Marek Jenöffy
email: mj@bueroamcarlsplatz.de.

A Seesaw Model of Choices

In 2019, Galberti called for the formulation of a theory of "how decision makers change worldviews." He was looking for a "theory of persuasive rhetoric" that goes "beyond Bayesianism." In this field, there is insight of ancient rhetoric, and empirical results of modern communications research. I discuss these results and extract possible variables for a theory of persuasive rhetoric. I model a decision as a seesaw. Seesaws follow the principle of the lever. The model explains why the assumption of constant preferences in economic models often makes sense.

various alternatives of acting which are available and from which the individual can choose…According to these preferences, the individual assesses the various alternatives at his disposal, he weighs up the pros and cons, the costs and benefits of the alternatives against each other and finally chooses that (those) alternative(s) which come(s) closest to his preferences or which promise(s) to bring about the maximum net benefit."

The origin of the preferences is vague. "The preferences are derived from the intentions of the individual, they reflect the individual's ideas of value as they have been developed during the process of socialization, and they are principally independent of the actual possibilities of action" (Kirchgässner 2008, p.12). This thought gives rise to several questions: (1) How do preferences accrue during the socialization? (2) When does the socialization end? (3) Can preferences change after the process of socialization had ended? (4) Is each child is born with an unchangeable grid of preferences? There is little research in economics addressing the origin of preferences. There is work by [START_REF] Becker | The Endogenous Determination of Time Preferences[END_REF], [START_REF] Krackhardt | Endogenous Preferences: A Structural Approach[END_REF], [START_REF] Palacios-Huerta | A Theory of Markets, Institutions, and Endogenous Preferences[END_REF] and Jenőffy-Lochau (1997, 2012, 2013[START_REF] Jenöffy-Lochau | The Origin of Preferences, Economic Decision Theory and Yaari[END_REF].

A. Empirical Results of Communications Research

On the other hand, there is a great deal of literature in communications research theorizing how "opinions" form. Numerous empirical studies examine how "signals" influence the "opinions" of "recipients." This research might have been overlooked by economists due to differences in wording. Nevertheless, this research provides stable empirical results gained from sophisticated experiments.

These experiments have analyzed the role of information in decision-making processes. [START_REF] Hovland | The Influence of Source Credibility on Communication Effectiveness[END_REF], e.g., concluded that "credible information" changed the decision of 23% of the individuals in one of their experiments at Yale. Information that has better credibility is more likely to change a decision than less credible information. [START_REF] Whittaker | Cognitive Dissonance and the Effectiveness of Persuasive Communications[END_REF] posited that the "distance" between new information and existing preferences determines whether a decision is reversed by an individual ("cognitive dissonance" and the "boomerang effect"). [START_REF] Freedman | Involvement, Discrepancy and Change[END_REF] conducted experiments with "high-involvement" and "low-involvement" decisions. In the low-involvement category, he found greater changes in decisionmaking after the exposure of the individuals to new information. [START_REF] Bochner | Communicator Discrepancy, Source Credibility, and Opinion Change[END_REF] found that highly credible information (a "Nobel prize winner") caused greater behavioral change than information with medium credibility. [START_REF] Laroche | A Model of Attitude Change in Groups Following A Communication: An Attempt at Formalizing Research Findings[END_REF] tested the findings of various experiments and identified "credibility" as an important variable (p.253). Lilien and Rangaswamy (1997, p.214ff) listed several studies in the field of marketing that stated an effect of advertising expenditures on the sales volume. Several authors found that food advertisements impacted eating behavior. [START_REF] Zimmerman | Association of Television Content Type and Obesity in Children[END_REF] found that "each hour per day of commercial viewing" by children increased their body mass index (BMI) five years later. [START_REF] Viner | Television Viewing in Early Childhood Predicts Adult Body Mass Index[END_REF] made similar findings. [START_REF] Dixon | The Effects of Television Advertisements for Junk Food Versus Nutritious Food in Children's Food Attitudes and Preferences[END_REF] found that information on "healthy food" improved the respective preferences of individuals. [START_REF] Beaudoin | Promoting Healthy Eating and Physical Activity[END_REF] found that positive information about "fruits and vegetables" improved those preferences in a low-income urban population in New Orleans. Boyland and Halford (2013, p.240) concluded that the impact of "information" on "eating behavior" has been "robustly shown." Altogether, the fact that information and credibility of information influences behavior is common knowledge in communications research. Jenőffy-Lochau (1997) discussed the empirical results of communications research in greater detail.

B. Preferences and Economic Decision Theory

Economic decision theory also links information to preferences. Tullock (2005, p.225ff.), e.g., described how influence groups use information for rent-seeking.

Von [START_REF] Von Neumann | The Theory of Games and Economic Behavior[END_REF] developed the concept of "expected utilities." In the basic model, a "state" is a financial outcome that is assigned a "probability." The preferences of the individual are stable. The individual generally acts rationally and decides in favor of the alternative with the highest expected utility.

Bayes' Theorem [START_REF] Savage | The Foundation of Statistics[END_REF] is an endogenous way of depicting new information in an expected utility function. New information may alter a "prior probability" before receiving it to a "posterior probability" after receiving it [START_REF] Hirshleifer | The Analytics of Uncertainty and Information[END_REF]. Key variables are exogenous given conditional probabilities of new information given a state.

Following the discussion of bounded rationality, [START_REF] Kahneman | Prospect Theory: An Analysis of Decision under Risk[END_REF] developed Prospect Theory. They analyzed "paradoxes" of Expected Utility Theory. Prospect Theory works with an "editing phase" and an "evaluation phase." Individuals attach subjective "values" to the alternatives. These values determine the decision the individual makes, not the pure "consequence" (outcome) of the alternative. Kahneman and Tversky measured a "value function" as being concave above a reference point and convex below.

Several similar models were developed, respectively, by [START_REF] Machina | Expected Utility' Analysis Without the Independence Axiom[END_REF], [START_REF] Quiggin | A Theory of Anticipated Utility[END_REF], [START_REF] Chew | A Generalization of the Quasilinear Mean with Applications to the Measurement of Income Inequality and Decision Theory Resolving the Allais Paradox[END_REF], and [START_REF] Tversky | Loss Aversion in Riskless Choice: A Reference Dependent Model[END_REF]. [START_REF] Blavatskyy | Preference Reversals and Probablistic Decisions[END_REF] and [START_REF] Lindsay | The Arguments of Utility: Preference Reversals in Expected Utility of Income Models[END_REF] examined "preference reversals" in those models. [START_REF] Holt | Risk Aversion and Incentive Effects[END_REF] found strong evidence that people are risk-averse even "with low stakes."

Several papers analyzed reference points. [START_REF] Kőszegi | A Model of Reference-Dependent Preferences[END_REF] modeled endogenous reference points. [START_REF] Yaari | The Dual Theory of Choice Under Risk[END_REF] developed Dual Theory. He transformed outcomes of decision problems into an [0,1] interval resulting in different axioms in comparison to Expected Utility Theory. [START_REF] Bikhchandani | A Theory of Fads, Fashion, Custom, and Cultural Change as Information Cascades[END_REF] and [START_REF] Banerjee | A Simple Model of Herd Behavior[END_REF] developed models of information cascades and herd behavior, in which "signals" triggered new "signals. [START_REF] Viscusi | Risky Investment Decisions: How are Individuals Influenced by Their Groups[END_REF] found that "groups" influence behavior even if people have full knowledge of probabilities and payoffs. [START_REF] Kamenica | Bayesian Persuasion[END_REF] and Galperti (2019) also worked with "signals." Galberti (2019) analyzed the chances and challenges of a "persuader" to change people's "worldviews" and concluded (p.996) that several aspects of "persuasion" cannot be captured "in the standard Bayesian framework." He requested the creation of a "theory of persuasive rhetoric. [START_REF] Bergemann | The Design and the Price of Information[END_REF] analyzed the price of information and the impact of "supplemental information" on the buyers' "beliefs."

