text:
En-Yi Chen

Si-Xu Peng

Liang Peng

Marco Di Michiel

Gavin B M Vanghan

Yao Yu

Hai-Bin Yu

Beatrice Ruta

Shuai Wei

Lin Liu

Pd42.5Ni42.5P15 Yi Chen

Gavin B M Vaughan

Glass-forming ability correlated

Keywords: Crystallization, Phase transformation kinetics, Metallic glass, Time-temperaturetransformation, Nuclear magnetic resonance

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The unsatisfactory glass-forming ability is a major bottleneck of the structural application of metallic glasses even though they show superior mechanical properties [1,2]. Over the past half century, profound studies bring a series of breakthroughs in GFA of metallic glass, which also deepen the fundamental understanding of the glass formation and crystallization process [3][4][5]. As the formation of glass is a competing process between supercooled liquid and crystalline phases, the understanding of GFA is mainly examined through the lens of classical nucleation theory (CNT), where GFA is related to the crystal nucleation rate per unit volume, In, and low nucleation rate means good GFA [6][7][8][9][10]. Here

In is expressed as

3 v n 2 B 16 exp ( ) 3 [ ( )] A I T k T g T       
, where Av is a constant, (T) is the viscosity of undercooled liquid,  is the interfacial energy between liquid and nuclei and g(T) is the free energy difference between liquid and crystalline phases. Therefore, the evolution of the supercooled liquid and the differences between the supercooled liquid and crystalline phases are commonly believed to be the most important factors affecting GFA [7,11]. However, growing evidences of multistep nucleation with much higher nucleation rate contradict the basic assumption of CNT, suggesting that the CNT encounters some limitations in the interpretation of the kinetics and pathway of crystallization [12][13][14][15][16].

These limitations strongly indicate that the current understandings of GFA are far from comprehensive. Recently, more factors have been taken into consideration [17][18][19][20], while there are still many issues about GFA which are not well understood.

Among all the factors that may affect GFA, the evolution of the alloy melt above its liquidus temperature Tliq is the least considered. The main reason is that the equilibrium melt is commonly thought as a simple liquid with a very short (~10 13 s) relaxation time.

It seems impossible that the changes in the melt above Tliq could affect the behaviors of undercooled liquid, let alone the crystallization process [21]. Thus, it is commonly accepted that the GFA is irrelevant to the state of equilibrium melt.

However, the situation could be quite different for the alloy melt with a liquid-liquid transition taking place above Tliq. Contrary to the conventional understanding, this melt is very complex, and exhibits two distinct liquid phases [22]. In addition, the transition between the two liquids shows the characteristics of first-order phase transition, which implies that both liquid states could be undercooled to the temperature far below Tliq, even approaching the glass transition temperature Tg. Consequently, the influences of the complexity of the alloy melts together with the kinetics of the first-order LLT should be taken into consideration on the GFA of the melts.

Herein, a glass-forming alloy of Pd42.5Ni42.5P15 is selected, and the influence of LLT on its GFA is studied. The liquidus temperature of the Pd42.5Ni42.5P15 system was determined as 993 K by the flash differential scanning calorimetry (FDSC) (Fig. S1). In situ to the changes in structure [22,23], is plotted in Fig. 1a as a function of temperature (T).

Ks varies linearly above 1063 K with a slope of -0.03 ppm/K (red line), but with a slope of 1.73 ppm/K (pink line) below 1063 K, indicating a significant change in the P-centered local structures. This result implies that an LLT may take place at TLL = 1063 K. Two typical 31 P spectra above and below TLL are shown in the insets of Fig. 1a. Each spectrum is a single Lorentzian peak and the integral areas of the peaks remain identical, indicating that the system above or below TLL is a homogeneous liquid without any loss of the contributing P atoms.

In an ideal metallic liquid, the magnetic coupling between nuclei and s-like conduction electrons through the Fermi contact interaction is the dominant mechanism of both Knight shift and spin-lattice relaxation, leading to the Korringa relation

2 e 2 1s 2 Bn 4 TT K f k   
, where 1 T is the spin-lattice relaxation time (Fig. S2), e and n are respectively the electron and nucleus gyromagnetic ratio, and kB are respectively the reduced Planck and Boltzmann constant, and f is a constant related to the electron-electron interaction [START_REF] Abragam | Principles of Nuclear Magnetism[END_REF][START_REF] Slichter | Principles of Magnetic Resonance[END_REF][START_REF] Korringa | [END_REF]. Thus, the value of

2 1s
TT K is supposed to be a constant. However, in the presence of strong covalent bonds, the electrons tend to be localized, remaining in the vicinity of nuclei for longer time, and thus the spin-lattice relaxation process would be more efficient. Therefore, the actual relaxation time 1

T is shorter compared with the case in ideal metallic liquid, leading to the breakdown of Korringa relation [27,28]. These results clearly show that the stable liquid above 1063 K (high-temperature liquid, named as HTL) can be undercooled below TLL and finally transforms to the stable liquid below 1063 K (low-temperature liquid, named as LTL). Such behavior is consistent with the first-order phase transition [START_REF] Turnbull | Solid State Physics[END_REF]. The average incubation time  of three independent measurements at each temperature versus the degree of undercooling T = TLL  Tiso is shown in Fig. 1d. As T increases from 8 to 20 K (i.e., Tiso decreases from 1055 to 1043 K), the incubation time decreases rapidly from 240 s to 30 s. The inset shows the plot of log(Tiso / ) versus log(T), which can be well fitted with a linear function, indicating a power-law relation of iso / ( ) m TT   with m = 2.1. Similar power-law was also observed in the LLTs in La50Al35Ni15 liquid [22] and molten sodium acetate trihydrate [START_REF] Liu | [END_REF].

To further explore the difference between HTL and LTL, two glassy samples, labeled as HTA and LTA accordingly, were prepared by quenching the melt from 1223 K (above TLL)

and 1023 K (below TLL) using melt-spinning technique, respectively. High-energy synchrotron X-ray diffraction (XRD) was then employed to examine the structure of the two glassy samples. As shown in Fig. 2a, no sharp Bragg peaks corresponding to any crystallites are detected on the structure factors S(q), confirming the amorphous nature of the two samples. These results are consistent with the high-resolution transmission electron microscopy (HRTEM) results (Fig. S3). The full width at half maximum (FWHM) of the first peak in S(q) are about 0.44 Å 1 and 0.34 Å 1 for HTA and LTA, respectively. The narrower FWHM of LTA suggests the existence of more ordered structures in this glass.

The structural details can be better appreciated from real space analysis by looking at the pair correlation function G(r) obtained by the Fourier transformation of the corresponding S(q) (Fig. 2b). The positions difference of the first maxima of G(r) is very subtle (2.75 Å for LTA and 2.74 Å for HTA). The increased order in the structure of the LTA is reflected in well-defined oscillations up to the 12 th shell in the LTA while only up to the 8 th shell in the HTA. This behavior is clearly identified from the difference in G(r) between HTA and LTA, obtained by subtracting the former from the latter (inset of Fig. 2b). The difference between these two G(r) curves are negligible up to the second minimum distance (r  5.9 Å), but beyond this distance, LTA shows an enhanced correlation which is still pronounced even up to r  25 Å. These results suggest that the structure of short-range clusters in LTA and HTA are almost the same, but a more pronounced medium-range ordering presents in LTA.

LLTs were supposed to take place in several metallic glass-forming liquids, but the structural mechanism associated with the LLT was not clear [31][32][33]. NMR observables are sensitive to the interaction between electrons and nuclei, and can provide information of all nearest-neighbor atoms surrounding the atom and possibly beyond. Combined with the evidence of synchrotron XRD, more detailed structural changes can be revealed. Since the glass is commonly considered as "frozen liquid", the results of HTA and LTA imply that the structures of short-range clusters in LTL and HTL could be almost identical, but the correlation between the short-range clusters in LTL and HTL should be different. Recalling the significantly enhanced covalent bonding in LTL suggested by the breakdown of Korringa relation (Fig. 1b), it is reasonable to assume that the transition from HTL to LTL is associated with the increase of the short-range clusters and stronger correlation between the clusters, consistent with the two-order-parameter model [34,35].

