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

How to Shape Preferences? Testing a Simple Economic Model of Endogenous Preferences

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

Preferences" is a key concept in economic theory. Economics has not, however, been able to satisfactorily explain the origin of preferences. A changing media system reveals the importance of clarifying the origin of preferences. Preferences originating means endogenous preferences. The Signal-Preference Model (SPM) provides a new algorithm for modeling endogenous preferences using empirical results of communications research. This paper examines how the SPM performs in the framework of economic decision theory. The results of the SPM are compared with Expected Utility Theory, Bayes, and Prospect Theory. Surprisingly, this endogenous preference model seamlessly fits into microeconomics and decision theory.

Approaching the Concept of Preferences

Many of today's prominent online outlets did not exist or were in their infancy two decades ago. These resources have given people unfiltered access to information and have empowered individuals not connected with traditional media outlets to reach the masses for the first time. These online resources have also enabled the gathering of massive amounts of data regarding consumers' preferences. While the Internet has been greatly empowering, it has also fostered the dissemination of false and pernicious information. This convoluted situation makes it important to take an impartial look at the economic concept of preferences.

Economic theory differentiates between preferences and restrictions. Kirchgässner (2008, p.12) described this concept. "In a given situation the restrictions limit the individual's leeway of action.… Within this leeway, there are 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." However, 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]. Jenőffy-Lochau (1997) analyzed the empirical results of communications research.

Empirical Results in Communications Research

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." "Credibility" is an important variable. 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 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 decision-making 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 Persuasive Communication: An Attempt at Formalizing Research Findings[END_REF] tested the findings of various experiments and identified "credibility" as an important variable (p.253), a concept that goes back to Aristotle ("the speaker worthy of credence," Aristotle, 2004, p.74), and[START_REF] Cicero | De Oratore I[END_REF]. 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.

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. Many theories use the concepts of "states" and "probability of states. [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. New information may alter this 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. Key variables are exogenous given 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 Re-arrests for Drinking and Driving[END_REF][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, andBaillon, Cabantous andWakker, 2012). [START_REF] Kahneman | Prospect Theory: An Analysis of Decision under Risk[END_REF] developed Prospect Theory. This theory analyzes "paradoxes" of Expected Utility Theory. It works with two phases -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. There are several competing similar models 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] Kahneman | Advances in Prospect Theory: Cumulative Representation of Uncertainty[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. Kahneman and Tversky measured a "value function" as being concave above a reference point and convex below. Several subsequent papers analyzed reference points. [START_REF] Kőszegi | A Model of Reference-Dependent Preferences[END_REF] modeled endogenous reference points. [START_REF] Park | Loss Aversion and Consumption Plan with Stochastic Reference Points[END_REF] modeled the influence of reference points on consumption. [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" trigger new "signals. [START_REF] Viscusi | Risky Investment Decisions: How are Individuals Influenced by Their Groups[END_REF] measured that "groups" influence behavior even if people have full knowledge of probabilities and payoffs.

Useful Critics

None of the above economic models focuses on the origin of preferences. The "information cascades" and "herd behavior" models come the closest to modeling the origin of preferences. Within an unchallenged framework of "states" and "probabilities of states," the models analyzed the endogenous creation of information as "signals" that influences the behavior of individuals.

In advocating for a holistic model of preference formation, Hausman (2012, p.118) identified four sources of preferences: (1) means-end reasoning, (2) attribute-based valuation, (3) emotional influence, and (4) physiological needs. He attributed the first two sources to economics and the latter two to psychology. According to Hausman, "means-end reasoning," which is basically economic decision theory as described above, is only one of four possible sources of preferences. A holistic model would be capable of integrating other sources of preference formation than just lottery outcomes.

Insofar as it analyzes lotteries, Expected Utility Theory, Bayesian learning, Prospect Theory and Dual Theory deal with relatively rare cases that do not occur so frequently in "real life." [START_REF] Machina | States of the World and the State of Decision Theory[END_REF] 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.