C. Critics

As early as 1959, Simon described the "bottleneck of the perceptual apparatus" that makes it impossible for the individual to have complete information (Simon, 1959, p.272f). According to him, "alternatives are not given but must be sought."

With mainly analyzing lotteries, Expected Utility Theory, Bayesian learning, Prospect Theory, and Dual Theory deal with relatively rare cases. Machina (2003, p.25) wrote: "Outside the gambling hall most economic decisions…are defined in terms of uncertain events rather than numerical probabilities." [START_REF] Taleb | The Black Swan[END_REF] criticized the pure use of probabilities of states derived from past events. He created the concept of the "Black Swan" as an allegory for unexpected events.

In his best-selling book, [START_REF] Kahneman | Thinking, Fast and Slow[END_REF] named "two modes of thinking." System 1 is "experimental" (fast, emotional). System 2 is "analytic" (slow). Kahneman (2011, p.21) described System 2 as the "conscious, reasoning self that has beliefs, makes choices, and decides what to think about and what to do." System 1 is, on the other hand, described with "effortlessly originating impressions and feelings that are the main sources of the explicit beliefs and deliberate choices of System 2." "Humans" other than "Econs" rely on System 1 which triggers "several errors of intuitive judgement and choice" (Kahneman, 2011, p.416).

D. Ancient Rhetoric

Ancient rhetoric analyzed the impact of a "speech" on the behavior of individuals long before Economic Decision Theory was created.

Around 340 B.C., Aristotle (2004, p.74ff) created the concepts of "logos" ("the speech itself") and "ethos" ("character of the speaker"). He outlined: "It is necessary both to state the subject-matter and to demonstrate it….it is impossible without having stated the matter to prove it or having stated it not to prove it (Aristotle, 2004, p. 245).

Aristotle (2020, p.4) outlined three "modes of persuasion." These are (1) the "character of the speaker;" (2) the "frame of mind" of the audience; and (3) the "speech itself." In order to be "persuasive," a speaker must display "common sense, virtue and goodwill" (Aristotle, 2004, p.141). "Proofs from character are produced whenever the speech is given in such a way as to render the speaker worthy of credence" (Aristotle, 2004, p.74). Aristotle stated that "…one must also look to see if there is some false claim outside the matter. For such things seem an indication that the other claims too are false…" (Aristotle, 2004, p.255). For more information on Aristotle's rhetoric see [START_REF] Rapp | Aristotle's Rhetoric. The Stanford Encyclopedia of Philosophy[END_REF]. Cicero (1967, p. 280f) named three major elements for persuasion: "the proof of our allegations, the winning of our hearers favor, and the rousing of their feelings."

The translation of 1755 (Cicero, 1755, p.164) was closer to the original Latin text: "The whole business of speaking depends upon three points of persuasion; to prove the side we take to be right; to conciliate the favor of our audience, and to direct their passions to every emotion that the nature of the cause requires." ("…ut probemus vera esse, quae defendimus; ut conciliemus eos nobis, qui audiunt; ut animos eorum, ad quemcumque causa postulabit motum …"). Transferring the principle of the lever to the preference model, I state that the preferences swing to the left if the information on the left side is "heavier" and more to the rim of the seesaw. On the other hand, the seesaw swings to the right, the "heavier" the information on the right side is and the more it is positioned on the right rim of the seesaw. This consideration raises the question: What is "heavy" information? Following Aristotle, "heavy" information is clear and credible information. I formalize the Seesaw Model of economic preferences. The model goes back to [START_REF] Jenöffy-Lochau | Medien, Propaganda und Public Choice[END_REF], 2012, 2013[START_REF] Jenöffy-Lochau | The Origin of Preferences, Economic Decision Theory and Yaari[END_REF].

II. The Seesaw Model

I define the following variables.

Definition 1: An information source is an emitter of information.

Definition 2: A signal π carries exactly one piece of information. (3) The more precise the message of the information is, the higher is, ceteris paribus, the impact the information will have on the preferences of the individual. ( 4) The more credible the information is, the more influence this information will have, ceteris paribus, on the preferences of the individual; (5) The more opposing information an individual receives, the weaker is, ceteris paribus, the impact of my information. (6) The more credible the perceived opposing information is, the weaker is, ceteris paribus, the impact of my signals.

III. The Seesaw Model and Existing Economic Models

The Seesaw Model, Bayes' Theory, Prospect Theory, and Bikhchandani's et al.

information cascades recognize the existence of new information. In the Seesaw Model, new information is transferred as a "signal" that provides an "information value" with a "credibility." This goes beyond Bayesianism. New information influences directly the preferences of the individual. Thus, preferences are endogenous what is different to the other models. "Emotions" and "needs" [START_REF] Hausman | Preference, Value, Choice, and Welfare[END_REF] can be integrated into the model as signals. Table 1 summarizes the key differences between the Seesaw Model and other economic decision models. exogenous in order to reduce the complexity of the models ("complete information;" Equation 5).

This explanation seems closer to reality than other attempts to "justify" constant preferences like the theory of experience goods [START_REF] Nelson | Information and Consumer Behavior[END_REF], "meta-preferences" [START_REF] Becker | Habits, Addictions, and Traditions[END_REF], or preferences for characteristics of goods [START_REF] Lancaster | Consumer Demand: A New Approach[END_REF]).

V. Conclusion

The Seesaw Model is designed to explain how "persuasion" works and how

  Summing up Aristotle's and Cicero's insight, I identify three variables for persuasion: (1) the speech itself; (2) the proof of a speech; and (3) whether a speaker reaches attention. This insight and the empirical results of communication research show a path to a radical new model of preferences. As a methodological change, such a model would not work with "states" and "probabilities of states." Instead, such a model would use "ancient," "pre-Savage" variables. The "speech itself" corresponds to the variable information value. The "proof" corresponds to the variable credibility of an information. Whether the speaker reaches attention is the perceptibility of an information. Preferences form only from perceived information. Preferences are the aggregated perceived information received in past periods. E. Yaari's Dual World and the Principle of the Lever I work within the interval Yaari (1987) used for Dual Theory. All preferences are depicted between 0 and 1. I name this the "Yaari interval." I add a fulcrum to the Yaari interval and create so Figure 1. I receive a decision as a seesaw.

FIGURE

  FIGURE 1. PREFERENCES AS A SEESAW 0 1/4 1/2 3/4 1

Figure 1

 1 Figure 1 shows the decision of the individual depending on the preferences PN. If PN > 0.5, the seesaw swings in favor of Alternative 1. If PN < 0.5, the seesaw swings in favor of Alternative 0. At PN = 0.5, the individual is indifferent between both alternatives. Equation 2 defines the information value ωπ of a signal depending on the credibility of a signal.

  choice are made. The Seesaw Model is an algorithm that puts the information an individual has received in the past ("signals") and the preferences of an individual into context without the use of "states." New information directly influences the preferences of the individual. The preferences (P) determine the decision. The model is capable of predicting which preferences of individuals are stable and which preferences can be possibly shifted by information. The Seesaw Model works inYaari's [0,1] interval. The model also works with non-numerical signals that can be attached an information value. With the concept of "complete information," economic theory treats preference accrual exogenous in order to keep models simple. This simplification is often helpful. I show a path of including endogenous preferences into economic theory. Altogether, it is surprising that a model which promotes such a radically new approach to the concept of persuasion and preferences fits into economic theory so seamlessly. The model also offers a great opportunity to reduce doctrinal friction between economics and the other social sciences.