The GFA of the two liquids were examined by FDSC experiments through measuring the critical cooling rate Rc, which is the slowest cooling rate at which equilibrium liquid can be quenched into glass without detectable crystallites, and a lower Rc stands for a better GFA [36,37]. The sample was first heated to a predetermined temperature Tq = 1073 (i.e., 10 K above TLL) at a constant rate of 100 K/s and kept there isothermally for 30 s, then cooled to room temperature at a series of cooling rate q  (50 ~ 40000 K/s) to obtain samples with different content of amorphous phase. After this pretreatment, the contents of amorphous phase in these samples were measured by FDSC via heating each sample from room temperature to 1073 K at a constant rate of 100 K/s (see the inset of Fig. 3a for temperature protocol). For comparison, these procedures were repeated for Tq = 1023 K (i.e., 40 K below TLL). Fig. 3a shows a representative DSC heating curve for the sample obtained from Tq = 1073 K and q  = 40000 K/s. The two exothermic peaks (around 685 K and 770 K) are related to the polyamorphic transition [38,39] and the crystallization of the amorphous phase, respectively, and the endothermic peaks (around 880 K) represent the melting process. Fig. 3b plots the area of the second exothermic peak (H) versus T. Here, H of each sample was normalized to that of the sample obtained from Tq = 1073 K and q  = 40000 K/s (this sample was used as the reference because it is fully amorphous, see the discussion below), and this value is directly proportional to the content of amorphous phase in each sample. For samples cooled from Tq = 1023 K (i.e., from LTL), the content of amorphous phase does not change when q  > 6000 K/s, but drops significantly when q  < 6000 K/s, suggesting that Rc is about 6000 K/s for LTL. However, for samples cooled from Tq = 1073 K (i.e., from HTL), the content of amorphous phase remains constant until q  < 100 K/s, indicating that Rc is about 100 K/s for HTL. The results demonstrate clearly that HTL exhibits much better GFA compared to LTL.

The significance of the current experiments is that the GFA is observed to be closely related to the liquid-liquid transition event. It is shown unambiguously that an alloy melt can exhibit two significantly different GFA without change in composition. Due to the first-order nature of the LLT, both HTL and LTL can be maintained to the temperature far below Tliq, and further vitrified into different glasses (Fig. 2a). The evolutions of the two liquids are schematically shown in Fig. 4a. As HTL and LTL are distinct liquid states, it is reasonable that they show different crystallization kinetics and hence different GFAs.

The LLT plays a crucial role in the crystallization of HTL. On the one hand, it provides an alternative crystallization pathway for HTL. The crystallization of HTL would follow one of the two possible pathways: either crystallize directly from HTL state (Path I in Fig. 4a), or crystallize via LTL after the LLT takes place (Path II in Fig. 4a). In the latter case, the supercooled LTL acts as an intermediate state between the supercooled HTL and crystalline state. The existence of Path II is coincident with previous studies [38,39], where it was suggested that the HTA transformed firstly to a supercooled liquid (supercooled liquid I) above its glass transition temperature, and then to another supercooled liquid It is of interest to note that HTL exhibits a better GFA than LTL. Although the detailed kinetics of the direct crystallization process of HTL is experimentally unachievable due to the interference of LLT, it can be concluded qualitatively from the poor GFA of LTL that the crystal nucleation rate per unit volume In from LTL should be much higher than that from HTL. This may result from the formation of the clusters with medium-range ordering in the supercooled LTL, and such clusters may act as precursors for the nucleation of the crystalline phase [11], reducing the interfacial energy σ and leading to a lower energy barrier for the formation of the crystal nuclei and hence the poor GFA of LTL.

In summary, our in situ high-temperature NMR studies show that the glass-forming liquid Pd42.5Ni42.5P15 presents a first-order LLT at the temperature of 1063 K, high above the liquidus temperature of 993 K, accompanied by a drastic enhancement of the covalent bonding below 1063 K. The two liquids can be vitrified into two corresponding glasses which are different in the medium-range ordering rather than the structure of short-range clusters. These results suggest that the LLT may be a result of the increase of the shortrange clusters. The FDSC studies reveal that the high-temperature liquid exhibits much better GFA than the low-temperature liquid, which may be ascribed to the enhancement of medium-range ordering in the supercooled LTL. Further analyses indicate that the LLT can provide an indirect crystallization pathway for HTL, and moreover, the kinetics of LLT has a significant influence on the GFA. This effects of LLT provides a new way for future study of the process of crystallization and is also important for the fabrication of metallic glasses. What is more, our work may also provide an alternative understanding for some traditional phenomena. For instance, many metallic glass-forming liquids exhibit overheating effects, where the nucleation behavior of the system or the mechanical properties of the metallic glasses show markedly difference with different overheating temperature [42,43]. Till now, there are only qualitative understandings for these phenomena. It is proposed to be related to the heterogeneities in the liquid, which dissolve above a threshold temperature. However, such behavior could be quantitatively explained within our LLT scenario, where TLL is the threshold temperature. is the critical cooling rate to bypass the effective TTT curve of HTL.

Fig. 1b plots the value of 2 1s

 2 TT K versus T, which is almost constant above 1063 K, but drops substantially below 1063 K with decreasing temperature, indicating the breakdown of Korringa relation. This result suggests that the covalent bonding in the liquid is significantly enhanced below 1063 K, which could be the structural origination of the LLT. Further, the kinetics associated with the LLT was examined. The sample was heated to 1173 K and held there isothermally for 30 min, and then fast cooled to one of the undercooled temperature (with respective to TLL = 1063 K) Tiso = 1055, 1053, 1050, 1047, 1045, and 1043 K in about 1.5 min, and held there isothermally. Once the temperature stabilized at each Tiso, NMR spectra were recorded every 10 s to monitor any possible transition. Fig. 1c shows the measured Ks at different Tiso. When reaching Tiso, Ks initially follows the linear extrapolation (red line) of the T-dependent Ks above 1063 K measured in the step cooling experiments. After a certain incubation time , Ks starts to jump to the expected value determined by the linear fit of the T-dependent Ks below 1063 K (pink line).

(

  Fig. 4b schematically shows a possible relationship between the crystallization timetemperature-transformation (TTT) curves of HTL (green dashed line) and LTL (red line), together with the TTT curve of LLT (cerulean line). Here, the critical cooling rate of HTL, HTL c R , is no longer related to the intrinsic TTT curve of HTL, but related to the effective-TTT curve (dark dotted line), which is the superposition of the TTT curve of LLT and the crystallization TTT curve of LTL, with its nose point around the lower intersection of the two curves. The minimum cooling rate to bypass this effective-TTT curve can be determined as HTL HTL c LL en en ( ) /  R T T t , where HTL en T and HTL en t are the temperature and time

Fig. 1 .

 1 Fig. 1. Liquid-liquid transition in the equilibrium Pd42.5Ni42.5P15 melt characterized by NMR. (a) Temperature dependence of 31 P Knight shift (Ks). The two linear fits (red and pink dashed lines) intersect at 1063 K. The insets are two typical spectra (blue line) above and below the transition temperature with the Lorentzian fitting of the spectrum (red line). (b) Value of

Fig. 2 .

 2 Fig. 2. Structural difference of HTA and LTA characterized by high-energy synchrotron XRD. (a) Structure factors S(q) of HTA and LTA. (b) Pair correlation functions G(r) of HTA and LTA. The inset shows the difference in G(r) between LTA and HTA.

Fig. 3 .

 3 Fig. 3. Glass-forming ability of the two liquids characterized by FDSC. (a) A typical FDSC heating curve of the sample obtained from Tq = 1073 K and q  = 40000 K. The enthalpy of crystallization is denoted as H. The inset shows the temperature protocol of the FDSC experiments. (b) The content of amorphous phase as a function of cooling rate q  of the samples obtained from Tq = 1073 K and 1023 K, respectively.

Fig. 4 .