The Signal-Preference Model of Endogenous Preferences (SPM)

These critiques plus the intention of explaining the origin of preferences, and the numerous empirical results of communications research led to a radical new model of preferences. The Signal-Preference Model (SPM) creates a broader model of preference formation. The SPM 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]. There are two basic methodological changes. First, the model does not work with "states." Second, the model does not work with "probabilities of states." Instead, it uses the information value of a "signal" and the credibility of the signal as the variables of preference formation. Thus, preferences are the aggregated information received in past periods.

2.1.Definitions

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. Definition 3: A signal is perceived or not perceived. If the signal is perceived, it transmits the information from the information source to an individual.

Even back around 80 B.C., Cicero mentioned the "rousing of [the listeners'] feelings" to have an impact with a speech ("…ut animos eorum, ad quemqumque causa postulabit motum…," Cicero, 1967, p.280f).

Definition 4: A signal may have a type k. Signals of the same type carry similar information. Definition 5: A perceived signal has two characteristics: an information value and credibility.

This definition corresponds to Aristotle's concepts of "logos" ("the speech itself" = information value) and "ethos" ("character of the speaker" = credibility) outlined around 340 B.C. (Aristotle 2004, p.74ff). In his Book 3, Aristotle refers to "two parts of the speech" naming them "narration" and "proof" (Aristotle, 2004, p. 245). Credibility also corresponds to one of Cicero's major elements of the impact a speech has ("…ut probemus vera esse, quae defendimus…," Cicero, 1967, p. 280.) Definition 6: The information value ω of a signal describes the type of information the signal transmits.

Definition 7: The credibility γ of a signal describes whether the information value of the signal is believed to be true by the individual who receives the signal. Definition 8: An alternative is the choice an individual has.

Definition 9: The preferences of the individual determine which alternative the individual chooses.

2.2.Assumptions

The SPM 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}. π 0 and π 1 . (3) All information is located in an interval between 0 and 1. (4)

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

The information value parameter of these signals

π 0 is ω 0 . ω 0 ∈ [0,0.5]. (6)
A signal of the type k=1, π 1, provides the information: "Alternative 1 is better." (7) The information value parameter of the signals

π 1 is ω 1 . ω 1 ∈ [0.5,1]. (8) The credibility γ 0 of π 0 is -1 ≤ γ 0 ≤ 0. Perfectly credible signals π 0 have γ 0 =-1. (9)
The credibility γ 1 for π research that even noncredible informatio preferences from one alternative to the other signal π j+1 . The number of signals that swing calculated in Appendix 2.

1 : 0 ≤ γ ≤ 1. Perfectly credible signals π 1 have γ 1 =1. (10) Overall, it is -1 ≤ γ j ≤ 1.

2.6.Implications of the SPM For

Equation 4 indicates why the assumption of constant preferences makes sense in many economic models. If the individual had → ∞ , preferences tend to be constant (Equation 6mainstream economics implicitly assumes. The number of signals that swings preferences from one alternative to the other is Implications of the SPM For Constant Preferences why the assumption of constant preferences makes sense in many ic models. If the individual had received a great number of signals in the past ( to be constant (Equation 6) using the SPM. This is the case that mainstream economics implicitly assumes. It is Conversely, if the preferences rest on few o even no signals they are unstable (Equation 7). A new information π j+1 providing a new information value ω j+1 then has a great impact on the preferences. It forms the preferences. lim → ,

, , , = , 7

Ongoing consuming processes rest upon a greater number of signals received in the past. Consequently, it makes sense to treat preferences as constant and exogenous in order to reduce the complexity of the models ("complete information;" Equation 6).

Summing up the Differences Between the SPM and Existing Economic Models

Table 1 summarizes the key differences between the SPM and other economic decision models.

Expected The above economic models normally deal with lotteries. Lotteries generally work with outcomes X j . There are generally few restrictions on these outcomes. The SPM, 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 providing a core idea towards a comprehensive model of endogenous preferences. In order to scale the outcomes into the Yaari interval, I make the following assumptions.

(1) X jϵ{1,…,n} is the j-th outcome of a decision problem.