TABLE 1 -

 1 METHODOLOGICAL DIFFERENCES BETWEEN ECONOMIC DECISION MODELSOngoing consuming processes rest upon a greater number of signals received in the past. Consequently, it makes sense to treat those preferences as constant and

		Expected	Bayes'	Prospect	Information	Seesaw
		Utility	Theory	Theory	Cascades	Model
	New information?	No	Yes	Yes	Yes	Yes
	New		New	New
	information	---	probability	probability of	Signal	Signal
	leads to?		of state	state
	New information influences?	---	Probability of states	Probability of states	Probability of states	Preferences
				Constant;
	Preferences	Constant	Constant	value	Constant	Endogenous
				function
	Emotions, needs	Not part of the model	Not part of the model	Partly analyzed ("coding")	Not part of the model	Provide signals
	Decision variable	EU	EU	Value function	EU	P
	The Seesaw Model has several advantages in comparison to other economic
	decision models. (1) it explains the origin of preferences; (2) it reduces complexity;
	(3) it integrates the variable credibility into economic decision theory; (4) it helps
	to integrate emotions and needs into economic decision theory and (5) it increases
	the compatibility with other social sciences.
	IV.	Implications of the Seesaw Model for Constant Preferences
	Equation 5 (below) indicates why the assumption of constant preferences makes
	sense in many economic models. If the individual had received a great number of

Definition 3: An information can be, e.g., a number, an attribute, an emition, a physical need, or a statement. The Seesaw Model makes the following assumptions.

i. There are two alternatives, Alternative 0 and Alternative 1. ii. There are two types k of signals with k ϵ {0;1}. π0 and π1. iii. All information is located in an interval between 0 and 1. iv. A signal of the type k=0, π0, provides the information: "Alternative 0 is better." v. The information value parameter of these signals π0 is ω0. ω0 ∈ [0,0.5]. vi. A signal of the type k=1, π1, provides the information: "Alternative 1 is better."


Dr Marek Jenöffy-Lochau
email: mj@bueroamcarlsplatz.de

The Impact of a Photo on Decisions

Keywords: Persuasion, Information, Uncertainty, Preference Formation. JEL: D81, D82, D83

come

The Impact of a Photo on Decisions

Marek Jenöffy-Lochau

Research of the Impact of a Photo on Decisions

In psychology and communications research, there a several articles that measure the impact of a photo on decisions. Hsee and Rottenstreich (2004, p.26) found an effect for charity donations for pandas. Charity donations were higher if a photo was used showing a panda instead of a panda symbolized by dots. The donations did not differ remarkably between a photo with one panda and a photo with four pandas. If the pandas were symbolized by "dots," donations for four pandas were twice as high as for one panda. [START_REF] Västfjäll | Compassion Fade: Affect and Charity Are Greatest for a Single Child in Need[END_REF] found the design of photos of children in Mali impacting charity contributions. They found that the donations decreased when a photo showed more than one person. [START_REF] Västfjäll | Compassion Fade: Affect and Charity Are Greatest for a Single Child in Need[END_REF] measured donations of 24.9 SEK (Swedish krona) when a photo with one person was shown, 23.4 SEK for a photo with two persons, and 21.3 SEK for a photo with eight persons. [START_REF] Västfjäll | Compassion Fade: Affect and Charity Are Greatest for a Single Child in Need[END_REF] called this effect "compassion fade." Sorotka et al. (2016) analyzed the impact of two different photos on the support for military action. One photo showed a soldier with a child ("peacekeeping photo"), the other photo showed a soldier with a gun ("conflict photo"). The "peacekeeping photo" led to a higher support for the military engagement. Sorotka et al. (2016, p. 574) concluded that "framing implied by photos can have an important impact on support for military engagement." [START_REF] Lagomarsino | Choosing Imagery in Advertising Healthy Food to Childen. Are Cartoons the Most Effective Visual Strategy[END_REF] researched the effects of visual communication on children's healthy food choices. They analyzed children's preferences for apple, broccoli, carrot, fruit, and water. They found that children liked foods "displayed as cartoons the most" but preferred to consume foods "represented by photos" (p.487). They concluded that "it may be more effective to use photos of healthy foods rather than cartoons or animations" (p.487). [START_REF] David | News Concreteness and Visual-Verbal Association. Do News Pictures Narrow the Recall Gap Between Concrete and Abstract News[END_REF] found that "the addition of a representative picture to a news item improved the recall of that item." Concrete news items benefited more from an addition of a photo than abstract news items. [START_REF] Jeon | Stigma activation through dis-identification: cognitive bias triggered by mass media photos of people with obesity[END_REF] investigated the response to obesity comparing a "headless photo" and a photo of a "whole being." They found that the headless photo of obese people "promoted the dehumanizing perception of and a negative attitude towards individuals with obesity" (Jeon et al. 2019, p.498). They recommended "that pictures of headless obese people be discouraged" (Jeon et al. 2019, p.500). [START_REF] Wang | Smile Big or Not? Effects of Smile Intensity on Perceptions of Warmth and Competence[END_REF] researched the impact of "smile intensity" on photos. They compared the reaction to two photos. One photo showed a "slight smile," the other photo showed a "broad smile." They found that broad smile is perceived "warmer" but less competent. They compared the reaction of the photos in low-risk and high-risk decisions. They found that "a broad (…) smile leads to higher purchase intentions in a low-risk context. In a high-risk context, however, a broad (…) smile decreases behavioral intentions via less favorable competence perceptions" (Wang et al. 2017, p.798).

Emotions

Altogether, the investigation of the impact of a photo on behavior seems to touch the field of "emotions." This field is not so much discussed in economic research. There are numerous articles on this field in psychology that cannot be discussed here in total. Västfjäll and Slovic concluded (2013, p. 266) that "emotion is now seen as a prerequisite for good decision making." So, when creating a holistic model of preference formation, "emotions" need to be discussed. What are emotions? LeDoux and Brown (2017) defined that "subcortical circuits … provide nonconscious inputs that coalesce with other kinds of neural signals in the cognitive assembly of conscious emotional experiences."

According to [START_REF] Scherer | What are emotions? And how can they be measured?[END_REF], emotions consist of five components (1) cognitive appraisal, (2) bodily symptoms, (3) action tendencies, (4) expression, and (5) feelings. Aristotle (2004, p. 142 ff) named ten specific emotions to be studied. Positive emotions are "calm, friendship, favor, and pity." Negative emotions are "anger, fear, shame, indignation, envy, and jealousy." Ekman (1992) defined six "basic emotions:" anger, disgust, fear, happiness, sadness, and surprise. Cordaro et al. (2017) found several other emotions such as "awe," "triumph," "relief," "sympathy" etc. [START_REF] Hausman | Preference, Value, Choice, and Welfare[END_REF] concluded that "emotions" may be a source of preferences.

Economic Thoughts on Preferences

Economists have a different approach of analyzing decision-making. The decision process of a human being is described by Kirchgässner (2008, p. 12) as it follows: "[T]he individual assesses the various alternatives at his disposal, he weighs up the pros and cons, the costs and benefits of the alternatives against each other and finally chooses that (those) alternative(s) which come(s) closest to his preferences or which promise(s) to bring about the maximum net benefit."