 4 Fig. 4. Effects of LLT on the pathways and kinetics of crystallization. (a) Schematic evolution of enthalpy or volume upon cooling the melt. (b) Mechanism of the different GFA of HTL and LTL. The red and green dashed lines represent the intrinsic crystallization TTT curve of LTL and HTL, respectively. The cerulean line represents the TTT curve of LLT. The TTT curve of LLT intersects the TTT curve of LTL at high and low temperature and the black dotted line denotes the effective crystallization TTT curve of HTL with its nose around the low intersection. HTL c Ris the critical cooling rate to bypass the effective

Acknowledgement

The authors are grateful to the Analytical and Testing Center of HUST for technical assistance. This work was financially supported by the National Natural Science Foundation of China (Grant No. 51872105).

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.


Sacha Altay

Emma De Araujo

Hugo Mercier
email: hugo.mercier@gmail.com

Keywords: News sharing, Fake News, Accuracy, Interestingness-if-true, Misinformation, Social Media

    "If This account is True, It is Most Enormously Wonderful": Interestingness-If-True and the Sharing of True and False News

In 1835, New York City newspaper The Sun published a series of articles about the discovery of life on the moon, including extraordinary creatures such as man-bats. The discoveries were the talk of the day, and sales of the newspaper exploded. At the time, many respectable scientists believed life on the moon a possibility, and the author of the hoax had presented his articles as authentic scientific reports. Yet if the discovery of man-bats and other lunarians became so widely discussed, it was not only because the story was plausible-after all, newspapers are full of plausible stories. It was because, in the words of a contemporary observer, "if this account is true, it is most enormously wonderful" (quoted in Goodman, 2010, p. 268).

This "great moon hoax" would now be called fake news, understood as "fabricated information that mimics news media content in form but not in organizational process or intent" [START_REF] Lazer | The science of fake news[END_REF](Lazer et al., , p. 1094; see also [START_REF] Tandoc | Defining "fake news" A typology of scholarly definitions[END_REF]. Fake news has received a formidable amount of scholarly attention over the past few years [START_REF] Allen | Evaluating the fake news problem at the scale of the information ecosystem[END_REF]. If, on the whole, they represent at most 1% of people's news diet (Allen et al., 2020; see also [START_REF] Grinberg | Fake news on twitter during the 2016 US Presidential election[END_REF][START_REF] Guess | Less than you think: Prevalence and predictors of fake news dissemination on Facebook[END_REF]Guess et al., , 2020;;[START_REF] Nelson | The small, disloyal fake news audience: The role of audience availability in fake news consumption[END_REF][START_REF] Osmundsen | Partisan polarization is the primary psychological motivation behind "fake news[END_REF], some fake news have proven very culturally successful: for instance, in 2016, millions of Americans endorsed the (false) Pizzagate conspiracy theory, according to which high-level Democrats were abusing children in the basement of a pizzeria [START_REF] Fisher | Pizzagate: From rumor, to hashtag, to gunfire in DC[END_REF][START_REF] Jensen | Trump Remains Unpopular; Voters Prefer Obama on SCOTUS Pick[END_REF].

Even if the wide diffusion of a piece of fake news does not entail that it strongly affects those who endorse it (Guess et al., 2020;[START_REF] Kim | Identifying the effect of political rumor diffusion using variations in survey timing[END_REF][START_REF] Mercier | Not Born Yesterday: The Science of Who We Trust and What We Believe[END_REF], its diffusion is still culturally and cognitively revealing. But what exactly does it reveal? Several studies have found that most people are able to distinguish true from fake news, consistently giving higher accuracy ratings to the former than the latter [START_REF] Bago | Fake news, fast and slow: Deliberation reduces belief in false (but not true) news headlines[END_REF]Pennycook et al., 2019Pennycook et al., , 2020;;Pennycook & Rand, 2019). These results suggest that the issue with the sharing of fake news does not stem from an inability to evaluate fake news' accuracy, but instead from a failure to let these accuracy judgments guide sharing decisions.

Scholars have suggested different reasons why people might consume and share news they do not deem accurate (e.g., [START_REF] Duffy | Too good to be true, too good not to share: The social utility of fake news[END_REF]Tandoc, Ling, et al., 2018;[START_REF] Tsfati | Why Do People Watch News They Do Not Trust? The Need for Cognition as a Moderator in the Association Between News Media Skepticism and Exposure[END_REF]. One article found that people high in 'need for chaos,' who want to 'watch the world burn' were particularly likely to share politically offensive fake news (such as conspiracy theories)-not a motivation one would expect to be associated with concern for accuracy [START_REF] Petersen | A "Need for Chaos" and the Sharing of Hostile Political Rumors in Advanced Democracies[END_REF]. By contrast, other studies have stressed the phatic function of news sharing, when news are shared to create social bond, in which case the humorous character of a piece of news might be more important than its accuracy [START_REF] Berriche | Internet Users Engage More With Phatic Posts Than With Health Misinformation On Facebook[END_REF]Duffy & Ling, 2020).

Even if people share news for a variety of reasons (see, [START_REF] Kümpel | News sharing in social media: A review of current research on news sharing users, content, and networks[END_REF], the most common factor appears to be the interestingness of the news. People say they share news they expect recipients to find relevant (Duffy & Ling, 2020), and they share news higher in perceived informational utility [START_REF] Bobkowski | Sharing the news: Effects of informational utility and opinion leadership on online news sharing[END_REF]. Content judged more interesting by participants is more likely to spread on Twitter [START_REF] Bakshy | Everyone's an influencer: Quantifying influence on twitter[END_REF], and articles from The New York Times rated as more interesting or surprising are more likely to be in the Most Emailed List [START_REF] Berger | What makes online content viral[END_REF]. Beyond news, people talk more about interesting products [START_REF] Berger | What drives immediate and ongoing word of mouth[END_REF], and more interesting and surprising urban legends are more likely to be passed along (see, e.g. [START_REF] Heath | Emotional selection in memes: The case of urban legends[END_REF]. Furthermore, to entertain others, people are known to exaggerate stories by making them more interesting-which in turn increases their likelihood of being shared (e.g., [START_REF] Burrus | The truth never stands in the way of a good story: The distortion of stories in the service of entertainment[END_REF]; for a review see [START_REF] Berger | Word of mouth and interpersonal communication: A review and directions for future research[END_REF]. In pragmatics, according to Relevance Theory, human communication is governed by expectations of relevance, leading senders to maximize the relevance of communicated information-and interestingness is likely strongly related to relevance [START_REF] Sperber | Relevance: Communication and cognition[END_REF].

Accuracy is one of the factors that makes a piece of news interesting: ceteris paribus, more accurate information is more relevant information (see, e.g., [START_REF] Sperber | Relevance: Communication and cognition[END_REF].

When it comes to misinformation, it has been suggested that "most people do not want to spread misinformation, but are distracted from accuracy by other salient motives when choosing what to share" (Pennycook et al., 2019, p. 1). Indeed, even if people are able to detect fake news, by systematically judging it less accurate than true news, that does not seem to stop them from sharing fake news (Pennycook et al., 2019[START_REF] Pennycook | Fighting COVID-19 misinformation on social media: Experimental evidence for a scalable accuracy nudge intervention[END_REF]. One hypothesis is that people who are too distracted or too lazy share inaccurate news because of a failure to think "analytically about truth and accuracy" when deciding what to share (Pennycook et al., 2019, p. 1). In support of this account, it has been shown that people are more likely to take the accuracy of a piece of news into account in their sharing decision if they have just been asked to consider its accuracy, rather than if they have only been asked whether to share the news [START_REF] Fazio | Pausing to consider why a headline is true or false can help reduce the sharing of false news[END_REF]Pennycook et al., 2019[START_REF] Pennycook | Fighting COVID-19 misinformation on social media: Experimental evidence for a scalable accuracy nudge intervention[END_REF]. These results, among others (see, e.g., Pennycook & Rand, 2019), suggest that people have the ability to distinguish accurate from inaccurate news, but that, unless specifically prompted, they largely fail to use these abilities in their sharing decisions.