X j ∈ M with M ⊆ R ˄ |5|˂∞.
(2) X max is the maximum outcome of a decision problem. 4) p j is the probability of state of the j-th outcome of the decision problem. p j{1,…,n$ ∈ [0,1]. ( 5) ξ is the reference point. It determines whether an outcome X j is regarded a "win" or a "lose." It is ξ ϵ R. ( 6) It is < : > ? @0,1A → {0,1$ . It determines whether an outcome is a "win" or a "lose." (7) It is < B : > ? @0,1A → @-1,1A. CD determines the sign of the credibility. (8) It is < E : > ? @0,1A → @0,1A. CD determines the information value.

X max := |max("8 , … , 8 : $|. It is X max ϵ R + . (3) It is n ϵ N. (
The transformation of the X j into the Yaari interval is processed in three steps.

3.1.1. The Type of the Signal ("Win" or "Lose") Whether an outcome is a "win" or a "lose" is defined with respect to the reference point ξ. This determines of what type k the signal is (π 0 or π 1 ). 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 "lose" if it is below a safe outcome for another alternative. I assume

< : F 8 , 8 GHI , J = K L M L N F = 0 "win" Q< |X S | X TUV > ξ F = 1 "lose" Q< |X S | X TUV ≤ ξ \ 8 If |^_| ^`ab
≤ ξ, the signal favors the other alternative. If there is no other description, it is ξ = 0.

Determining the Credibility

Going back to Assumptions 8 and 9 in 2.2., signals of type π 0 have a credibility ∈ [-1,0]. Signals of type π 1 have a credibility ∈ [0,1]. Traditional Economics assumes that a "state of the world" becomes reality with a probability of x%. The SPM argues that the outcome X j is believed to become true with a credibility of x%. In Hausman's cases of "means-end reasoning," which means lotteries, I use the probabilities of states (p j ) as credibility (γ j ) of the information of the signals (Equation 9). The type k of the signal (π 0 or π 1 ) determines the sign of γ j. The next two figures show the information values ω j of the signals depending on the credibility of the signals (Figure 4) and on the p8 p and X max (Figure 5) with ξ = 0.05.

Applying Traditional Expected Utility Theory

According to Expected Utility Theory (EUT), an individual picks the alternative with the highest expected utility. The expected utility for a risk neutral individual is the sum of the outcomes multiplied with the probabilities of the states [START_REF] Varian | Microeconomic Analysis[END_REF][START_REF] Varian | Intermediate Microeconomics[END_REF]; wx y ∑ c * 8 . The individual decides in favor of the alternative with the highest expected utility. In this paper, I generally assume risk neutral individuals. Table 2 shows a simple case with two alternatives "A" and "B" and two states "I" and "II." For simplicity, I will use the notation used by [START_REF] Kahneman | Prospect Theory: An Analysis of Decision under Risk[END_REF].

Applying the SPM

The SPM works with outcomes provided by signals and credibility. The individual receives four signals that provide the outcomes X A1 , X A2 , X B1 , and X B2 . These signals are attached a credibility. The model works in four steps, as outlined above.

• f 1 : First, I determine whether an outcome is a "win" or a "lose" (Equation 8).

• f 2 : Second, I determine the γ j (Equation 9).

• f 3 : Third, I transform the outcomes into the Yaari interval (Equation 10).

• Fourth, I apply the SPM (Equation 1).

When analyzing Table 2, there are four signals. All outcomes X j are greater than a reference point ξ = 0. Thus, the signals "A" favor Alternative 0 (π 0 ). The signals "B" favor Alternative 1 (π 1 ). Table 3 shows the and the P N .

Prospect Signal Type Outcome X j Credibility γ j Information value ω j A π 0 X A1 = 150 -p 1 = -0.6 The sum of the information values is 2,02. The preferences of the individual are P N = 0.505. According to the SPM the individual has preferences for "B." For X j > ξ and X j ≠ 0, the individual decides in favor of "B" as long as (calculation in Appendix 2).