The key factor for the decision of an individual is in many cases a so called "expected utility." The expected utility is derived from an outcome of an alternative and the probability that the outcome occurs. [START_REF] Savage | The Foundation of Statistics[END_REF] defined an outcome as a "state." How can a photo have an impact on a decision in this world? A photo can either have an impact on the state or an impact on the probability of this state. But how would this work, once both variables, the outcome and the probability of state, are mainly numerical, a photo, however, is mainly non-numerical?

In his best-selling book, [START_REF] Kahneman | Thinking, Fast and Slow[END_REF] outlined "two modes of thinking" that he called "systems." "System 1" is "experimental" (fast, emotional) thinking. "System 2" is "analytic" (slow) thinking. Kahneman (2011, p. 21) described System 2 as the "conscious, reasoning self that has beliefs, makes choices, and decides what to think about and what to do." System 1 is, on the other hand, described with "effortlessly originating impressions and feelings that are the main sources of the explicit beliefs and deliberate choices of System 2." "Humans" rely on System 1 which triggers "several errors of intuitive judgement and choice" (Kahneman 2001, p. 416).

A photo might have a place in Kahneman's System 1 that depicts emotions. Insofar Kahneman's approach helps to surpass the focus on "gambling hall" [START_REF] Machina | States of the World and the State of Decision Theory[END_REF] events. It opens up for measuring "emotional influence" that Hausman (2012, p. 118) identified as one of four sources of preferences. It opens up to analyze non-numerical information as a source of decisions. [START_REF] Galperti | Persuasion: The Art of Changing Worldviews[END_REF] requested economists to establish a general theory of "how decision makers change worldviews". He asked for a "theory of persuasive rhetoric" going "beyond Bayesianism". Such an approach would require to process non-numerical information. Kahneman (2011, p. 202) outlined the process of an experimenter changing people's minds: "Choosing a topic on which minds are not completely made up, (…) the experimenter measures people's attitudes. Next, the participants see or hear a persuasive pro or con message. Then the experimenter measures people's attitudes again; they usually are closer to the [more] persuasive message…"

4. The Experiments -The Impact of Non-numerical Signals on Decisions I conducted experiments at Humboldt-University of Berlin. The participants, mainly students of business administration, were exposed to four information signals. Additionally, the participants were exposed to non-numerical information, two photos. I provided first 181 (2019), and then 184 students (2020) of Humboldt University of Berlin with different information. All students received four signals about a description of fictitious movies. These movies were called "The Grandfather I never wanted," "The Mystery of the Oaktree," "Zeppelin Jr," and "Aberystwyth." The content of the movies was described in one sentence.

The Grandfather I Never Wanted (π1): A cool Jewish guy from California finds out that his grandfather was fathered during WW2 with Hitler's genetic material. A shock with dramatic consequences. The Mystery of the Oaktree (π2): A ruthless investment banker from New York City comes to Germany in order to "restructure" a company that means create bonuses for himself. An old jinx destroys him. Zeppelin jr (π3): A crooked executor of a will has a wealthy grandfather incapacitated in order to steal his fortune from his underage grandson. Aberystwyth (π4): A fraudulent director of a famous fashion brand tries to destroy his company from inside. A private investigator narrowly escapes him.

The participants received a Questionnaire 3 containing the above description of the movies. They were asked to rank the movies from "1" (most interesting) to "4" least interesting.

A Questionnaire 3a of the experiments showed photos of potential actors playing in the movie. Both photos had a similar size. In Experiment 1 (2019), the participants were divided in two random groups. Group 1 received the description of the four movies with no photo. Group 2 received the two photos additionally.

The students ranked the movies from "1" (most interesting) to "4" least interesting. In Experiment 2 (2020), all participants received the additional photos a few minutes after they had ranked the movies, and they were asked to rank the movies again.

Results of Experiment 1 (2019)

Table 1 shows the rankings of the movies by the participants. "The Grandfather I Never Wanted" received, e.g., 37 top ranking in the group with no photos (Group 1) and also 37 top rankings in the group that received the additional photos (Group 2). "Aberystwyth" had 24 top ranking with no photos and only 16 top ranking with the photo handed.

I now attach points to the ranking. A top ranking receives five points. A second place receives three points. A third place receives one point and a last place doesn't receive any point. 1 shows an impact of the photos on the interest of the students in the respective movie. "Aberystwyth" sank from 24 top rankings to only 16 top rankings ending up with only 23.7% of the total points interest instead of 29.2% before. Apparently, the photo of Pamela Reif reduced the interest in "Aberystwyth." On the other hand, the photo of Elyas M'Barek increased the interest in "The Mystery of the Oaktree" from 23.1% to 24.9% of the points. Overall, an impact of the "emotional signal" photo was measurable. The photo changed the ranking of the movies from A > D > B > C to A > B > D > C.

Results of Experiment 2 (2020)

Experiment 2.A shows the ranking of the participants with no photos handed. Experiment 2.B shows the results with the two photos ( I measured an impact of the photo on the interest of the participants in the movie. "Aberystwyth" sank from 49 top rankings to only 32 top rankings ending up with only 21.1% of the total points instead of 28.5% before. Again, the photo of Pamela Reif apparently reduced the interest in "Aberystwyth." On the other hand, the photo of Elyas M'Barek increased the interest in "The Mystery of the Oaktree" from 23.5% to 26.6% of the points. Overall, an impact of the non-numerical signal was measurable. The photo changed the ranking of the movies from A > D > B > C to A > B > D > C as it did in Experiment 1.

In Experiment 1, the chi-square statistic for a 2 x 2 contingency table was 6.79. The p-value was .079115. Both variables (film/photo) were significant at p < .1. In Experiment 2, the chisquare statistic for a 2 x 2 contingency table was 73.60. The p-value was .000001. Both variables were also significant dependent at p < .01. The results stood with the Yates correction.

A Bayesian Analysis of the Results

How would Bayesian economics explain the results empirically measured? A posterior probability of the movie "The Mystery of the Oaktree" must have increased. The question is what preferences are involved? Do preferences for the movie "The Mystery of the Oaktree" in particular exist? Or, do the participants have preferences for "a movie worth to watch"? Are there preferences for "being entertained?" Bayes would assume, e.g., constant preferences for "a movie worth to watch." The movie "The Mystery of the Oaktree" is worth to watch at the prior probability is p(OAK). The posterior probability p(OAK|M'B) is the probability of "The Mystery of the Oaktree" worth to watch given the information Elyas M'Barek plays in that movie. It is

𝑝(𝑂𝐴𝐾|𝑀 𝐵) = 𝑝(𝑀 𝐵|𝑂𝐴𝐾) p(M B) * 𝑝(𝑂𝐴𝐾) (1)
We can measure the prior probability and the posterior probability, and so evaluate the impact of the photo on the probabilities. If the probability that Elyas M'Barek plays in "The Mystery of The Oaktree" (𝑝(M B)) is exogenously given, we can determine 𝑝(𝑀 𝐵|𝑂𝐴𝐾) from the data. Bayes observes a changed posterior probability. Bayes' focus, however, is not to explain why the probability has changed. The calculation gets more complicated with multiple observations. If you want to market "The Mystery of the Oaktree," working with the factor ( | ) ( )

doesn't make it easy to depict the exact effects of your communication.

