser, and Achiever. BrainHex is based on a top-down approach, taking inspiration from neurobiological research [START_REF] Bateman | Player Typology in Theory and Practice[END_REF]. For instance, Lavoué et al. [START_REF] Lavoué | Adaptive Gamification for Learning Environments[END_REF] use BrainHex to adapt five game elements to users' dominant player type (i.e. the highest scoring type).

Marczewski more recently developed the Gamification User Types Hexad framework [START_REF] Marczewski | Even Ninja Monkeys like to play[END_REF] specifically for gamification. This typology is based on SDT [START_REF] Ryan | Self-determination theory and the facilitation of intrinsic motivation, social development, and well-being[END_REF]. The Hexad typology designates six different user types: Philanthropists, Socialisers, Free Spirits, Achievers, Players, and Disruptors. Several recent experimental studies have been conducted in order to identify the motivational impact of game elements regarding the Hexad profile [START_REF] Mora | Effect of personalized gameful design on student engagement[END_REF][START_REF] Orji | Personalizing Persuasive Strategies in Gameful Systems to Gamification User Types[END_REF]. Finally, a few recent studies [START_REF] Jia | Personality-targeted Gamification: A Survey Study on Personality Traits and Motivational Affordances[END_REF][START_REF] Orji | Towards Personality-driven Persuasive Health Games and Gamified Systems[END_REF] on tailored gamification consider "personality traits" to identify user preferences, mainly the Big Five Factors [START_REF] Lewis | The development of markers for the Big-Five factor structure[END_REF]. The five user types are: Openness to experience, Conscientiousness, Extraversion, Agreeableness, and Emotional stability.

In this context, we first question the influence of the use of one particular user model for tailored gamification. Studies on tailored gamification were conducted using a particular user model, making it difficult to exploit the results obtained. For instance, in the field of persuasive technologies for health, three different studies contribute to identify strategies the most suited to the user profile using BrainHex [START_REF] Orji | Modeling the efficacy of persuasive strategies for different gamer types in serious games for health[END_REF], Big Five [START_REF] Orji | Towards Personality-driven Persuasive Health Games and Gamified Systems[END_REF] and Hexad [START_REF] Orji | Personalizing Persuasive Strategies in Gameful Systems to Gamification User Types[END_REF]. But the results obtained are not compared and designers are not advised on a particular typology or model to use. Furthermore, even if some user types have the same name, they do not have the same definitions, or represent the same user motivations (e.g. Achievers in BrainHex like collecting everything, whereas achievers in Hexad are motivated by mastery). In our study, we propose to test all three commonly used user models, and to compare the influences found for each user model dimension in relation to their definitions.

We also question the relevance of considering only the dominant type for player typologies when tailoring gamification. Most of the studies only consider the dominant user type, i.e. the type that has the highest score [START_REF] Gil | Validating gamification mechanics and player types in an E-learning environment[END_REF][START_REF] Geiser | An ontology engineering approach to gamify collaborative learning scenarios[END_REF][START_REF] Lavoué | Adaptive Gamification for Learning Environments[END_REF][START_REF] Ferro | Towards personalised, gamified systems: an investigation into game design, personality and player typologies[END_REF][START_REF] Thue | Interactive Storytelling: A Player Modelling Approach[END_REF]. Studies considering personality traits take all dimensions into account [START_REF] Orji | Towards Personality-driven Persuasive Health Games and Gamified Systems[END_REF] and few very recent studies do the same for player typologies [START_REF] Orji | Personalizing Persuasive Strategies in Gameful Systems to Gamification User Types[END_REF] or establish clusters with hybrid profiles for more fine-grained analysis [START_REF] Mora | Effect of personalized gameful design on student engagement[END_REF]. These considerations could have an impact on tailoring gamification.

Motivational strategies and game elements

Werbach et al. [START_REF] Werbach | For the win: How game thinking can revolutionize your business[END_REF] propose the DMC (Dynamics, Mechanics and Components) framework to classify game elements through three levels, from the most abstract to the most concrete elements. Dynamics are "the big-picture aspects of the gamified system" which are not directly used (constraints, emotions, narrative, etc.). Mechanics are "the basic processes that drive the action forward and generate player engagement" (challenges, chance, competition, etc.). Finally, components are "the specific instantiations of mechanics and dynamics" (achievements, avatars, badges, etc.).

In the persuasive technology field, studies are mainly focused on the game mechanics level, often named "persuasive strategies" or "motivational strategies" [START_REF] Orji | Modeling the efficacy of persuasive strategies for different gamer types in serious games for health[END_REF]. In field studies on the impact of motivational strategies, authors use commonly accepted categories of strategies such as competition, simulation, rewards, or comparison [START_REF] Hamari | Does gamification work?-a literature review of empirical studies on gamification[END_REF][START_REF] Lehto | Persuasive features in web-based alcohol and smoking interventions: a systematic review of the literature[END_REF][START_REF] Orji | Towards Personality-driven Persuasive Health Games and Gamified Systems[END_REF]. These studies usually rely on the evaluation of only one implementation of a given motivational strategy, and we can question the influence of the implementation choices on the effect of tailored gamification. Furthermore, the categories of persuasive strategies on which they rely do not clearly distinguish the motivational strategies from their implementation. For example, points and rewards are considered at the same level in [START_REF] Hamari | a. Do persuasive technologies persuade?-a review of empirical studies[END_REF], whereas rewards can be considered as a higher level concept that could be implemented using badges or points.

In the gamification field, studies generally focus on the "components" level of the DMC framework to evaluate the motivational impact of one or several commonly used game elements. For example, [START_REF] Attali | Gamification in assessment: Do points affect test performance[END_REF] examines how points affect test performance in mathematics. [START_REF] Denny | Empirical Support for a Causal Relationship Between Gamification and Learning Outcomes[END_REF] compares the effectiveness of badges and points systems in an educational setting. [START_REF] Orji | Improving the Efficacy of Games for Change Using Personalization Models[END_REF] uses badges and leaderboards in an app designed to remedy unhealthy eating habits. [START_REF] Mekler | Towards understanding the effects of individual gamification elements on intrinsic motivation and performance[END_REF] compares the effects of points, leaderboards, and levels on user motivation, competence and performance in an image annotation task. However, these studies generally do not consider the higher level of the motivational strategies they implement (mechanics and dynamics of the DMC framework).