Accuracy, however, is only one component of relevance or interestingness. The statement "I have a prime number of geraniums in my garden" would be irrelevant in nearly every possible context, irrespective of its accuracy. Since we are not aware of any fully developed theory of the interestingness of statements, we rely on Relevance Theory, arguably the dominant theoretical framework in pragmatics (see, e.g., [START_REF] Carston | Relevance theory: Applications and implications[END_REF][START_REF] Clark | Relevance theory[END_REF][START_REF] Sperber | Relevance: Communication and cognition[END_REF][START_REF] Wilson | Meaning and relevance[END_REF]. Within Relevance Theory, with cognitive processing costs held constant, the relevance of a message, which we equate here with its interestingness, is a function both of the plausibility of the message, and of its potential cognitive effects: whether it would generate rich inferences, and create substantial changes of mind (whether in beliefs or intentions). The statement about the geraniums is irrelevant as no useful inferences can be drawn from it, and it doesn't change anyone's prior beliefs. On the other hand, the statement "COVID-19 is a bioweapon that has been developed and released by the Chinese government" would have very significant cognitive effects if it were true, for instance by making us think that a conflict with China was more likely, or by making us distrust Chinese products. Thus, unless one is entirely sure that this statement is false, it has some relevance-indeed, more relevance than many true statements (such as the statement about the geraniums). There are many ways for a statement to elicit cognitive effects: to be about people we know, to bear on issues we have strong opinions on, to elicit strong emotions, to call for drastic action, etc.

For convenience, we will refer interchangeably here to interestingness and to the more technical, well-defined concept of relevance from Relevance Theory. Within this framework, interestingness-if-true should differ from interestingness in systematic ways. Interestingnessif-true assumes that the piece of news being considered is true. By contrast, as mentioned above, interestingness should vary with the perceived accuracy of the news. As a result, in order to understand sharing decisions, interestingness-if-true is a more natural complement of accuracy than interestingness.

The relative weight of accuracy and interestingness-if-true will vary as a function of one's goal (among other factors). When one's main motivation in sharing news is informing others, accuracy should play a crucial role. However, laypeople's main motivation to share news stories is often more social than informational [START_REF] Ihm | The hidden side of news diffusion: Understanding online news sharing as an interpersonal behavior[END_REF][START_REF] Lee | News sharing in social media: The effect of gratifications and prior experience[END_REF]. To fulfil certain social goals, such as to entertain or comfort, the accuracy of a piece of news might play a less important role: "users may have low expectations in terms of the credibility of online news, and simply share news stories as long as they are interesting and relevant to attract attention and initiate interactions" (Ma et al., 2014, p. 612). Still, whatever one's goal might be, both accuracy and interestingness-if-true should influence sharing decisions, since they are both necessary, to some degree at least, to make a statement interesting.

The interestingness of at least some fake news has been recognized (e.g. [START_REF] Tsfati | Causes and consequences of mainstream media dissemination of fake news: Literature review and synthesis[END_REF] and several studies have attempted to understand what makes some fake news attractive, finding that successful fake news tends to share some traits, for instance evoking disgust, being surprising, or bearing on celebrities [START_REF] Acerbi | Cognitive attraction and online misinformation[END_REF][START_REF] Vosoughi | The spread of true and false news online[END_REF].

However, these studies have not attempted to disentangle what we suggest are the two main components of a piece of news' relevance: its accuracy, and how interesting it would be if it were true.

The ability to evaluate how interesting a piece of information would be if it were true is important. When we encounter a piece of information that we think very interesting if true, but whose accuracy is uncertain, we should be motivated to retain it, and to inquire further into its accuracy. For example, when encountering threat-related information that we deem mostly implausible (say, that a neighbor we liked is in fact violent), it is good to realize the import the information would have if it were true, and to attempt to establish its validity.

The interplay of the accuracy and the interestingness-if-true of a piece of information, and their impact on people's propensity to share it, could be studied in a number of ways.

Qualitative work might attempt to elicit whether participants explicitly ponder not only the accuracy, but also the interestingness-if-true of a piece of information, in the manner of the observed quoted above as saying, of a story about life on the moon, "if this account is true, it is most enormously wonderful." Using trace data analysis, it might be possible to test whether successful news-whether true or fake-tends to be interesting-if-true. Here, we have adopted an experimental approach, for two main reasons. First, we needed to measure, and establish, the validity of the concept of the interestingness-if-true of a piece of news. Second, the experimental design allows us to measure whether news that are more interesting-if-true are more likely to be shared, while controlling for a variety of factors that make trace data analysis more difficult to interpret (e.g. the source of the news, how participants become exposed to them, etc.). With these precise measures, it is easier to fit statistical models informing us of the relative role of accuracy and interestingness-if-true in sharing intentions.

The present experiments offer, to the best of our knowledge, the first evidence that these two factors-accuracy and interestingness-if-true-interact in the willingness to share news, whether they are true or false, and that interestingness-if-true systematically differs from interestingness. Participants were presented with news items-half of which were true news, the other fake news-, asked to rate the accuracy and interestingness-if-true of the items (and, in Experiment 3, their interestingness), and to indicate how willing they would be to share the items.

Based on the literature reviewed above, we suggested three main hypotheses (preregistered for all three experiments): H 1 : Participants judge fake news to be less accurate than true news (see, [START_REF] Bago | Fake news, fast and slow: Deliberation reduces belief in false (but not true) news headlines[END_REF]Pennycook et al., 2019[START_REF] Pennycook | Fighting COVID-19 misinformation on social media: Experimental evidence for a scalable accuracy nudge intervention[END_REF]Pennycook & Rand, 2019).

Because people share news they expect others will find relevant [START_REF] Bobkowski | Sharing the news: Effects of informational utility and opinion leadership on online news sharing[END_REF]Duffy & Ling, 2020) and that relevance depends on accuracy and on interestingness-if-true [START_REF] Sperber | Relevance: Communication and cognition[END_REF], both factors should drive sharing intentions.

H 2 : The more accurate a piece of news is deemed to be, the more willing participants are to share it.

H 3 : The more interesting-if-true a piece of news is deemed to be, the more willing participants are to share it.

Experiments

In each experiment, participants were presented with ten news stories in a randomized order (five true and five fake) and asked to rate their accuracy, interestingness-if-true, and to indicate how willing they would be to share them. Experiment 2 is a replication of Experiment 1 with additional research questions not directly related to our main hypotheses (such as how trust in mass media correlates with fake news detection). Experiment 3 is a replication of the first two experiments with novel materials and additional questions aimed at establishing the validity of the interestingness-if-true question (such as its face validity and whether it differs from interestingness and accuracy as we predict it does).

We pre-registered the experiments' sample size, exclusion criterion, hypotheses, research questions, and statistical analyses.

Participants

U.S. participants were recruited on Prolific Academic and paid $0.53. In Experiment 1, we recruited 301 participants, and removed two who failed the attention check, leaving 299 participants (154 women, M Age = 33.07, SD = 12.26). In Experiment 2, we recruited 303 participants, and removed four who failed the attention check, leaving 299 participants (171 women, M Age = 32.23, SD = 11.81). In Experiment 3, we recruited 300 participants, and removed one who failed the attention check, leaving 299 participants (162 women, M Age = 32.77, SD = 11.06).

Methods

Materials

In Experiment 1 and Experiment 2, we selected 15 recent fake news stories related to COVID-19 from fact-checking websites such as "Snopes.com" and from a recent study [START_REF] Pennycook | Fighting COVID-19 misinformation on social media: Experimental evidence for a scalable accuracy nudge intervention[END_REF]. We selected 15 true news stories related to COVID-19 from reliable mainstream media such as The New York Times or The Wall Street Journal, and from [START_REF] Pennycook | Fighting COVID-19 misinformation on social media: Experimental evidence for a scalable accuracy nudge intervention[END_REF]. The news stories were presented in a 'Facebook format' with a headline and a picture, without a source. We did not entirely rely on the news of Pennycook et al. (2020) because some of them were already outdated.

Experiment 3 used a novel set of 15 true news since the ones used in Experiments 1 and 2 were outdated, but relied on the same fake news stories as in Experiments 1 and 2.