4.4. Extracting the Impact of the Photos I will use the measured numbers in order to go beyond Bayesians. I regard the decision process as a seesaw. Applying the seesaw works in three steps. First, I define the preferences and information signals involved. Second, I transform the data into a [0,1] interval. Such an interval used [START_REF] Yaari | The Dual Theory of Choice Under Risk[END_REF] for his Dual Theory. Third, I determine information values of the received information.

In both experiments, there are two relevant alternatives and two types of information signals. I define: Alternative 0 is "The Mystery of the Oaktree." Alternative 1 is "Aberystwyth." The preference space stretches from 0 to 1. At 0, there are strong preferences for "The Mystery of the Oaktree." At 1, there are strong preferences for "Aberystwyth." Figure 1 shows the seesaw of this decision process.

Figure 1: Preferences for the Two Movies Information signal type 𝜋 is "The Mystery of the Oaktree is more interesting." The information value (𝜔 ) of information signals supporting this alternative are smaller than .5 (𝜔 < .5). Signal type 𝜋 is "Aberystwyth is more interesting.". The information value (𝜔 ) of information signals supporting this alternative are bigger than .5 (𝜔 > .5). The fulcrum of the seesaw is at .5. There, the participants are indifferent between both alternatives. Information on the left side is a "pro." The heavier the "pro," the more the seesaw leans to the left. Information on the right side is a "con." The heavier the "con," the more the seesaw leans to the right. If the information received would push the seesaw heavily towards "Aberystwyth," this would mean the information value of this information is 1. Conversely, information heavily supporting "The Mystery of the Oaktree" had the information value 0. The strictest outcome of the experiment would be that "Aberystwyth" finished at place 1 for all participants and "The Mystery of the Oaktree" at fourth place for all participants. Then, "Aberystwyth" had 100% of the points. PN

0 1/4 1/2 3/4 1 P N
The Mystery of the Oaktree Aberystwyth would be 1. All ω would be 1. The strictest outcome favoring "The Mystery of the Oaktree would be all participants having it on place 1. Then, PN would be 0. All ω would be 1. What did I measure?

Experiment 1: I analyze the movies "The Mystery of the Oaktree" and "Aberystwyth." Without the photos, both movies received 426 points. Among that, "Aberystwyth" received 55.9% of this share. "The Mystery of the Oaktree" received 44.1% of this share. With the photos, both movies received together 357 points. Among that, "Aberystwyth" received 48.7% of the points. Summing up, the photos shifted the decision of the participants. Non-numerical information triggered a change in the decision.

The information value of the photos

In order to measure an impact of the photos and use it for future predictions, I extract an information value of the photos. The information value measures the average impact of the photos on the decision among the participants.

In order to do so, I determine an average information value of the texts and the photos, once I measured both signals together. The average information value of the texts is 𝜔 . The average information value of the photos is 𝜔 . I work with the following assumptions:

 The participants didn't have any information about the movies prior to the experiments. I ensure this with working with fictitious movies.  The information signals 𝜔 and 𝜔 regarding "The Grandfather I Never Wanted" and "Zeppelin jr" did not affect the preferences for "The Mystery of the Oaktree," and "Aberystwyth." Thus, this information is neglected for reducing the complexity. In Experiment 1, the average information value of the two photos was at .415 moving the preferences towards "The Mystery of the Oaktree." In Experiment 2 the average information value of the photos was at .158. The results of both experiments were similar. The two photos

The Impact of a Photo on Decsions information value is always the average information value of the respective target group. It is a only approximation of the information value of the whole population.

Conclusion

I exposed students of Humboldt University of Berlin to different information signals. They had to rank how interesting the content of four fictitious movies appeared to them. I conducted two experiments. At Experiment 1, one group received and additional information about two actors starring at one of the movies each. A Experiment 2, all participants received the movies after the already had answer the questionnaire in order to answer it a second time. I found that the photos decisively changed the behavior of the participants. One of the movies fell down in ranking, another rose. I did a non-Bayesian analysis of the results. I identified an aggregated information value of the photos. With this variable, it is possible to predict the impact of future communication on the behavior of consumers. This approach is a first step toward an economic theory persuasive rhetoric. This reduces the complexity of the model decisively and makes it easier to use the results of the research

  Elyas M'Barek; Photo: Deutsche Bahn AG Pamela Reif, Photo: Pamela Reif The first photo (π5) showed Elyas M'Barek, one of Germany's biggest movie stars. The photo was attached to the movie "The Mystery of the Oaktree." The other photo (π6) showed Pamela Reif, an Instagram personality rather known for fitness videos than as an actress.



  Both photos have the same impact. I determine the average information values of the texts 𝜔 as the initial preferences 𝑃 . The average information values of the photos 𝜔 depend on the change between the initial preferences 𝑃 and the posterior preferences 𝑃 .

Table 1 :

 1 Table 1 shows how many points the movies received and what percentage this is of the total points. Ranking of the Movies With, and Without the Additional Signals in Experiment 1

	Movie	Group No.1 No.2 No.3 No.4 Points %
	The Grandfather I Never Wanted	1	37	16	18	19	251 30.9
		2	37	18	16	10	255 34.7
	The Mystery of the Oaktree	1	17	27	22	25	188 23.1
		2	19	20	28	15	183 24.9
	Zeppelin jr	1	11	16	33	29	136 16.7
		2	10	17	21	35	122 16.6
	Aberystwyth	1	24	34	16	16	238 29.2
		2	16	26	16	23	174 23.7

Table 2 :

 2 Table 2). The Ranking of the Movies in Experiment 2

	Movie	Experiment No.1 No.2 No.3 No.4 Points %
	The Grandfather I Never Wanted	2.A	76	32	23	50	499 30.3
		2.B	78	31	26	34	509 33.9
	The Mystery of the Oaktree	2.A	40	43	59	40	388 23.5
		2.B	37	56	46	28	399 26.6
	Zeppelin jr	2.A	19	47	56	61	292 17.7
		2.B	20	43	48	53	277 18.4
	Aberystwyth	2.A	49	60	45	29	470 28.5
		2.B	32	37	47	51	218 21.1

Table 3 :

 3 The Shift of the Decision by the Photos. Experiment 1 Experiment 2: Without the photos, both movies received together 858 of the points. Among that, "Aberystwyth" received 54.8% of this share. "The Mystery of the Oaktree" received 45.2% of this share. With the photos, both movies received together 617 points. Among that, "Aberystwyth" received 35.3% of the points. "The Mystery of the Oaktree" received 64.7% of the points. I measured 𝑃 = .548 with no photos, and 𝑃 = .353 with the photos.

	"The Mystery of the Oaktree" received 51.3% of the points. I measured 𝑃	= .559 with no
	photos, and 𝑃	= .487 with photos.
		Movie	Group No.1 No.2 No.3 No.4 Points %
	The Mystery of the Oaktree	1	17	27	22	25	188 44.1
			2	19	20	28	15	183 51.3
		Aberystwyth	1	24	34	16	16	238 55.9
			2	16	26	16	23	174 48.7
		Total	1					426
			2					357
		Movie	Group No.1 No.2 No.3 No.4 Points %
	The Mystery of the Oaktree 2.A	40	43	59	40	388 45.2
			2.B	37	56	46	28	399 64.7
		Aberystwyth	2.A	49	60	45	29	470 54.8
			2.B	32	37	47	51	218 35.3
		Total	2.A					858
			2.B					617

Table 4 :

 4 Table 3: The Shift of the Decision by the Photos. Experiment 2

Table 5

 5 shows the preferences measured in the Yaari interval.