More theoretical research provides lists of game elements as a first step to a more structured and systematic approach in the domain. For instance, [START_REF] Ferro | Towards personalised, gamified systems: an investigation into game design, personality and player typologies[END_REF] presents an extensive review of related literature to identify the commonly used game elements: achievements, combos, bars, leaderboards, points,

Strategy

Game element Equivalent to

Rewards

Badges Badges [START_REF] Ferro | Towards personalised, gamified systems: an investigation into game design, personality and player typologies[END_REF][START_REF] Jia | Personality-targeted Gamification: A Survey Study on Personality Traits and Motivational Affordances[END_REF] Rewards [START_REF] Jia | Personality-targeted Gamification: A Survey Study on Personality Traits and Motivational Affordances[END_REF] Badges or Achievements [START_REF] Marczewski | Even Ninja Monkeys like to play[END_REF][START_REF] Tondello | The Gamification User Types Hexad Scale[END_REF] Points

Points [START_REF] Ferro | Towards personalised, gamified systems: an investigation into game design, personality and player typologies[END_REF][START_REF] Jia | Personality-targeted Gamification: A Survey Study on Personality Traits and Motivational Affordances[END_REF], Reward [START_REF] Orji | Towards Personality-driven Persuasive Health Games and Gamified Systems[END_REF][START_REF] Orji | Personalizing Persuasive Strategies in Gameful Systems to Gamification User Types[END_REF][START_REF] Orji | Modeling the efficacy of persuasive strategies for different gamer types in serious games for health[END_REF] Teams Cooperation [START_REF] Orji | Towards Personality-driven Persuasive Health Games and Gamified Systems[END_REF][START_REF] Orji | Personalizing Persuasive Strategies in Gameful Systems to Gamification User Types[END_REF][START_REF] Orji | Modeling the efficacy of persuasive strategies for different gamer types in serious games for health[END_REF] Teamwork [START_REF] Jeng | Personality and motivations for playing online games[END_REF] Guilds or Team [START_REF] Marczewski | Even Ninja Monkeys like to play[END_REF][START_REF] Tondello | The Gamification User Types Hexad Scale[END_REF]

Discussion

Social network [START_REF] Marczewski | Even Ninja Monkeys like to play[END_REF][START_REF] Tondello | The Gamification User Types Hexad Scale[END_REF] Progress Compared Leaderboards [START_REF] Ferro | Towards personalised, gamified systems: an investigation into game design, personality and player typologies[END_REF][START_REF] Jia | Personality-targeted Gamification: A Survey Study on Personality Traits and Motivational Affordances[END_REF][START_REF] Lavoué | Adaptive Gamification for Learning Environments[END_REF]] Competition and Comparison [START_REF] Orji | Modeling the efficacy of persuasive strategies for different gamer types in serious games for health[END_REF] Comparison [START_REF] Orji | Towards Personality-driven Persuasive Health Games and Gamified Systems[END_REF][START_REF] Orji | Personalizing Persuasive Strategies in Gameful Systems to Gamification User Types[END_REF] Social Comparison [START_REF] Marczewski | Even Ninja Monkeys like to play[END_REF][START_REF] Tondello | The Gamification User Types Hexad Scale[END_REF] Task Bars [START_REF] Ferro | Towards personalised, gamified systems: an investigation into game design, personality and player typologies[END_REF] Progress [START_REF] Jia | Personality-targeted Gamification: A Survey Study on Personality Traits and Motivational Affordances[END_REF] Self-monitoring and suggestion [START_REF] Orji | Modeling the efficacy of persuasive strategies for different gamer types in serious games for health[END_REF] Self-monitoring and feedback [START_REF] Orji | Towards Personality-driven Persuasive Health Games and Gamified Systems[END_REF][START_REF] Orji | Personalizing Persuasive Strategies in Gameful Systems to Gamification User Types[END_REF] Advancement [START_REF] Jeng | Personality and motivations for playing online games[END_REF] Levels or progression [START_REF] Marczewski | Even Ninja Monkeys like to play[END_REF][START_REF] Tondello | The Gamification User Types Hexad Scale[END_REF] Table 1: The 12 game elements we used grouped by motivational strategy, and their equivalents in previous studies.

status, badges, bonuses, levels, reward schedule, customization, quests, inventory (see [START_REF] Huotari | Defining Gamification: A Service Marketing Perspective[END_REF][START_REF] Kapp | The gamification of learning and instruction: game-based methods and strategies for training and education[END_REF][START_REF] Werbach | For the win: How game thinking can revolutionize your business[END_REF] for other lists). Some theoretical studies identify direct links between game elements and the game mechanism they support [START_REF] Vassileva | Motivating participation in social computing applications: a user modeling perspective[END_REF], but they have not been tested on real ground yet.

In conclusion, previous field studies on the impact of game elements on user motivation either consider low-level game elements (Components) without considering the motivational strategies (Mechanics and Dynamics) they support, or highlevel strategies each represented by one single implementation.

In our study, we structure game elements according to two different levels: an abstract level connected to motivational strategies and a more concrete level allowing to compare different implementations of these strategies. allowing us to study how user motivation varies with the implementation. We present the game elements used in our study in Section 3.

STUDY DESIGN

Our study seeks to identify the factors that will support design choices when tailoring gamification to user profiles. These choices underline a general question which is how we can identify users' preferences for game elements. From the related work analysis, we address several research questions:

• Considering the game elements, "Do game elements implementing a same motivational strategy have different impacts on user motivation ?"

• Considering the user typologies, "Is the dominant user type sufficient to discriminate users' preferences? And which typology should be chosen for tailored gamification?"

• Considering the user activity and domain, "To which extent does the context influence the motivational impact of game elements?"

To explore these questions, we consider 5 motivational strategies, implemented by 12 game elements. This list was created from the references listed in table 1, then filtered to only keep elements that are not directly linked to the content (such as storytelling) as they did not make sense for a domain independent task. We then grouped these game elements into an overarching motivational strategy they implement. The game elements are illustrated using storyboards that show implementations of motivational strategies independently from any specific user activity and domain. The perceived motivational impact of each element is evaluated using a paired comparison protocol which has been shown to be more reliable than direct rating [START_REF] Perez | A practical guide and software for analysing pairwise comparison experiments[END_REF][START_REF] Nihar | Estimation from Pairwise Comparisons: Sharp Minimax Bounds with Topology Dependence[END_REF]. We compare variations based on users' profiles according to the three most commonly used user models: BrainHex, Big Five Factor and Hexad.