Procedure

After having completed a consent form, each participant was presented with five fake news stories and five true news stories in a randomized order. Participants had to answer questions, also presented in a randomized order, about each piece of news. The number of questions per piece of news vary across experiments (three questions in Experiment 1, five questions in Experiment 2, and four questions in Experiment 3).

Before finishing the experiment, participants were presented with a correction of the fake news stories they had read during the experiment, including a link to a fact-checking article. Fact-checking reliably corrects political misinformation and backfires only in rare cases (see, e.g., [START_REF] Walter | Fact-Checking: A Meta-Analysis of What Works and for Whom[END_REF]. Finally, participants completed an attention check that required copying an answer hidden in a short paragraph (see ESM) and provided demographics information. Participants were recruited between the sixth of May 2020 and the the seventh of July 2020.

Design

In Experiment 1, we measured how accurate participants deemed the headlines using the same accuracy question as Pennycook and Rand (2018): "To the best of your knowledge, how accurate is the claim in the above headline?" (1[Not at all accurate], 2[Not very accurate], 3[Somewhat accurate], 4[Very accurate]). We measured news' interestingness-iftrue with the following question: "Imagine that the claim made in the above headline is true, even if you find it implausible. If the claim were true for sure, how interesting would it be?" ). Note that this scale was intentionally inflated to avoid potential ceiling effects (in particular, we expected some fake news to receive very high ratings). We used the following question to measure sharing intentions: "How likely would you be to share this story online In Experiment 3, we added one question per news, three questions at the end of the survey to evaluate how participants felt about the interestingness-if-true question, and an additional question in the demographics (the same as in Experiment 2 regarding trust in the media). In addition to rating news on accuracy, interestingness-if-true, and willingness to share, participants answered the following questions: "How interesting is the claim made in the above headline ?" on the same scale as the interestingness-if-true question, i. Before the demographics, participants read the following text:

We thank you for answering questions about all these pieces of news. Before we move on to the demographics, we have a few more questions. For each piece of news, we've asked you: "Imagine that the claim made in the above headline is true, even if you find it implausible. If the claim were true for sure, how interesting would it be?".

And they were asked the three following questions in a randomized order: "Were you able to make sense of that question?", "Did you find it difficult to answer that question?", and "Did you feel that you understood the difference between this question and the question "How interesting is the claim made in the above headline?". For each of these questions, participants had to select "Yes," "No," or "Not sure." The aim of these questions was to test whether participants understood the concept of interestingness-if-true, and were able to answer questions that relied on it.

Results and Discussion

Note on the statistical analyses

All the statistical analyses below are linear mixed effect models with participants as random factor. We initially planned to conduct linear regressions in the first experiment, but realized that it was inappropriate as it would not have allowed us to control for the nonindependence of the data points-a linear regression would have treated participants' multiple answers as independent data points. We refer to 'statistically significant' as the p-value being lower than an alpha of 0.05. All the betas reported in this article have been standardized. The Confidence Intervals (CI) reported in square brackets are 95% confidence intervals. All the effects that we refer to as statistically significant hold when controlling for demographics and all other predictors (see Electronic Supplementary Materials (ESM)). All statistical analyses were conducted in R (v.3.6.1), using R Studio (v.1.1.419). On OSF we report a version of the results with two additional research questions, and a clear distinction between confirmatory analyses (main hypotheses and research questions) and exploratory analyses. We do not make this distinction in the present manuscript because it excessively hinders the readability of the results section. Preregistrations, data, materials, ESM, and the scripts used to analyze the data are available on the Open Science Framework at https://osf.io/9ujq6/?view_only=892bb38d2647478f9da5e8e066ef71c1. We report the results of two pre-registered research questions regarding the link between sharing decisions and the estimated percentage of Americans who have already read or heard of the pieces of news in ESM and on OSF. One experiment was conducted to test the same hypotheses before the three experiments reported here (see ESM and OSF). Unfortunately, its between-participants design proved unsuitable to conduct appropriate statistical tests-allowing us to only compare the mean ratings per news item. Still, the results were qualitatively aligned with those of the two experiments reported here (see ESM and OSF).

Main findings

Validity of the interestingness-if-true measure

We start by establishing the validity of our interestingness-if-true measure, using two broad strategies. First, we use indirect measures, looking at four different ways in which the interestingness-if-true ratings should behave, if our construct is valid. Second, we turn to the questions that have explicitly asked about the participants' understanding of the concept.

We first test whether participants' rating of the news was coherent with our construct of interestingness-if-true, we conducted four different analyses. The first analysis tests whether interestingness-if-true is orthogonal to accuracy, as suggested in the introduction. By contrast, interestingness should partly depend on accuracy (i.e. more plausible news should be deemed more interesting, everything else equal). As a result, we predicted that the (perceived) accuracy of the news would be more strongly correlated with the news' interestingness than with the news' interestingness-if-true, which his what we observed: the perceived accuracy of the news was indeed more strongly correlated with the news' interestingness (cor = 0.15, t(2988) = 8.59, p < 0.001) than with the news' interestingness-if-true (cor = -0.04, t(2988) = -2.17, p = 0.03) (Hotelling's t(2987) = 17.40, p < .001).

Second, since interestingness, but not interestingness-if-true, should partly depend on accuracy, and that sharing should also partly depend on accuracy, sharing should be more closely related to interestingness than to interestingness-if-true. In line with this hypothesis, sharing intentions were more strongly correlated with the news' interestingness (cor = 0.48, t(2988) = 30.19, p < 0.001) than with the news' interestingness-if-true (cor = 0.39, t(2988) = 22.91, p < 0.001) (Hotelling's t(2987) = 9.33, p < .001).

Third, interestingness-if-true is, by definition, how interesting a piece of news would be if it were true. By contrast, the interestingness of a piece of news takes into account its accuracy, which is maximal if the news is deemed true, and can only decrease from there.

Thus, for each piece of news, its interestingness should be at most equal to its interestingnessif-true and in many cases-when the news isn't deemed completely certain-lower. In accordance with this hypothesis, for each piece of news, the average interestingness score was never higher than the average interestingness-if-true score (see the full descriptive statistics in ESM).

Fourth, when a piece of news is deemed true, its interestingness and its interestingness-if-true should converge. By contrast, if the piece of news is deemed implausible, it might be deemed much more interesting-if-true than interesting. Thus the more accurate a piece of news is judged, the more its interestingness and interestingness-if-true should be correlated. In line with this hypothesis, the news' interestingness and interestingness-if-true were more strongly correlated among news perceived as more accurate (ß = 0.08, [0.06, 0.10], t(2981.79) = 8.15, p < .001) (for a visual representation of the interaction see Figure S2 in ESM).

Turning to the explicit questions asked to test the validity of the interestingness-if-true construct, we found that 98% of participants (293/299) reported having understood the difference between the question on the news' interestingness and the news' interestingness-iftrue, 81% of participants (243/299) reported having understood the question on interestingness-if-true, and 90% of participants (269/299) reported that they found it easy to answer the interesting-if-true question.

We thus have solid grounds for relying on the answers to the interestingness-if-true questions, since (i) the answer provided behave as expected in relation with better established constructs such as accuracy and, (ii) the vast majority of participants explicitly said they understood the question.

Having established the validity of the interestingness-if-true questions, we turn to the tests of our hypotheses.

Participants deemed fake news less accurate than true news (H 1 )

In all three experiments, participants rated fake news as less accurate than true news (see Figure 1 and Table 1). This effect is large, and confirms previous findings showing that, on average, laypeople are able to discern fake from true news [START_REF] Allen | Scaling up fact-checking using the wisdom of crowds[END_REF][START_REF] Bago | Fake news, fast and slow: Deliberation reduces belief in false (but not true) news headlines[END_REF]Pennycook et al., 2019[START_REF] Pennycook | Fighting COVID-19 misinformation on social media: Experimental evidence for a scalable accuracy nudge intervention[END_REF]Pennycook & Rand, 2019).