		Signals P
	Experiment 1
	No Photo	2	.559
	Photo	4	.487
	Experiment 2
	No Photo	2	.548
	Photo	4	.353
	Table 5: Preferences Measured

Table 6 :

 6 Table 3 shows the aggregated information values measured in the experiments. Average Information Values Measured in the Experiments

		Signals P 𝜔	𝜔
	Experiment 1
	No Photo	2	.559 .559	--
	Photo	4	.487 .559	.415
	Experiment 2
	No Photo	2	.548 .548	--
	Photo	4	.353 .548	.158

The Impact of a Photo on Decsions changed the behavior of the participants. The Seesaw Model can depict the impact of the photos on the preferences of the individuals. The impact of the photos was stronger in Experiment 2.

Predictions about the Impact of Photos on Decisions

I measured an average information value of the photos of .158 in Experiment 2. Its impact came more from a declining interest in "Aberystwyth" than in an increasing interest in "The Mystery of the Oaktree." Aberystwyth lost over half of its points after the exposure of the participants to the photos. That is surprising because Pamela Reif would be generally regarded an attractive woman with 8.2 million followers on Instagram (2022). With the determination of an information value it is possible to predict the impact of a on the preferences. Here, the producer will probably not face stable preferences, if the movie is a new production. There might be stable preferences of the individuals whether they want to go to the cinema in general. Relatively stable preferences might exist also for sequels or remakes. In 2019, three out of four movies with the greatest US box office (calendar grosses) were sequels ("Avengers: Endgame," "Toy Story 4," "Frozen II").

In order to influence the preferences of the individual, we must take into account several important variables.

 Will the individuals perceive my signals?

 How many signals will I be able to transfer?  Will the individuals receive opposing signals from another party?

In the movie business, there will be a second sort of signals that appear after people had watched the respective movie. People will start talking about how they liked the movie. These signals are possibly stronger than the signals transmitted by the producer because they come from people's "friends" or "acquaintances" who they trust. So, these signals have a higher credibility than advertisement signals. Signals may go "viral." The photo of Elyas M'Barek as the main actor also has a high credibility. People trust M'Barek because he is so successful that they either just want to watch him or trust him that he would only sign for a thrilling screenplay.

Critics

The population of the study provided stable results. The population of the study was approximately twice as big as Kahneman and Tversky's (1979) when they created Prospect Theory and also created stable results. I tested other distributions of points (4/3/2/1), (5/3/2/0). They provided similar results. I chose the distribution (5/3/1/0) because it seemed most reasonable for the topic of choosing a movie. The measured information values depend on the participants. Different participants could lead to different information values. The average


Dr Marek Jenöffy
email: mj@bueroamcarlsplatz.de

Can the Seesaw Model Depict the Certainty Effect?

Keywords: Information, Uncertainty, Preferences, Communication, Preference Formation, Endogenous JEL: D81, D82, D83

HAL is

Economic Theory and Its Paradoxes

Economic decision theory links information to preferences. Generally, most theories use a concept of "states" and "probability of states" in order to model a decision-making process.

Von [START_REF] Von Neumann | The Theory of Games and Economic Behavior[END_REF] developed a concept of "expected utilities." A "state" is a financial outcome that is assigned a probability. With stable preferences, the rational, riskneutral individual decides in favor of the alternative with the highest expected utility.

Bayes' Theorem [START_REF] Savage | The Foundation of Statistics[END_REF] assumes new information having an impact on the probabilities. Information may alter a "prior probability" before receiving it to a "posterior probability" after receiving it. Key variables are exogenous conditional probabilities of new information given a state. Several subsequent studies found that individuals followed Baysian patterns (DeAngelo and Charness, 2009;[START_REF] Sloan | Deterring Domestic Violence: Do Criminal Sanctions Reduce Repeat Offenses[END_REF]. Other studies focusing on ambiguity didn't find this pattern [START_REF] Poinas | Updating Beliefs with Imperfect Signals: Experimental Evidence[END_REF]Roussillon, 2012, and[START_REF] Baillon | Aggregating Imprecise or Conflicting Beliefs: An Experimental Investigation Using Modern Ambiguity Theories[END_REF][START_REF] Baillon | Aggregating Imprecise or Conflicting Beliefs: An Experimental Investigation Using Modern Ambiguity Theories[END_REF]. [START_REF] Kamenica | Bayesian Persuasion[END_REF] and Galberti (2019) both worked on "Baysian persuasion." Galberti (2019, p.996) concluded that a reluctance to change someone's "worldviews" cannot be captured in the "standard Bayesian framework." He requested a "theory of persuasive rhetoric." [START_REF] Kahneman | Prospect Theory: An Analysis of Decision under Risk[END_REF] analyzed so-called "paradoxes" of Expected Utility Theory. They found a "certainty effect." People weigh prospects more favorably if they are certain in comparison to those that are merely probable. They also found a "reflection effect." People are risk-averse with gains and risk loving when it comes to losses. [START_REF] Holt | Risk Aversion and Incentive Effects[END_REF] found strong evidence that people are risk-averse even "with low stakes." Adam (2018) found "qualified support" for the reflection effect over "money outcomes" and "strong support" over "health outcomes." Bouchouicha and Vicider (2017) found the tendency of "people to be risk seeking for small outcomes" and to display "risk-aversion" as stakes increase.

Based on their findings, [START_REF] Kahneman | Prospect Theory: An Analysis of Decision under Risk[END_REF] developed Prospect Theory. In an "editing phase," individuals attach subjective "values" to alternatives. In an "evaluation phase," people decide in favor of an alternative on grounds of these values. Kahneman and Tversky measured a concave value function above a reference point and a convex one below a reference point. Kőszegi and Rabin (2006) modeled endogenous reference points. [START_REF] Yaari | The Dual Theory of Choice Under Risk[END_REF] developed Dual Theory transforming outcomes of decision problems into an [0,1] interval resulting in different axioms in comparison to Expected Utility Theory. [START_REF] Bikhchandani | A Theory of Fads, Fashion, Custom, and Cultural Change as Information Cascades[END_REF] and [START_REF] Banerjee | A Simple Model of Herd Behavior[END_REF] developed models where information triggers new information itself ("information cascades," "herd behavior"). [START_REF] Bergemann | The Design and the Price of Information[END_REF] analyzed the price of information and the capability of this good to influence the buyers' "beliefs."

The Seesaw Model

Jenöffy-Lochau (1997,2012,2013,2014,2019) proposed a different decision-making approach. The model neither works with "states," nor with "probabilities of states." The model depicts the preferences of an individual based on an information value of signals and the credibility of these signals. Preferences are the aggregated information received in past periods. The model is based on ancient rhetoric and on the empirical results of communication theory. It explains the origin of preferences that traditional economics does not explain. The definitions of the model are outlined in [START_REF] Jenöffy-Lochau | How to Shape Preferences[END_REF]. The Seesaw Model makes the following assumptions.

(1)

There are two alternatives, Alternative 0 and Alternative 1. (2)

There are two types k of signals with k ϵ {0;1}. π0 and π1. (3)

All information is located in an interval between 0 and 1. (4)

A signal of the type k=0, π0, provides the information: "Alternative 0 is better." (5)

The information value parameter of these signals π0 is ω0. ω0 ∈ [0,0.5]. (6)

A signal of the type k=1, π1, provides the information: "Alternative 1 is better." (7)

The information value parameter of the signals π1 is ω1. ω1

∈ [0.5,1]. (8)
The credibility γ0 of π0 is -1 ≤ γ0 ≤ 0. Perfectly credible signals π0 have γ0=-1. ( 9)

The credibility γ1 for π1: 0 ≤ γ ≤ 1. Perfectly credible signals π1 have γ1=1. (10) Overall, it is -1 ≤ γk ≤ 1.