Materials

We designed a storyboard for each game element independent of any activity and domain (see an example in figure 1). This methodology was inspired by [START_REF] Orji | Towards Personality-driven Persuasive Health Games and Gamified Systems[END_REF][START_REF] Orji | Personalizing Persuasive Strategies in Gameful Systems to Gamification User Types[END_REF][START_REF] Orji | Modeling the efficacy of persuasive strategies for different gamer types in serious games for health[END_REF]. Each of the storyboards depicts three panels where a user completes a generic "task" with the game element changing accordingly. The full storyboards are presented in the supplementary materials.

Rewards game elements

In the Points storyboard, the user receives points each time s/he completes a task, his/her total score is shown in the game element area. For Badges the user gains a badge for completing the task, s/he can see a list of the badges s/he has obtained, as well as the badges s/he can still obtain in the game element area. For Useful rewards, the user completes a task and gains a "Give example" power. The area on the right shows the users inventory, with items such as "Skip task" and "Help" that suggest their usage.

Goals game elements

Both of the Goals storyboards have the same general structure: the game element area on the right shows a list of goals that the user has to complete, each one has a checkbox that shows whether a given goal has been completed or not. For External Goals, the storyboard shows the user completing a task, after which a popup informs him/her that the system has given them a new goal. A new goal and checkbox appear in their goal list. For Self Goals there is a button in the game element area that opens a window where the user can add a new goal himself/herself instead.

Time game elements

The Schedule storyboard shows a five day calendar. The user has to complete at least one task per day. Each day that a user completes a task, a check mark is placed in the corresponding day. After completing five days, the user receives a bonus. For the Timer storyboard, the user is timed the see how quickly s/he can complete a task. In the game element area, s/he is shown a table of his/her previous times. After completing a task the table updates, and the user is informed if s/he performed a new record (faster time than before).

Social Interaction game elements

In the Trading storyboard, a user selects a task to complete in the task area. A popup informs him/her that s/he needs a "key" to start that particular task, which s/he acquires by using the "chat" on the right to trade another user for it. For the Teams storyboard, the user acquires points each time s/he completes a task, the user can see his/her team score. A set of notifications on the right show when another user in his/her team completes a task and increases the team score. The Discussion storyboard shows a user stuck on a task. S/he uses the chat on the right to ask other users for help. Another user provides a solution to their problem and s/he can complete the task.

Progress game elements

Both of the Progress game element storyboards have a similar design. They both use a progress bar in the game element area that fills up when a user completes a task. In the Compared Progress storyboard, the bar shows the class average on the side and opens a popup when the user advances into the top 50% of their class. In the Task Progress storyboard the class average is replaced by a simple marking to show how much of the task the user has completed (50%, 60% etc.).

Storyboard validation

To ensure that these context-independent storyboards would be understood by all participants, we ran a pre-study comparing them to similar storyboards for a math learning activity. We asked participants to describe in their own words each storyboard. The descriptions were then reviewed by two different evaluators and graded out of 3. After an initial set of evaluations using 8 participants, we iterated on our storyboard design, and validated the final design using a further 2 participants. We found that the descriptions given for the context-free storyboards matched those given for the task-specific ones. Furthermore, to ensure that the comprehension of the storyboards was not influenced by age, or familiarity with video games (or game mechanics in general), we calculated the correlation between these factors. We found a very low correlation (0.10) between participant age and understanding, and a low correlation (0.28) between video game familiarity and understanding. We therefore judged that our storyboards could be understood as well as context-specific storyboards by all participants.

Procedure

As stated above, we used a paired comparison technique to evaluate the perceived motivational impact of each game element. Participants were shown pairs of storyboards, and were asked to choose which one they estimate "would motivate them more to use the system" (forced-choice methodology). Such paired comparison protocol offers 3 advantages over Likerttype rating [START_REF] Perez | A practical guide and software for analysing pairwise comparison experiments[END_REF]: (1) the experimental task is less cognitively demanding [START_REF] Andrew P Clark | Why rate when you could compare ? Using the " EloChoice " package to assess pairwise comparisons of perceived physical strength[END_REF] (choosing a preference between two items is easier than providing an ordinal rating); (2) it avoids normalization issues which occur, for instance, when some users avoid extreme response categories; (3) it has been shown to provide higher sensitivity and lower measurement error [START_REF] Nihar | Estimation from Pairwise Comparisons: Sharp Minimax Bounds with Topology Dependence[END_REF].

We opted for a full paired-comparison design, meaning that each participant evaluates all possible pairs of storyboards, i.e. n 2 = n(n -1)/2 pairs with n the total number of storyboards. In our experiment n = 12 leading to 66 comparisons. This full design, as opposed to incomplete ones, is more time consuming for individual participants but allows a complete Figure 1: An example of one of the 12 storyboards created to illustrate the game elements that implement the 5 motivational strategies. This particular one depicts the Badges game element related to the Rewards strategy. evaluation of participant agreement and consistency. Note that the order of pairs is randomized for each participant.

Data collection

As commonly used in HCI research (e.g., [START_REF] Heer | Crowdsourcing Graphical Perception: Using Mechanical Turk to Assess Visualization Design[END_REF][START_REF] Orji | Improving the Efficacy of Games for Change Using Personalization Models[END_REF][START_REF] Orji | Personalizing Persuasive Strategies in Gameful Systems to Gamification User Types[END_REF]), we leveraged the power of crowdsourcing to recruit a large number of participants. Our study used the Figure Eight platform 1 and proposed a task divided into two parts: firstly, participants were asked to complete the paired-comparison experiment described above; secondly, they were asked to fill questionnaires allowing us to determine their BrainHex, Hexad and Big Five profile. For the first two, we used the official questionnaires [START_REF] Tondello | The Gamification User Types Hexad Scale[END_REF][START_REF]BrainHex questionnaire[END_REF], for the last one, we used a simplified version of traditional big five questionnaires called TIPI (Ten Item Personality Measure) [START_REF] Samuel | A very brief measure of the Big-Five personality domains[END_REF]. Using the tools provided by the crowdsourcing platform we ensured that our participants came from a wide variety of different countries and that they could respond to our task only once. Participants were paid a total of US$1.25, and spent between 15 and 25 minutes to complete the surveys.