Participants deemed fake news more interesting-if-true than true news

In all three experiments, participants deemed fake news more interesting-if-true than true news (see Figure 1 and Table 1). The difference between the interestingness-if-true of true and fake news was smaller than their difference in term of accuracy. Note that, as expected, fake news were particularly over-represented among the news rated as "One of the most interesting news of the year."

Participants were more likely to share true news than fake news

In all three experiments, participants were more likely to share true news than fake news (see Figure 1 and Table 1). In line with previous findings (Pennycook et al., 2019[START_REF] Pennycook | Fighting COVID-19 misinformation on social media: Experimental evidence for a scalable accuracy nudge intervention[END_REF], participants deemed fake news much less accurate than true news, but were only slightly more likely to share true news compared to fake news. In all three experiments, participants were more likely to share news perceived as more accurate (see Figure 2 and Table 2).

Participants were more willing to share news perceived as more interesting-if-true (H 3 )

In all three experiments, participants were more likely to share news perceived as more interesting-if-true (see Figure 2 and Table 2). Together, accuracy and interestingness-iftrue explained 21% of the variance in sharing intentions.

Table 2. Effect of the accuracy, interestingness-if-true, and interaction between interestingness-if-true and accuracy, on sharing decisions for all news, true news, and fake news. ß in bold represent p-values below p < .001. Participants were more willing to share news perceived as both more interesting-if-true and accurate In all three experiments, the more a piece of news was deemed both interesting-if-true and accurate, the more likely it was to be shared (See Figure 3 and Table 2). This effect held true for both fake news and true news (see Table 2).

Other findings

In parallel to the main focus of the paper-the relation between interestingness-if-true and news sharing-we investigated three questions often broached in the literature on misinformation: (i) How does trust in mass media relates to fake news detection and fake news sharing? (ii) Does asking people to think about accuracy reduce fake news sharing? (iii) Do people come to believe in fake news because they have been repeatedly exposed to them?

Relation between trust in mass media, fake news detection, and fake news sharing (Experiments 2 and 3)

People with low trust in the media have been found to pay less attention to the media in general, or to seek out alternative media sources [START_REF] Ladd | Why Americans hate the news media and how it matters[END_REF][START_REF] Tsfati | Media skepticism and climate of opinion perception[END_REF][START_REF] Tsfati | Online news exposure and trust in the mainstream media: Exploring possible associations[END_REF][START_REF] Tsfati | Mainstream media skepticism and exposure to sectorial and extranational news media: The case of Israel[END_REF]. Maybe as a result of these choices, people with low trust in the media also tend to be less well-informed [START_REF] Ladd | Why Americans hate the news media and how it matters[END_REF]. We investigated whether lower trust in the media correlates with a poorer capacity to discern fake from true news.

To measure the relation between trust in mass media and the capacity to distinguish fake from true news we tested the interaction between trust in mass media and accuracy ratings for fake and true news. We found that lower trust in mass media was associated with a poorer capacity to distinguish fake from true news (Experiment 2: ß = 0.12, [0.07, 0.17], t(2689) = 4.41, p < .001; Experiment 3: ß = 0.15, [0.09, 0.22], t(2689.00) = 4.70, p < .001). However, contrary to previous findings (e.g., [START_REF] Hopp | Why Do People Share Ideologically Extreme, False, and Misleading Content on Social Media? A Self-Report and Trace Data-Based Analysis of Countermedia Content Dissemination on Facebook and Twitter[END_REF]see also, Noppari et al., 2019;[START_REF] Ylä-Anttila | Populist knowledge:'Post-truth'repertoires of contesting epistemic authorities[END_REF] lower trust in mass media was not significantly associated with a greater willingness to share fake news (ß = -0.02, [-0.11, 0.07], t(297) = 0.48, p = .63).

The 'accuracy nudge' (Experiment 1)

Several studies have found that asking participants to rate how accurate a piece of news is before sharing it reduces the propensity to share fake news (more than true news) [START_REF] Fazio | Pausing to consider why a headline is true or false can help reduce the sharing of false news[END_REF]Pennycook et al., 2019[START_REF] Pennycook | Fighting COVID-19 misinformation on social media: Experimental evidence for a scalable accuracy nudge intervention[END_REF]. The small number of questions per news in Experiment 1 (presented in a randomized order), allowed us to measure to effect of this accuracy nudge, whereas in the other experiments there might have been too many questions between the accuracy and the sharing questions.

As expected from previous studies on the accuracy nudge, we found that asking participants to rate how accurate a piece of news is before considering sharing it, in comparison to after, decreased participants' willingness to share the news (before: M = 2.31, SD = 1.53; after: M = 2.51, SD = 1.61; ß = -0.12, [-0.18, -0.06], t(1986.92) = -4.10, p < .001). However, contrary to previous findings [START_REF] Fazio | Pausing to consider why a headline is true or false can help reduce the sharing of false news[END_REF]Pennycook et al., 2019[START_REF] Pennycook | Fighting COVID-19 misinformation on social media: Experimental evidence for a scalable accuracy nudge intervention[END_REF], this ordering effect was not significantly stronger for fake news than for true news (interaction term: p = .90), nor was it stronger for less accurate compared to more accurate news (interaction term: p = .39). The small effect sizes, and the non-specificity to fake news, does not offer strong support for the accuracy nudge.

The illusory truth effect (Experiment 2)

A growing body of research suggests that people may come to believe in fake news because they have been repeatedly exposed to them (Pennycook et al., 2018;Pennycook & Rand, 2018), an effect of repetition on truth judgments known as 'illusory truth,' which had been observed in many contexts before being applied to fake news (for a general review see, [START_REF] Dechêne | The Truth About the Truth: A Meta-Analytic Review of the Truth Effect[END_REF].

In line with the illusory truth effect, we found that participants deemed more accurate news that they had encountered prior to the experiment (M = 2.84, SD = 1.06), than news that they didn't remember encountering (M = 2.18, SD = 0.84) (ß = 0.30, [0.27, 0.34], t(2653.43) = 16.41, p <.001).

However, the illusory truth effect is only one potential explanation for this finding.

Alternatively, the effect of prior exposure could be due to participants having encountered a piece of news in at least one trusted outlet. If the illusory truth explanation is correct, we expect that the effect of prior exposure should be approximatively as strong for true and fake news. By contrast, if the latter explanation is correct, we expect the effect to be much stronger for true news, since participants are much more likely to have encountered true rather than fake news in trustworthy outlets.

We found that the effect of having already encountered a piece of news was much stronger for true news (encountered: M = 3.36, SD = 0.66; new: M = 2.44, SD = 0.79), than for fake news (encountered: M = 2.16, SD = 1.09; new: M = 1.95, SD = 0.81) (ß = 0.33, t(2548.40) = 10.00, [0.27, 0.39], p<.001) (see Figure 5 for a visual representation of this interaction). This effect thus appears to have been largely due to participants deeming more accurate true news they have already encountered in trusted outlets. In turn, the effect of prior exposure might account for a large share of the effect of trust in media on Accuracy Ratings we observed (i.e. the fact that higher trust in mass media was associated with a greater ability to discern true from fake news). This benefit of higher trust in the media could result from prior exposure, with people who trust the mass media having a higher probability of having been exposed either to the true news we used (on the positive relationship between trust in the media and knowledge of the news, see [START_REF] Ladd | Why Americans hate the news media and how it matters[END_REF].

In accordance with this explanation, participants with higher trust in mass media were more likely to have previously encountered true news compared to fake news (interaction term: ß = 0.12, [0.05, 0.20], t(2402.27) = 3.29, p<.001) (see Figure S1 in ESM for a visual representation of the interaction).

Limitations

Our study has several limitations. Three are common to many experimental studies on the determinants of news sharing, the first of these being that we do not record actual sharing decisions, but only sharing intentions. However, past studies have shown that sharing intentions correlate with actual sharing [START_REF] Mosleh | Self-reported willingness to share political news articles in online surveys correlates with actual sharing on Twitter[END_REF], and that people's rating of the interestingness of pieces of news correlates with their popularity on social media [START_REF] Bakshy | Everyone's an influencer: Quantifying influence on twitter[END_REF].