Transformation of Lottery Outcomes Into the Yaari Interval

Many economic models deal with lotteries. Lotteries generally work with outcomes Xj. There are generally few restrictions on these outcomes. The Seesaw Model, as developed above, works in the [0,1] interval ("Yaari interval") of preferences (Equation 1). Dual Theory by [START_REF] Yaari | The Dual Theory of Choice Under Risk[END_REF] also works with this method. In order to scale the outcomes into the Yaari interval, I make the following assumptions.

(1) Xjϵ{1,…,n} is the j-th outcome of a decision problem. Xj ∈ M with M ⊆ R ˄ |𝑀|˂∞.

(2) Xmax is the maximum outcome of a decision problem. Xmax :

= |max({𝑋 , … , 𝑋 }|. It is Xmax ϵ R + . (3) It is n ϵ N.
(4) pj is the probability of state of the j-th outcome of the decision problem. pj{1,…,n} ∈ [0,1].

(5) ξ is the reference point. It determines whether an outcome Xj is regarded a "win" or a "lose." It is ξ ϵ R. ( 6) It is 𝑓 : 𝑅 𝑥 [0,1] → {0,1} . It determines whether an outcome is a "win" or a "lose."

(7) It is 𝑓 : 𝑅 𝑥 [0,1] → [-1,1]. 𝐼𝑡 determines the sign of the credibility. (8) It is 𝑓 : 𝑅 𝑥 [0,1] → [0,1]. 𝐼𝑡 determines the information value.
The transformation of the Xj into the Yaari interval is processed in three steps.

3.1.The Type of the Signal ("Win" or "Lose") Whether an outcome is a "win" or a "lose" is defined with respect to a reference point ξ. This determines of what type k the signal is (π0 or π1). An outcome ".001" can be "lose" if all other outcomes are, e.g., "1." If ".001" is the maximum outcome, it may be "win." An outcome may be "loose" if it is below a safe outcome for another alternative. I assume

𝑓 : 𝑘(𝑋 , 𝑋 , 𝜉) = ⎩ ⎪ ⎨ ⎪ ⎧ 𝑘 = 0 ("win") 𝑖𝑓 |X | X > ξ 𝑘 = 1 ("lose") 𝑖𝑓 |X | X ≤ ξ (2)
If k=1, the signal favors the other alternative. If there is no other description, it is ξ = 0. ) Between 0 and ξ = 0.05

After the outcomes Xj are transformed, the preference function (Equation 1) is used in order to determine the preferences PN of the individual.

4. The Experiment I will test several decision problems. I conducted the experiment at Humboldt University of Berlin. 181 students received a questionnaire where they could pick between different prospects concerning the certainty effect and the reflection effect. I wanted to find out whether a model of endogenous preferences depicts these paradoxes of Prospect Theory better than Expected Utility Theory. I compared my results with the results of [START_REF] Kahneman | Prospect Theory: An Analysis of Decision under Risk[END_REF] 5. The Results for the Certainty Effect Prospects [START_REF] Kahneman | Prospect Theory: An Analysis of Decision under Risk[END_REF] empirically found a pattern that they called the "certainty effect." They found that people place greater weight on outcomes that are certain than on outcomes that are merely probable. What does the Seesaw Model predict in those cases that Prospect Theory describes as "paradoxes?" Can the Seesaw Model solve these paradoxes? I want to lower the expectations. As noted by Yaari (1987, p.96): "Roughly speaking, we find each theory resolving "paradoxes" in the other theory."

The results of the experiments and shown in Table 1. Column 1 names the authors of the experiment, Column 2 lists the names of the prospects. shows the prospect Expected Utility Theory predicts. Column 14 shows the prospect the Seesaw Model predicts. For simplicity, I am using the notation used by [START_REF] Kahneman | Prospect Theory: An Analysis of Decision under Risk[END_REF]. For how to get the result of column 14 see the next chapter. I found that the Seesaw Model predicts the certainty effect quite well other than Expected Utility Theory. For Prospects KT3 [START_REF] Kahneman | Prospect Theory: An Analysis of Decision under Risk[END_REF], Jen 1, and Yaari 1, the Seesaw Model predicts the certainty effect. I varied Prospect Jen1 to Jen2 with 444 more in outcome for XA and surpassing 3,000 in XB. In spite of this the individuals still chose "B." as the Seesaw Model predicted. For Prospects Jen5, Jen 6, Jen7 and Jen8, the Seesaw Model predicts the empirical results other than Expected Utility Theory. This is also the case for Kahneman and Tversky's Prospect KT5. For Jen9, both decision models predict the empirically measured outcome. For KT11, and KT14, Expected Utility Theory is indifferent, the Seesaw Model predicts the empirical measured outcome. This is also the case for Lindsay's prospect.

Explicitly Explaining the Results of Column 14

How do I get the results depicted in Column 14? The Seesaw Model works with outcomes provided by signals and credibility shown in Table 1. The individual receives three signals that provide the outcomes XA1, XA2, and XB1. These signals are attached a credibility. The Seesaw Model works in four steps.

 f1: First, I determine whether an outcome is a "win" or a "lose" (Equation 2).  f2: Second, I determine the γj (Equation 3).  f3: Third, I transform the outcomes into the Yaari interval (Equation 4).  Fourth, I apply the Seesaw Model (Equation 1).

According to Equation 9, the Seesaw Model predicts "B" as long as XB1 > 2,400 for KT3/Jen1. Expected Utility Theory predicts "B" for 𝑋 > 𝑋 * 𝑝 = 3,200. The Seesaw Model switches quicker to the "safer" Alternative "B."

Depicting the General Pattern

Equation has another interesting implication. As long as XB1 is above a reference point ξ, and p1 > 0.5, the Seesaw Model predicts "B." Figure 5 shows the predictions of Expected Utility Theory and the Seesaw Model for KT3/Jen2. In the area "A" and "B," both decision models choose the respective alternative. Inside the triangle area "AB" in the middle, Expected Utility Theory switches to the less safe Alternative "A" while the Seesaw Model still picks the "safer" Alternative "B." Risk aversion is at a certain level inherent in the Seesaw Model algorithm. For very small XB1, the individual might regard these outcomes as losses. So, the XB1 would be below a reference point ξ. These prospects lie within an area that is also marked with "A." Both decision models pick "A" there. The Prospects KT3, Jen1, Jen2, and Jen5-9, are located within the triangle "AB." In all cases, Expected Utility Theory would choose "A." The Seesaw Model predicts expects "B" as empirically measured. Even for Prospect Jen8 with EUA=1,240 decisively higher that EUB=700, 63% of the individuals preferred "B." To compare Jen6 and Jen7 is interesting.

Although B provides 28.6% less outcome for Jen9, only 4% of the individuals switch from "B" to "A." The certainty effect seems to be a strong pattern of human behavior. Prospects Jen3, and Jen4 hint of another potential paradox. Although the expected utilities EUA are higher for Jen4, the individual chose "A" for Jen4, and "B" for Jen3.