Data filtering

As with all crowdsourced studies, certain measures are required to ensure that the responses given by participants are genuine. We employed two mechanisms to filter careless participants (we did not filter any of the answers to the personality or player type questionnaires):

(1) In the pairwise comparison task, we inserted four "test" questions where participants were expected to answer a certain way. For example, one "test" question presented a situation where a user would gain 20 points, and another where the user would lose 10 points for performing the same actions. Participants were therefore expected to chose the first one as the more motivational. Participants with less than three correct answers to these four test questions were rejected.

(2) To evaluate the reliability of each participant, we checked their individual consistency, by calculating the number of cyclic triads occurring in their choices. A cyclic triad occurs when a pair comparison is intransitive, (e.g., A is preferred to B, B is preferred to C and C is preferred to A). The coefficient of consistency [START_REF] Maurice | On the method of paired comparisons[END_REF] is then computed as follows for each observer:

ζ = 1 -24c n 3 -n
where n is the number of stimuli (12 in our experiment) and c the number of cyclic triads. ζ = 1 when 1 https://www.figure-eight.com/ there is no circular triads (i.e. perfect consistency) and will decrease to zero as the number of circular triads, and thus the inconsistency, increases. Participants' results were rejected if their coefficient of consistency was inferior to 0.75, as in [START_REF] Fb Leloup | Geometry of illumination, luminance contrast, and gloss perception[END_REF]. This limit was decided to allow for some degree of input error (i.e. clicking on the wrong button) whilst still removing the most inconsistent participants.

A total of 616 participants performed the whole task; 180 were rejected according to (1) and 136 were rejected according to (2) giving a final set of 300 valid and consistent participants. This strict filtering insures a high reliability of our results. Participants came from a wide variety of backgrounds, a summary of the demographic information and distribution of the different user types is presented in the supplementary materials.

Data Analysis

We describe in this section the different tools used for data analysis. Note that we used Bonferroni's correction to compensate for the multiple comparisons in our statistical tests.

Perceived motivation score

As explained in the Procedure, each participant provides a "vote" for a storyboard for each of the n 2 possible pairs (n = 12 in our case). Results per participant can be recorded in a n × n preference matrix. These per-participant preference matrices are then summed into a single one. In this summed matrix P, each element P i, j represents the number of times the storyboard i was judged to be more motivating than storyboard j. An example of such a matrix is given in the supp. mat.

As classically done with pairwise comparison experiments [START_REF] Perez | A practical guide and software for analysing pairwise comparison experiments[END_REF], we can then consider the number of votes received by each storyboard as its score of perceived motivational impact, which may then be divided by the number of comparisons per storyboard for normalization purposes. This score computation can be done either for each individual participant, or for groups of participants (e.g., for calculating the preference scores for each dominant user type).

Note that more sophisticated statistical methods exist for inferring scale values from a preference matrix [START_REF] Bradley | Rank Analysis of Incomplete Block Designs: I. The Method of Paired Comparisons[END_REF][START_REF] Thurstone | A law of comparative judgments[END_REF]. However they were not shown to give a better representation of perceived motivational impact score than the vote counts. For example, we observed an average correlation of 0.999 (SD: 0.0002) between scores obtained by vote counts and Thurstone's Law of Comparative Judgements, Case V [START_REF] Thurstone | A law of comparative judgments[END_REF].

Participant agreement

Beyond motivational scores, it is also interesting to analyze the agreement of participants in their choices, i.e. the similarity of their votes. The coefficient of agreement u was defined by Kendall and Smith [START_REF] Maurice | On the method of paired comparisons[END_REF] as:

u = 2Σ ( s 2 )( n 2 )
-1 where s is the number of participants and Σ is the sum of the number of agreements between all s 2 possible pairs of participants and n 2 possible pairs of stimuli. It ranges from 1 (perfect agreement) to -1/(s -1), if s is even, and -1/s, if s is odd.

PLS-PM

To calculate how well each user type affects the scores for each implementation we used a method called partial least squares path modelling (PLS PM) [START_REF] Jr | A primer on partial least squares structural equation modeling (PLS-SEM)[END_REF]. PLS PM is a method of structural equation modelling which allows estimating complex cause-effect relationship models with latent variables, that has been previously used in studies on the effects of gamification on user motivation [START_REF] Orji | Towards Personality-driven Persuasive Health Games and Gamified Systems[END_REF][START_REF] Orji | Personalizing Persuasive Strategies in Gameful Systems to Gamification User Types[END_REF][START_REF] Orji | Modeling the efficacy of persuasive strategies for different gamer types in serious games for health[END_REF][START_REF] Tondello | The Gamification User Types Hexad Scale[END_REF]. Essentially we use it to see how the values for each user type influence the scores for each game element. The influence values vary between -1 and 1 depending on how strong the effect is. As this is a statistical evaluation we use the calculated p-value to determine the validity of the given influences.

RESULTS

R1: Perceived motivation for different implementations of motivational strategies

As explained in Section 2, a given motivational strategy can be implemented in the form of different game elements. To investigate if different implementations of a same motivational strategy lead to different levels of perceived motivation, we analyzed the motivation scores obtained for the game elements on the entire set of participants. Scores are computed from the preference matrix as explained in Section 3. Instead of a single score per game element, we compute a score distribution using a bootstrap technique [START_REF] Bradley Efron | An Introduction to the Bootstrap[END_REF]: scores are computed 200 times, each time on a random set of participants of the same size as the original set, generated by sampling with replacement. The bootstrap distributions allows for statistical testing and their percentiles provide the 95% confidence intervals.

Figure 2 illustrates the perceived motivation scores. For each motivational strategy, we performed pairwise paired t-tests over the score distributions to assess if significant differences exist between game elements.