The second limitation we share with other studies is that our sampling of true and fake news is somewhat arbitrary, that this sampling is likely to influence our results and that we cannot generalize to all fake news stories and true news stories. For example, we find that a piece of news' interestingness-if-true explained a larger share of the variance in sharing intentions than its perceived accuracy. Had we selected news that were all approximatively equally interesting-if-true, the role of this factor would have dropped. The contrast was clear when we compared true and fake news. True news varies much less in perceived accuracy than fake news. It is thus not surprising that, compared to interestingness-if-true, perceived accuracy played a much larger role in explaining the intention to share fake news than true news. These considerations suggest that past studies asking participants about the interestingness of news from the mass media might have effectively approximated interestingness-if-true, given the overall high Accuracy Ratings of news from the mass media (and thus the little role differences in accuracy judgment would play in evaluating interestingness). Still, even if the exact extent of variation in interestingness-if-true and accuracy in the news people encounter would be difficult to measure, our results clearly reveal that, provided some variation in either measure, both play a significant role in the intention to share news.

A third limitation concern our within-participants design: by simultaneously asking participants how willing they are to share a piece of news, how accurate it is, and how interesting it would be if true (as well as how interesting it is in Experiment 3), we risk (i) inflating the correlations between the responses and (ii) compromising the ecological validity of the willingness to share measure (e.g. since when making real life sharing decisions, people are not asked to explicitly evaluate the accuracy of the news). Controlling for question order is not enough to fully address these issues; instead, a between-participants design in which participants are asked only how willing they are to share the news is required. The first experiment that we pre-registered in this project but did not report here had a betweenparticipants design (see ESM), which allows us to compute the correlations between the answers in that between-participants experiments and the present Experiments 1 and 2, which were within-participants experiments (Experiment 3 used a different set of news). If the concerns above are genuine, we should observe low correlations between people's decisions in the two designs. Across experimental designs, the mean sharing (r experiment1 = 0.78, r experiment2 = 0.85), interestingness-if-true (r experiment1 = 0.77, r experiment2 = 0.79) and accuracy (r experiment1 = 0.98, r experiment2 = 0.96) scores of news stories were very strongly correlated. The strength of these correlations is similar to the strength of the correlations between Experiment 1 and Experiment 2 (r sharing = 0.78, r interestingness-if-true = 0.98, r accuracy = 0.95). These results suggest that our within-participants design did not introduce drastic distortions in the answers.

A fourth limitation is more restricted to our study. If we can expect people to be able to gauge the interestingness of a piece of news, being able to explicitly isolate its interestingness-if-true might be a more cognitively complex task. In particular, it might be difficult for people to imagine a world in which a piece of information they deem very unlikely to be true would be true, and thus to evaluate the interestingness of this piece of information in such a world. People find it easier to create counterfactuals of events that nearly happened (e.g. people are more likely to imagine having caught a flight if they have only missed it by a few minutes, than a few hours, see, [START_REF] Meyers-Levy | When timing matters: The influence of temporal distance on consumers' affective and persuasive responses[END_REF][START_REF] Roese | Counterfactuals, causal attributions, and the hindsight bias: A conceptual integration[END_REF]. Similarly, it might be easier for people to understand the full interestingness-if-true of information they think is potentially accurate, than of information they are sure is inaccurate. As a result, interestingness-if-true ratings could be affected by Accuracy Ratings, thereby reducing the explanatory power of the interestingness-if-true ratings. Our results thus offer only a lower bound on the explanatory power of the interestingness-if-true of news.

Conclusion

Why do people share news of questionable accuracy, such as fake news? Is it because they fail to take accuracy into account? Alternatively, fake news could have other qualities that make up for its questionable accuracy. In particular, fake news could be very interesting if it were true, and this 'interestingness-if-true' could make up for the lack of perceived accuracy in explaining people's decisions to share fake news.

Past studies have already shown that the interestingness of a piece of news plays an important part in people's decision to share it (e.g., [START_REF] Bakshy | Everyone's an influencer: Quantifying influence on twitter[END_REF]. However, interestingness encompasses both perceived accuracy (a piece of news perceived as more accurate is, ceteris paribus, more interesting), and interestingness-if-true. In this article, we attempt to separate the roles of accuracy and of interestingness-if-true in the decision to share true and false pieces of news. To this end, in three experiments participants were presented with a series of true or false pieces of news, and asked to rate their accuracy, how interesting they would be if they were true (as well as simply how interesting they are in Experiment 3), and to say how likely they would be to share the news.

First, participants deemed true news to be more accurate than fake news (ß = 0.78, [0.74, 0.81], p < .001), the type of news explaining 15% of the variance in accuracy judgments. Second, even if participants were more likely to say they would share true news than fake news, the effect was much smaller than the effect of true vs. fake on perceived accuracy (ß = 0.14, [0.11, 0.17], p < .001), explaining 0% of the variance in sharing intentions. Moreover, considered on its own, perceived accuracy only explained 6% of the variance in sharing intentions (ß = 0.24, [0.22, 0.25], p < .001). These results replicate previous studies (Pennycook et al., 2019[START_REF] Pennycook | Fighting COVID-19 misinformation on social media: Experimental evidence for a scalable accuracy nudge intervention[END_REF] in showing that perceived accuracy alone is not sufficient to understand sharing decisions.

Second, our measure of interestingness-if-true explained more than twice as much variance in sharing intentions (14%) than accuracy (ß = 0.37, [0.35, 0.38], p < .001). Fake news was deemed more interesting-if-true than true news (ß = 0.20, [0.17, 0.24], p < .001), which could explain why, even though fake news was rated as much less accurate than true news, people did not intend to share fake news much less than true news.

Our results suggest that people may not always share news of questionable accuracy by mistake. Instead, they might share such news because they deem it interesting-if-true.

Several results suggest that participants can have positive reasons of sharing news of questionable accuracy, reasons that might relate to the interestingness-if-true of the news.

For instance, older adults are more prone than younger adults to share fake news [START_REF] Grinberg | Fake news on twitter during the 2016 US Presidential election[END_REF][START_REF] Guess | Less than you think: Prevalence and predictors of fake news dissemination on Facebook[END_REF]. However, older individuals are also better at discerning fake from true news [START_REF] Allcott | Social media and fake news in the 2016 election[END_REF]Pennycook & Rand, 2019). As a recent review suggests, this apparent contradiction can be resolved if we think that older individuals "often prioritize interpersonal goals over accuracy" (Brashier & Schacter, 2020, p. 4). Their use of social media is more oriented toward strengthening ties with peers and relatives than gaining new information and, as a result, it is understandable that accuracy should matter less than other traits-such as interestingness-if-true-in their sharing decisions (compared to other populations, who might have other goals) [START_REF] Sims | Information and communication technology use is related to higher well-being among the oldest-old[END_REF].

Another motive that might lead people to share news of questionable accuracy is the congruence of the news with people's political views. Politically congruent headlines are only found to be slightly more accurate than politically incongruent headlines, but they are much more likely to be shared than politically incongruent headlines (Pennycook et al., 2019). This does not mean that people necessarily neglect accuracy in their sharing decisions. Instead, other factors might motivate them more to share politically congruent news, even if they aren't deemed more accurate, such as justifying their beliefs, signaling their identity, derogating the out-party, proselytizing, or because they expect that their audience will find them more interesting if they are true (e.g. [START_REF] Brady | The MAD Model of Moral Contagion: The role of motivation, attention and design in the spread of moralized content online[END_REF][START_REF] Donath | Public displays of connection[END_REF][START_REF] Guess | Less than you think: Prevalence and predictors of fake news dissemination on Facebook[END_REF][START_REF] Hopp | Why Do People Share Ideologically Extreme, False, and Misleading Content on Social Media? A Self-Report and Trace Data-Based Analysis of Countermedia Content Dissemination on Facebook and Twitter[END_REF][START_REF] Mourão | Fake news as discursive integration: An analysis of sites that publish false, misleading, hyperpartisan and sensational information[END_REF][START_REF] Osmundsen | Partisan polarization is the primary psychological motivation behind "fake news[END_REF][START_REF] Shin | Partisan selective sharing: The biased diffusion of factchecking messages on social media[END_REF].