Conclusion

The Signal-Preference Model (Seesaw Model) is designed to explain "persuasion" as well as the origin of preferences. When testing the model on lotteries, several interesting outcomes can be seen. First, the Seesaw Model delivers the same results Expected Utility Theory does for symmetric choices with two alternatives and two outcomes each. Second, the Seesaw Model is similar to Bayesian learning but is more conservative when it comes to low outcome signals. Third, the Seesaw Model predicts some anomalies of Prospect Theory like the "certainty effect," and the "reflection effect" better than traditional economic theory. Fourth, information processing of signals gives insight into coding and the fanning out of indifference curves. The results were found in own experiments at Humboldt University of Berlin as well as using data of Kahneman and Tversky. Altogether, this model of endogenous preferences not only fits well into economic decision theory. Moreover, it is even capable to solve paradoxes of economic decision theory and gives new insight on the impact of information on human behavior. Surprisingly, this endogenous preference model seamlessly fits into microeconomics and decision theory. As a side effect, the model also reduces doctrinal friction between economics and the other social sciences.

Figure 1

 1 Figure 1 depicts the preferences PN of the individual and the alternative the individual chooses.

Figure 1 :

 1 Figure 1: The Decision of the Individual Depending on PN

3. 2 .

 2 Determining the Credibility Going back to Assumptions 8 and 9, signals of type π0 have a credibility 𝛾 ∈ [-1,0]. Signals of type π1 have a credibility 𝛾 ∈ [0,1]. Traditional Economics assumes that a "state of the world" becomes reality with a probability of x%. The Seesaw Model argues that the outcome Xj is believed to become true with a credibility of x%. For lotteries, I use the probabilities of states (pj) as credibility (γj) of the information of the signals (Equation 3). 𝑓 : 𝛾 (𝑋 , 𝑝 ) = 𝛾 = -𝑝 𝑓𝑜𝑟 𝑠𝑖𝑔𝑛𝑎𝑙𝑠 𝑜𝑓 𝑡𝑦𝑝𝑒 𝜋 𝛾 = 𝑝 𝑓𝑜𝑟 𝑠𝑖𝑔𝑛𝑎𝑙𝑠 𝑜𝑓 𝑡𝑦𝑝𝑒 𝜋 (3) The type k of the signal determines the sign of γj. 3.3. Determining the Information Values I tested several 𝑓 . Equation 4 is a function 𝑓 𝑋 that transforms the outcomes 𝑋 ∈ R into the Yaari interval with 𝜔 ∈ [0,1] and 𝛾 ∈ [0,1]. I preferred Equation 4 over other functions tested because it depicts best the information processing of a signal. 𝑓 : 𝜔 (𝛾 , 𝑋 , 𝑋 , The next three figures show the information values ωj of the signals depending on the credibility of the signals (Figure 2) and on the 𝑋 and Xmax (Figures 3, 4) with ξ = 0.05.

Figure 2 :FigureFigure 4

 24 Figure 2: ωj(γj) according to Equation 4

Figure

  Figure 4: ωj( |𝐗 𝐣 | 𝐗 𝐦𝐚𝐱

  Columns 3-6 list the outcomes (X1, X2) of the prospects and the respective credibility (γ1, γ2). The credibility is the probability of the states with positive signs for signals of type π0 and negative signs for signals of type π1. Column 7 ("D") shows the empirically measured decision. Column 8 contains the maximum outcome (Xmax). Column 9-10 shows the information values of the signals ωj. Column 11 contains the number of signals involved. Column 12 contains the sum of the information values and below the preferences PN of the individual. If PN > 0.5, the individual prefers Alternative 1. If PN < 0.5, the individual prefers Alternative 0. At PN = 0.5 the individual is indifferent. Column 13

  It is 𝛾 = -1 𝑎𝑛𝑑 𝑋 = |𝑋 | and XA1, XB1 > 0 or XA1, XB1 < 0. The Seesaw Model predicts "B" as long as 1

Figure 5 :

 5 Figure 5: Decision of the Individual for KT3 With XB1 > 0 Depending on p1

Table 1 :

 1 Certainty Effect Experiments Show Results According to the Seesaw Model

	1	2	3	4	5	6	7	8	9	10	11	12	13	14
			X1	γ1 X2	γ2	D Xmax	ω1	ω2	N	Σω, PN	EUT	Seesaw Model
	KT3	A 4,000 -.8	0	.2	20	4k	.1	.6	3	1.57	X
		B 3,000	1			80	4k	.88			.525		X
	Jen1	C 4,000 -.8	0	.2	20	4k	.1	.6	3	1.57	X
		D 3,000	1			80	4k	.88			.525		X
	Yaari1 A	.4	.8	0	-.2 20	.4	.10	.60	3 1.575	X
		B	.3	-1			80	.4	.88			.525		X
	Jen2	C 4,444 -.8	0	.2	37 4,444 .1	.6	3	1.53	X
		D 2,912	1			63 4,444 .83			.509		X
	Jen3	C 3,990 -.8	0	.2	31 3,990 .1	.6		1.48	X	X
		D 2,200	1			69 3,990 .78			.492
	Jen4	C 4,000 -.71 0	.29 68	4k	.15	.65	3	1.54	X
		D 2,000	1			32	4k	.75			.513		X
	Jen5	A 4,444 -.2	0	.8	23 4,444 .4	.9	3	1.89	X
		B 777	1			77 4,444 .59			.629		X
	Jen6	A 4,000 -.2	0	.8	19	4k	.40	.90	3	1.89	X
		B 700	1			81	4k	.59			.629		X
	Jen7	A 3,990 -.2	0	.8	23 3,990 .4	.9	3	1.86	X
		B 500	1			77 3,990 .56			.621		X
	Jen8	A 4,000 -.31 0	.69 37	4k	.35	.85	3	1.78	X
		B 700	1			63	4k	.59			.59		X
	KT5	A	3	.5	0	-.5 22	3	.25	.75	3 1.667	X
		B	1	-1			78	3	.67			.556		X
	KT11 A 1,000 -.5	0	-5	16	1k	.25	.75	3	1.75 IND
		B 500	1			84	1k	.75			.583 IND	X
	KT 14 G 5,000 .001 0	-.999	72	5k	0.50 .9995 3 1.499 IND	X
		H	5	-1			28	5k	.000			.4997 IND
	Lindsay A	49	1			X 200	.78		3	1,13		X
		B 200 -.25 0	.75		200	.63	.13		.376

Table 2 :

 2 Solving KT3/Jen1 Using the Seesaw Model I applied the Seesaw Model to the identical prospects KT3 and Jen1 with the Seesaw Model. This works again in four steps. There are three signals. "A" consists of two signals π0 and one signal π1 (XA2 ≤ ξ) whereas "B" consists of one signal π1. Equation 1 leads to PN = 0.525. The Seesaw Model predicts "B." For KT3/Jen1, the Seesaw Model predicts the results Kahneman and Tversky empirically measured (Table2). Kahneman and Tversky measured 80% in favor of "B." I had exactly the same results with my own experiment.

	5.2. A General Pattern
	I analyze a general pattern with a certain alternative "B" compared to an uncertain alternative
	"A" with XA1, XB1 ≠ 0.

Table : 3

 : : A General Pattern to Certainty Effect ProspectsTable 3 contains the preferences of the individuals PN.

Table 1 :

 1 Certainty Effect Experiments Show Results According to the Seesaw Model

	F 911	1	72 3,990 0,386	0,63	X
	Jen17 G 4,000 -.05 0 .95 43	4k	0,475 0,98	1,96	X
	H	90	1	57	4k	0,511 0,80	0,65	X

Jen16 E 3,990 -.4 0 .6 28 3,990 0,700 0,80 1,89 X