The Rewards strategy shows highly significant differences among the motivational impact of its implementations. Badges is the best perceived, followed by Useful Rewards and finally Points (Badges-Points t:137.56, Points-Useful t:-60.25, Useful-Badges t:-114.23, p<.001). Similar results have been found by Denny et al. [START_REF] Denny | Empirical Support for a Causal Relationship Between Gamification and Learning Outcomes[END_REF] who showed that in educational settings their badge system was more effective than their points system. They attribute the differences to the fact that the points setting "lacked clear targets". Several other studies have also reported the efficacy of badge systems [START_REF] Anderson | Steering user behavior with badges[END_REF][START_REF] Denny | The effect of virtual achievements on student engagement[END_REF][START_REF] Grant | Encouraging user behaviour with achievements: an empirical study[END_REF]. Studies that show an effectiveness of Points [START_REF] Cheong | Quick Quiz: A Gamified Approach for Enhancing Learning[END_REF][START_REF] Farzan | When the experiment is over: Deploying an incentive system to all the users[END_REF] integrate this game element with others like leaderboards or badges, thus preventing an isolated impact of this particular game element.

Regarding the Goals strategy, the difference between the two implementations is also significant (t:70.34, p<.001). Externally set Goals are perceived as more motivating than Self set Goals. This could be explained by the fact that users may find it more difficult to set their goals by themselves, especially without a specific (and meaningful) task to carry out. The studies in [START_REF] Dong | Discovery-based games for learning software[END_REF][START_REF] Landers | Gamification of task performance with leaderboards: A goal setting experiment[END_REF] also show that External Goals are effective means for user performance and motivation.

Regarding the Time strategy, Timers score less than Schedule (t:-84.22, p<.001). We believe this to be due to the fact that Timers are usually seen as stressful for most users. In our storyboard, the Schedule game element shows the tasks accomplished on a week, users have more time to carry out their tasks and could perceive it as less stressful.

The three implementations of Social Interaction scored differently, with Trading scoring the highest, and Discussion scoring the lowest (Discussion-Teams t:-24,34, Teams-Trading t:-45.33, Trading-Discussion t:75.67, p<.001). Teams and Discussion are in the three least motivating game elements. Young [START_REF] Mingyi | Twitter Me: Using Micro-blogging to Motivate Teenagers to Exercise[END_REF] showed that discussion based interventions can be effective in situations where the users are intrinsically motivated by the task.

Finally the Progress implementations rank closely but still show a significant difference in scores (t:46.42, p<.001), with Progress Compared scoring higher. It is noteworthy that both game elements are ranked in the top four. Some previous studies also show the effectiveness of social comparison [START_REF] Hamari | Social Motivations To Use Gamification: An Empirical Study Of Gamifying Exercise[END_REF] and of progress bars [START_REF] Farzan | Encouraging user participation in a course recommender system: An impact on user behavior[END_REF].

As a conclusion, our results demonstrate that user motivation varies significantly with the different implementations of a same motivational strategy.

R2 a: Reliability of dominant user type

Many studies in tailored gamification or adaptive games consider only the dominant user type [START_REF] Geiser | An ontology engineering approach to gamify collaborative learning scenarios[END_REF][START_REF] Ferro | Towards personalised, gamified systems: an investigation into game design, personality and player typologies[END_REF][START_REF] Gil | Validating gamification mechanics and player types in an E-learning environment[END_REF][START_REF] Lavoué | Adaptive Gamification for Learning Environments[END_REF][START_REF] Thue | Interactive Storytelling: A Player Modelling Approach[END_REF] defined as the type that scores the highest for a given user profile. To evaluate the reliability of the dominant user type for tailored gamification, we looked at how they affect the perceived motivational impact of the game elements. To do so, we clustered participants according to their dominant user type (for both of the player typologies, as Big Five cannot be considered in this manner) and calculated the Kendall Coefficients of Agreement u within each group and compared to the global value (obtained on the whole set of participants). The idea is to study if users sharing the same dominant type perceive the same motivational impact of game elements (and thus show a higher agreement than whole set). Figure 3 shows the results.

We find the coefficients of agreement within each dominant user type cluster to be low (no group scored an agreement greater than 0.15). While most of these values are nevertheless higher than the global one (0.062), this still shows that dominant user types cannot be considered sufficient to differentiate users according to their game element preferences.

A recent study by Loria et al. also confirms this finding [START_REF] Enrica | Player Types and Player Behaviors: Analyzing Correlations in an On-the-field Gamified System[END_REF].

R2 b: Comparing user models

In this section we investigate more precisely the relationships between the user models (both player types and personality model) and game elements to identify which user typology is the most relevant to identify user preferences for game elements. Table 2 shows the PLS path coefficients that reflect the influence that each user model dimension has on the motivation score of the different game elements. We present our results grouped by user typology, and we discuss the extent to which our results are in line with the definition of each user type (the definitions are provided in the supp. mat.).

BrainHex

Daredevil affects positively two game elements of the Rewards motivational strategy: Badges and Useful Rewards.

According to the definition, Daredevils appreciate "rushing around at high speed whilst still in control" [START_REF] Lennart | BrainHex: preliminary results from a neurobiological gamer typology survey[END_REF]. Badges may reinforce the feeling of control and knowledge on the system, and Useful Rewards may help them to speed up progression. The Socialiser type influences two game elements: Discussion positively, and Progress Task negatively. Nacke et al. [START_REF] Lennart | BrainHex: preliminary results from a neurobiological gamer typology survey[END_REF] define Socialisers as "liking hanging around with, and helping people". This definition therefore tends to confirm that Socialisers are motivated by discussion. However, it does not explain the influence of this type on Progress Task.

The Conqueror user type has a significant positive influence on Teams, as well as a significant negative influence on External Goals. These influences are unrelated to the definition as conquerors are people who "like defeating impossibly difficult foes, struggling until they eventually achieve victory" [START_REF] Lennart | BrainHex: preliminary results from a neurobiological gamer typology survey[END_REF].

The Achiever user type has two negative influences: Timer and Progress Task. Achievers "like collecting anything they can collect, and doing anything possible" [START_REF] Lennart | BrainHex: preliminary results from a neurobiological gamer typology survey[END_REF]. The presence of a timer could hinder their abilities to achieve this. However the definition of Achiever does not provide any explanation for the negative influence on Progress Task. The Survivor user type shows a significant negative influence on the Progress Compared game element which is unrelated to the definition stating that survivors enjoy "escaping from terrifying situations" [START_REF] Lennart | BrainHex: preliminary results from a neurobiological gamer typology survey[END_REF].