Although the question of what makes people read or share a piece of news has received a lot of attention in media studies [START_REF] Kümpel | News sharing in social media: A review of current research on news sharing users, content, and networks[END_REF], these investigations have remained largely detached from work in cognitive science (for some exceptions, see [START_REF] Acerbi | Cognitive attraction and online misinformation[END_REF][START_REF] Berriche | Internet Users Engage More With Phatic Posts Than With Health Misinformation On Facebook[END_REF]. We suggested that Relevance Theory, which draws on cognitive science to illuminate the field of pragmatics, can be a useful theoretical framework to make sense of why people are more or less interested in reading or sharing a piece of news.

To the best of our knowledge, very little work has applied Relevance Theory to such questions, even though it has become a major analytical tool in other domains, such as literature (for a recent exception, see [START_REF] Chernij | On the value of pageviews as proxies for audience interest in news: A Relevance Theory approach[END_REF]. As a first step, we wanted to highlight a basic distinction between two factors that should contribute to the relevance of a piece of news: its plausibility, and its interestingness-if-true, defining the latter as the cognitive effects the piece of news would have if it were deemed true.

Future work might attempt to use the tools of Relevance Theory to integrate diverse literatures, such as work in social psychology on the cues people use to assess accuracy (see, e.g., [START_REF] Mercier | Not Born Yesterday: The Science of Who We Trust and What We Believe[END_REF][START_REF] Petty | Attitude change: Multiple roles for persuasion variables[END_REF], work in media studies on what makes people decide to read or share news [START_REF] Bright | The social news gap: How news reading and news sharing diverge[END_REF][START_REF] Kümpel | News sharing in social media: A review of current research on news sharing users, content, and networks[END_REF], and work bearing on related issues within cognitive science and linguistics. Relevance Theory also draws attention to sometimes neglected information processing factors, such as the effort involved in accessing or reading a news article (see, [START_REF] Chernij | On the value of pageviews as proxies for audience interest in news: A Relevance Theory approach[END_REF]. Drawing attention to the construct of interestingness-if-true in particular might allow bridges to be built between the numerous characterizations of what makes a piece of news interesting in media studies (e.g. [START_REF] Kormelink | What clicks actually mean: Exploring digital news user practices[END_REF] to work in cognitive science regarding what type of information is likely to elicit cognitive effects, and how people assess these cognitive effects when a piece of information is only entertained provisionally or hypothetically (see, e.g., [START_REF] Evans | Hypothetical thinking: Dual processes in reasoning and judgement[END_REF][START_REF] Harris | The Work of the Imagination[END_REF].

To conclude, we would like to relate our findings to broad observations about the media environment. As we mentioned in the introduction, fake news only represents a minute portion of people's media diet. It has previously been suggested that people mostly avoid sharing fake news because doing so would jeopardize their epistemic reputation [START_REF] Altay | Why do so few people share fake news? It hurts their reputation[END_REF], see also [START_REF] Duffy | Too good to be true, too good not to share: The social utility of fake news[END_REF][START_REF] Waruwu | Telling lies together? Sharing news as a form of social authentication[END_REF]. However, these reputational checks cannot entirely explain the rarity of fake news: in many experiments-such as oursparticipants declare a willingness to share fake news that is barely inferior to their willingness to share true news. Reputational checks on individuals thus cannot explain why even fake news that is deemed sufficiently accurate and interesting-if-true largely fails to spread.

Given the weak preference for sharing true news rather than fake news participants have evinced in several experiments (besides the present experiments, see Pennycook et al., 2019[START_REF] Pennycook | Fighting COVID-19 misinformation on social media: Experimental evidence for a scalable accuracy nudge intervention[END_REF], the quasi complete absence of fake news in people's media diets is unlikely to stem directly from people's ability to discriminate true from fake news, and to share more the former than the latter. Instead, the rarity of fake news is likely driven by a combination of (i) people's massive reliance on mainstream media for their media diets [START_REF] Allen | Evaluating the fake news problem at the scale of the information ecosystem[END_REF][START_REF] Grinberg | Fake news on twitter during the 2016 US Presidential election[END_REF] and, (ii) the rarity of fake news in the mainstream media (e.g. [START_REF] Cardon | Unfolding the Multi-Layered Structure of the French Mediascape[END_REF]. In turn, the rarity of fake news in the mainstream media is likely driven by many factors, such as the values journalists bring to the task (e.g. [START_REF] Deuze | What is journalism? Professional identity and ideology of journalists reconsidered[END_REF], but also fear of negative judgments by their audience. In this case, what would matter most isn't people's ability to identify fake news on the spot, but, more simply, their ability to hold a media accountable if it is later identified as having spread fake news (Knight Foundation, 2018;The Media Insight Project, 2016). More generally, we hope that future studies will keep trying to integrate the psychological mechanisms which make people likely to share fake news with considerations about the broad media ecosystem in which they make these decisions.

( 1 [

 1 Not interesting at all], 2[Not very interesting], 3[Slightly interesting], 4[Interesting], 5[Very interesting], 6 [Extremely interesting], 7[One of the most interesting news of the year]

  (for example, through Facebook or Twitter)?" (1[Extremely unlikely], 2[Moderately unlikely], 3[Slightly unlikely], 4[Slightly likely], 5[Moderately likely], 6[Extremely likely])(past work has shown a significant correlation between news people declare they want to share and news they actually share,[START_REF] Mosleh | Self-reported willingness to share political news articles in online surveys correlates with actual sharing on Twitter[END_REF].In Experiment 2, we added one question per news, and an additional question in the demographics. In addition to rating news on accuracy, interestingness-if-true, and willingness to share, participants answered the following question: "Have you read or heard of this news before?" ([Yes], [No], [Maybe], based onPennycook et al., 2018). In the demographics, we added the following question on trust in mass media used by Gallup Poll or Poynter Media Trust Survey[START_REF] Guess | All media trust is local? Findings from the 2018[END_REF][START_REF] Jones | US media trust continues to recover from 2016 low. Gallup[END_REF]: "In general, how much trust and confidence do you have in the mass mediasuch as newspapers, TV, and radiowhen it comes to reporting the news fully, accurately, and fairly?" (1[Not at all], 2[Not very much], 3[A fair amount], 4 [A great deal]).

  e. (1[Not interesting at all], 2[Not very interesting], 3[Slightly interesting], 4[Interesting], 5[Very interesting], 6 [Extremely interesting], 7[One of the most interesting news of the year]).

Figure 1 .

 1 Figure 1. Ratings of fake news and true news in Experiments 1, 2, and 3 (E1, 2, 3) (note that the true news of Experiment 3 were not the same as those of Experiments 1 and 2). Density plots represent the distribution of participants' answers according to the type of news (fake or true) for perceived accuracy, interestingness-if-true, and sharing intentions.

Table 1 .

 1 Ratings of true and fake news in Experiments 1, 2 and 3. The rightmost column correspond to the statistical difference between true and fake news. ß in bold represent pvalues below p < .001. ** = p < .01, * = p < .05 Participants were more willing to share news perceived as more accurate (H 2 )

Figure 2 .

 2 Figure 2. Main effects of interestingness-if-true and accuracy on sharing intentions in Experiments 1, 2, and 3 (E1, 2, 3). Scatter plots represent the distribution of sharing intentions as a function of the pieces of news' interestingness-if-true and accuracy. The red lines represent the regression lines, the shaded area in blue are the 95% confidence intervals.

Figure 3 .

 3 Figure 3. Heatmap representing the relationship between interestingness-if-true, accuracy, and sharing intentions in Experiments 1, 2, and 3 (combined data).

Figure 4

 4 Figure 4 offers a visual representation of this interaction.

Figure 4 .

 4 Figure 4. Interaction plot between participants trust in mass media and type of news (True or Fake) on news Accuracy Ratings in Experiments 2 (E2) and 3 (E3).

Figure 5 .

 5 Figure 5. Interaction plot between participants' prior exposure to the news (encountered before or not) and type of news (True or Fake) on news' Accuracy Ratings.