Seekers, defined as people who have interest in "finding strange and wonderful things" [START_REF] Lennart | BrainHex: preliminary results from a neurobiological gamer typology survey[END_REF], have no significant influences on any of the game elements tested. Finally, Mastermind have also no significant influences. Nacke et al. [START_REF] Lennart | BrainHex: preliminary results from a neurobiological gamer typology survey[END_REF] define them as people who "like solving puzzles and devising strategies", meaning that they might be more motivated by the task itself than the game elements used.

As a conclusion, for BrainHex, five user types have significant influences on the different game elements. Some of our results can be explained using the definition of BrainHex typology [START_REF] Lennart | BrainHex: preliminary results from a neurobiological gamer typology survey[END_REF], especially for Daredevil, and partially for Socialiser and Achiever. However most of our results cannot be backed up by the definitions given in the typology. In addition, Mastermind and Seeker user types definitions seem not well suited for gamification. This result is in line with recent empirical investigation on the psychometric properties of BrainHex that has shown low reliability scores [START_REF] Busch | Player Type Models: Towards Empirical Validation[END_REF][START_REF] Fortes Tondello | Towards a Trait Model of Video Game Preferences[END_REF]. This typology was built for games and there is no evidence of the generalizability of game motivation models to gameful design [START_REF] Tondello | Elements of Gameful Design Emerging from User Preferences[END_REF].

Big Five

The Openness to experiences trait has a significant positive influence on Teams. The appreciation for new ideas and curiosity [START_REF] Lewis | The development of markers for the Big-Five factor structure[END_REF] are two characteristics of this personality trait that can explain this result.

Regarding the Agreeableness trait, we observe a positive influence on Discussion and a negative influence on Progress Compared. The positive influence on social interactions is consistent with the definition stating that people with high agreeableness are generally generous, cooperative and helpful [START_REF] Lewis | The development of markers for the Big-Five factor structure[END_REF]. However the definition of this trait cannot explain why these people are demotivated by game elements related to the progression in the task.

Emotional stability shows no significant influences on any of the game elements. People with high emotional stability have a tendency to resist negative emotions such as anger or anxiety [START_REF] Lewis | The development of markers for the Big-Five factor structure[END_REF]. We can assume that people with this personality trait are not responsive to the game elements in terms of motivation. The Conscientiousness trait influences significantly only one game element, Trading negatively. This result is not related to the definition of this trait since conscientious people are defined as self-disciplined and well organised. Finally, Extraversion shows no significant influences. Extraversion is defined as a "pronounced engagement with the external world and enjoyment from interacting with people" [START_REF] Lewis | The development of markers for the Big-Five factor structure[END_REF]. To fit the definition, we would have expected a positive influence for game elements that implement the Social Interaction strategy.

As a conclusion regarding Big Five personality model, three traits have significant influences. As with BrainHex some of our results can be partially explained by the definition of the personality traits (openness to experiences and partially agreeableness), but most of them are not directly in line with the definitions. This result was predictable since Big Five is a general personality trait model and not specifically developed for games or gamification.

Hexad

The Socialiser player type affects positively the three Social Interaction game elements (Trading, Discussion and strongly Teams) and negatively External Goals and Progress Task.

Regarding social interactions, our results are consistent with the definition that states that Socialisers "like to interact with others and create social connections" [START_REF] Marczewski | Even Ninja Monkeys like to play[END_REF].

Disruptor has significant positive influence on both Progress Compared and Progress Task. This could be explained as disruptors seek to change a system [START_REF] Marczewski | Even Ninja Monkeys like to play[END_REF]. Perceiving the boundaries of the system thanks to progress elements could help them to expand beyond these limits. The Achiever user type has only a significant negative influence on Points. Some authors point out that reward systems (specifically points) can be perceived as useless if their implementation is not linked to the context [START_REF] Jia | Personality-targeted Gamification: A Survey Study on Personality Traits and Motivational Affordances[END_REF]. As Achievers are motivated by competence [START_REF] Marczewski | Even Ninja Monkeys like to play[END_REF], we can assume that they do not appreciate points as illustrated in our scenarios.

Free Spirit has only a significant negative influence on Timer.

According to the definition, Free spirits are motivated by autonomy. They like to explore within a system and act without external control [START_REF] Marczewski | Even Ninja Monkeys like to play[END_REF]. In this case, Timer can be perceived as constraining their freedom by time.

The Philanthropist user type has no effect on the motivation scores given for the different game elements. According to the definition [START_REF] Marczewski | Even Ninja Monkeys like to play[END_REF], philanthropists are motivated by purpose. Thus we can think that this user type does not influence any preferences for our elements that are not connected to a specific user activity and domain.

Finally, we did not find any significant influences for the Player user type. Players are defined as being motivated by extrinsic rewards. They will do anything to earn a reward within a system, independently of the type of the activity [START_REF] Marczewski | Even Ninja Monkeys like to play[END_REF]. Players seem to be able to appreciate anything, and therefore will react positively to almost any game element used, explaining that we do not find any particular influence.

As a conclusion regarding Hexad, four user types have significant influences, among which one is highly significant. Moreover, most of our results are consistent with the definitions of the Hexad typology [START_REF] Marczewski | Even Ninja Monkeys like to play[END_REF]. This result reinforces the fact that this typology was designed especially for gamification and most of its player types are based on SDT [START_REF] Ryan | Self-determination theory and the facilitation of intrinsic motivation, social development, and well-being[END_REF], the major theoretical foundation for gamification research.

Seeing as our results with Hexad are the most consistent with the definitions of its user types, and that its types have more influence on the perceived user motivation than those from BrainHex and Big Five, we can state that Hexad is the most relevant typology to identify user preferences for game elements and thus should be used to tailor gamification.

R3: Activity and domain influence on the motivational impact of game elements

We finally compare our results to the findings of previous studies when their game elements or persuasive strategies are similar to ours (see table 1 for correspondences). Previous studies were conducted in specific contexts (specific domain and user activity), with possible influence of users' intrinsic motivation for the activity and/or domain on the observed user motivation. It is noteworthy that whilst the study in [START_REF] Orji | Modeling the efficacy of persuasive strategies for different gamer types in serious games for health[END_REF] focuses on a serious game, it uses game elements in a similar way as a gamified system. In our study, we use storyboards that show implementations of motivational strategies independent from any specific context. Our analysis in this section aims to identify the extent to which the context has an influence on the motivational impact of game elements according to user types.

BrainHex

Our results are consistent with other studies for the Socialiser type, for which Orji et al. [START_REF] Orji | Modeling the efficacy of persuasive strategies for different gamer types in serious games for health[END_REF] also found a negative influence on self-monitoring (vs. Progress Task). Three of our results on the Achiever and Survivor user types contradict the previous studies. Regarding Achievers, Orji et al. [START_REF] Orji | Modeling the efficacy of persuasive strategies for different gamer types in serious games for health[END_REF] found a positive influence on self-monitoring, whereas we find a negative influence on Progress Task and Lavoué et al. [START_REF] Lavoué | Adaptive Gamification for Learning Environments[END_REF] predict a positive link with timer, whereas we find a negative influence. Concerning Survivors, Orji et al. [START_REF] Orji | Modeling the efficacy of persuasive strategies for different gamer types in serious games for health[END_REF] found a positive influence on competition & comparison, whereas we find a negative influence on Progress Compared. We also find influences for game elements that are not identified in previous work for the Daredevil type. Finally, other studies also found other influences for the 7 user types.

We can conclude that our results obtained with the BrainHex user typology are quite different from the other studies conducted in specific contexts (gamified health system [START_REF] Orji | Modeling the efficacy of persuasive strategies for different gamer types in serious games for health[END_REF] and experts' recommendations in education [START_REF] Lavoué | Adaptive Gamification for Learning Environments[END_REF]).

Big Five

Regarding the Big Five personality model, the positive influence we find of the Agreeableness trait on Discussion is consistent with the results of Orji et al. [START_REF] Orji | Towards Personality-driven Persuasive Health Games and Gamified Systems[END_REF] on cooperation. Regarding Emotional stability, Orji et al. [START_REF] Orji | Towards Personality-driven Persuasive Health Games and Gamified Systems[END_REF] studied people with a low emotional stability and also did not find any influences for those people. They stated that persuasion may not be effective for people who are emotionally unstable. In the same domain (health) but for a different activity, Jia et al. [START_REF] Jia | Personality-targeted Gamification: A Survey Study on Personality Traits and Motivational Affordances[END_REF] found negative influence on points, badges, progress and rewards and they argued that for people with high emotional stability gamification may not be an effective approach.

Our results contradict previous studies only for Openness to experiences, Orji et al. [START_REF] Orji | Towards Personality-driven Persuasive Health Games and Gamified Systems[END_REF] found a negative relation with cooperation, whereas we find a positive influence on Teams.

We also find a negative influence of Conscientiousness on Trading that is not identified in previous studies.

The three comparable studies also found other influences for Extraversion, Agreeableness and Conscientiousness, and the two studies held in the health domain do not find similar results. For instance for Agreeableness, Orji et al. [START_REF] Orji | Towards Personality-driven Persuasive Health Games and Gamified Systems[END_REF] found influences on four game elements (self-monitoring & feedback, comparison, competition and reward) whereas no influences were found for these in Jia et al. [START_REF] Jia | Personality-targeted Gamification: A Survey Study on Personality Traits and Motivational Affordances[END_REF].

Regarding the Big Five personality model, the comparisons with other studies highlight the differences in the results obtained both (1) between our study and studies conducted in a specific context, and (2) between the studies conducted in different contexts, even in the same domain like health.

Hexad

Our results are consistent with other studies for the Philanthropist user type, which do not find any influence on the motivational impact of game elements.

Our results are partially consistent both for the Socialiser and Disruptor user types. Regarding Socialisers and positive influences on social game elements, [START_REF] Tondello | The Gamification User Types Hexad Scale[END_REF] also suggest positive influences on Teams, Social Network and Social Comparison, while Orji et al. [START_REF] Orji | Personalizing Persuasive Strategies in Gameful Systems to Gamification User Types[END_REF] also found positive influences for Cooperation. Regarding Disruptors, all studies including ours observed positive influences for the Progress Compared element (Competition in [START_REF] Orji | Personalizing Persuasive Strategies in Gameful Systems to Gamification User Types[END_REF][START_REF] Tondello | The Gamification User Types Hexad Scale[END_REF]). We observe contradictions only with [START_REF] Orji | Personalizing Persuasive Strategies in Gameful Systems to Gamification User Types[END_REF] for these two player types regarding the External Goals and Progress Task elements. Our results are different from previous studies regarding three player types. We find influences for game elements that are not identified in previous works and other studies found other influences for Achiever and Free Spirit (previous work do not show any influence for elements comparable to the timer). Finally, regarding Players, we do not find any influences whereas [START_REF] Tondello | The Gamification User Types Hexad Scale[END_REF] found positive influences for every game elements and [START_REF] Orji | Personalizing Persuasive Strategies in Gameful Systems to Gamification User Types[END_REF] for most of game elements (except for Self-Monitoring & Feedback and Goal Setting & Suggestion).

As with Big Five, the results with the Hexad types are quite different from those found in studies conducted in specific different contexts (education [START_REF] Tondello | The Gamification User Types Hexad Scale[END_REF] and health [START_REF] Orji | Personalizing Persuasive Strategies in Gameful Systems to Gamification User Types[END_REF]), except for three user types (Philanthropist, Socialiser and Disruptor).

In conclusion, for all user typologies (BrainHex, Hexad) and the personality model (big five) we can see that the motivational impact of certain game elements varies according to the activities or the domain of gamified systems. In fact, our results are quite different (especially for BrainHex) from those found in contextualised studies. We also observe differences between the studies conducted in different contexts, even between two studies conducted in the same general domain (Health) with the Big Five user typology.

LIMITATIONS About the experimental protocol

Regarding the experimental protocol, one major difference with previous studies deals with how we collected our data. We used forced-choice paired comparison instead of declarative statements to identify the perceived impact of game elements on user motivation. As stated in Section 3, this protocol has been shown to be less cognitively demanding [START_REF] Andrew P Clark | Why rate when you could compare ? Using the " EloChoice " package to assess pairwise comparisons of perceived physical strength[END_REF] and to provide higher accuracy [START_REF] Nihar | Estimation from Pairwise Comparisons: Sharp Minimax Bounds with Topology Dependence[END_REF] as compared with Likert-type rating. We notice that it also impacts our results as it forces the users to choose which game elements they prefer. We therefore obtain a ranking of game elements (meaning that a user could not vote all game elements as equally motivating).

We believe this has a direct consequence on two profile dimensions (Hexad-Player, and Big Five-Extraversion) for which people will tend to appreciate most of game elements, leading to no specific significant influences when applying the PLS PM method. In addition, using PLS PM allows us to observe negative influences on the perceived motivational impact of game elements whereas some of the other studies only measure positive influences [START_REF] Lavoué | Adaptive Gamification for Learning Environments[END_REF][START_REF] Tondello | The Gamification User Types Hexad Scale[END_REF]. This could be a limitation to the comparisons we make in Section 4.4.

About the context-independent scenarios

We use context-independent scenarios to evaluate the motivational impact of game elements independently from a specific context. However certain game elements may be less motivating for users shown without a concrete task to carry out. We suppose this to be especially true for External Goals, Self Goals and Useful Rewards that are not perceived as the most motivating elements in our study and Progress Task that is negatively influenced for three user types. Furthermore, for some user types, no significant preferences can be shown without a specific task to carry out. We think this is especially true for the philanthropist who is motivated by purpose.

About the implementation of motivational strategies

Finally, the results we obtain may differ from other studies due to the fact that the implementations of our motivational strategies may be quite different from those used in other studies. For instance, the Rewards strategy in [START_REF] Orji | Personalizing Persuasive Strategies in Gameful Systems to Gamification User Types[END_REF] is implemented in the form of points that can be used to unlock new customisation options.This implementation can be considered as a combination of our Points and Useful Rewards (see Table 1). We believe that our approach allows us to study the isolated motivational impact for each game element more precisely.

IMPLICATIONS FOR DESIGN: TOWARDS TAILORED

GAMIFICATION

According to our findings, we recommend to consider two main factors when designing tailored gamification: the choice of the user typology and the implementation of the motivational strategies. In this section we discuss both factors, considering also the influence of the context of the gamified system.

User typology recommendations

First, we recommend using Hexad user types when designing tailored gamification. Our results reinforce the fact that Hexad was created especially to address gamification (compared to BrainHex which focuses on player types in games and Big Five which focuses on personality traits).

Second, our results show that considering only the dominant player type is not sufficient to discriminate users' preferences. We thus advise designers to consider users' profiles as a combination of several player types, especially the four that identify the most significant influences: Socialiser, Disruptor, Achiever and Free spirit. The Philanthropist type does not appear to identify motivating game elements in any of the studies in a discriminant way. The Player type is similar as it either shows no significant influences (in our study) or significant influences for all [START_REF] Tondello | The Gamification User Types Hexad Scale[END_REF] or most game elements [START_REF] Orji | Personalizing Persuasive Strategies in Gameful Systems to Gamification User Types[END_REF].

Finally, the comparison of our results with contextualized studies reveals that the motivational impact of game elements for the Hexad user types is more or less influenced by the context. For Socialisers, designers should preferably implement social interactions (recommendation also found in the other contextindependent study [START_REF] Tondello | Elements of Gameful Design Emerging from User Preferences[END_REF]). For Disruptors, progress compared is recommended. The design of these game elements can be made independently from the context. Whereas Achievers and Free-spirits have contradictory preferences according to the different studies. This can be explained by the fact that these two user types are highly dependent on the activity or on the environment of the gamified system, meaning that the design of game elements should take into account the context of the gamified system for these types of users.

Game element recommendations

First, care needs to be taken when implementing a motivational strategy. As shown in Section 4, different implementations of a same motivational strategy have different impacts on user motivation. Rewards is a good illustration of this: Badges is the highest rated of any of the implementations, whereas Points is one of the lowest rated ones (the same can be said for Timer and Schedule).

Whilst we cannot precisely recommend game elements for each user profile, we can make recommendations based how user motivation should vary with a game element using Hexad types. Badges and Schedules can be used as motivating game elements for all users. These were two of the highest scoring game elements and had no negative influences from any user types in both our study and related studies. Designers can therefore feel confident that these game elements will have no adverse effects on user motivation. Progress game elements (Compared and Task) and External Goals are generally considered as motivating and could be used for various user types. In particular, Progress compared game element is recommended for users who have a high score in the Disruptor type. At the contrary, we recommend to carefully use Progress Task for high Socialiser users, as a negative influence was observed and also for high Disruptor users since we found contradictory results with previous studies. All three of the social interaction game elements (Trading, Teams, and Discussion) are generally perceived as less motivating, except for the Socialiser type which shows positive influences in all studies. We thus recommend to attribute these game elements only to high Socialiser users. Points and Timer show low motivation scores and the only influences they have from the various profile types are negative ones. We can therefore advise against using these game elements to motivate users. Finally, no influences were found for Self goals and Useful items which means that these elements are probably highly dependent from the context. They should be designed closely with the activity to be perceived as motivating game elements.

CONCLUSION

In this paper we showed that two major factors influence user motivation in tailored gamification: the implementation of a given motivational strategy, and the choice of the user typology. We also studied the influence of the user activity and domain of the gamified system to be able to identify general recommendations for designers. We found valuable insights on how to tailor gamification, notably by showing that the Hexad user typology seems the most relevant to identify user preferences for game elements. We recommend designers to consider several user types, not only the dominant one, when assigning game elements to users. We also provide designers with recommendations on game elements to assign to specific user types, independently or dependently from the context of the gamified system. Our future work will focus on three axes 1) the identification of clusters of hybrid user profiles to consider the impact of a combination of user type scores , 2) the development of an adaptive gamification system based on the recommendations from this study, and 3) the inclusion of user behaviour analysis to support a dynamic adaptation of game elements.

Figure 2 :

 2 Figure 2: Perceived motivational impact scores of all game elements, for the whole set of participants. The error bars show the 95% confidence intervals. Full values are provided in the supp. mat.

Figure 3 :

 3 Figure 3: Coefficients of agreement for each dominant type. The error bars show the 95% confidence intervals. Full values are provided in the supp. mat.

Table 2 :

 2 PLS Path coefficients for each user type of each typology. Values in grey are not significant (p>.05), highlighted in dark grey are significant (p<.05), and highlighted in black are highly significant (p<.001).

ACKNOWLEDGEMENTS

This work is a part of the LudiMoodle project financed by the e-FRAN Programme d'investissement d'avenir, operated by the Caisse des Dépots.