ω A1 = 0.5 - } ' * |~• ' | B * ~€•' = 0.35 A π 0 X A2 = 300 -p 2 = -0.4 ω A2 = 0.5 - } ƒ * |~• ƒ | B * ~€•' = 0.30 B π 1 X B1 = 200 p 1 = 0.6 ω B1 = 0.5 + } ' * |~" ' | B * ~€•' = 0.70 B π 1 X B2 = 250 p 2 =0.4 ω B2 = 0.5 + } ƒ * |~" ƒ | B * ~€•' = 0.67 N = 4 X max = 300 P N = ∑ Σω j = 2 + } ' * |~" ' |… |~• ' | , } ƒ * |~" ƒ |… |~• ƒ | B * ~€•'
8 {B > 8 |B } ' * ~•' … ~"' } ƒ (12)
Equation 11 equals Equation 12. Then, both decision models --Expected Utility Theory and the SPM --deliver the same results. This is surprising because both models use approaches that are totally different at first glance. In these cases, Expected Utility Theory comes out as a special case of the SPM with the additional assumption that the credibility of the signals sums up to 1 implying that there are no contradictory signals.

Subjective Probabilities

Bayes' Theorem is an endogenous way of depicting new information in an expected utility function ("subjective probabilities"). Bayesian learning differs between "prior probabilities" and "posterior probabilities." The "prior probability" is the probability of one or more particular states before the new signal is received. The "posterior probability" is the probability of the same states after receiving new information (Hirshleifer and Riley 1992, pp.170ff).

Applying Bayes'

I modify the Prospect "B" above (Table 2) by adding new information about a third state with a probability p 3 with an outcome of 0. "A" remains unchanged.

c {E > 1 - 8 | * c | + 8 |B * c |B 8 {B * c |B + 8 { * c | 13
Below, I will compare the results of Bayes with the results of the SPM.

Applying the SPM

I now model the case shown in Table 4 using the SPM. Again, this works in four steps as outlined above.

• f 1 : Is the outcome a "win" or a "loss?" (Equation 8);

• f 2 : The determination of the signs (Equation 9);

• f 3 : The transformation into the Yaari interval (Equation 10);

• Determining the preferences (Equation 1);

One signal is below the reference point ξ. What does that mean? The individual receives a signal concerning "B" (Alternative 1). This signal does not say how good "B" is but rather how bad it is. I provides an outcome of 0. Thus, it is a signal that favors Alternative 0 ("A"). X B3 = 0 says "Rather pick "A"." So, this signal is of type π 0 with γ B3 < 0.

Column 4 (Table 5) shows the credibility of the signals. Column 5 shows the information value parameters ω j of the signals. It is Σω j = 2.47 and P N = 0.494. The individual has preferences for Alternative 0 ("A"). For X A1 , X A2 , X B1 , X B2 ≠ 0, the SPM chooses "A" as long as (calculation in Appendix 2)

c {E > c | * 8 { -8 | + c |B * 8 {B -8 |B 8 GHI 14 Prospect k Outcome X j γ j Information value ω j A π 0 X A1 =150 -p A1 = -0.6 ω A1 = 0.5 - } •' * |~• ' | B * ~€•' = 0.35 A π 0 X A2 = 300 -p A2 = -0.4 ω A2 = 0.5 - } •ƒ * |~• ƒ | B * ~€•' = 0.30 B π 1 X B1 = 200 p A1 = 0.6 ω B1 = 0.5 + } •' * |~" ' | B * ~€•' = 0.70 B π 1 X B2 =250 p A2 = 0.4 ω B2 = 0.5 + } •ƒ * |~" ƒ | B * ~€•' = 0.67 B π 0 X B3 = 0 -p B3 = -0.1 ω B3 = 0.5 - } " † B = 0.45 N = 5 X max = 300 P N = ∑ Σω j = 2.5 + } •' * |~" ' |… |~• ' | , } •ƒ * |~" ƒ |… |~• ƒ | B * ~€•' - } " † B
Table 5: Solving the Modified Decision Problem by Applying the SPM Equation 13 and Equation 14 are not identical. This is because the SPM does not change the initial γ j when there is a new signal. The SPM does not require that the γ j add up to 1. SPM can process contradictory signals. The SPM switches to "A" at p B3 > 0.033 (Equation 14), Bayes only at p B3 > 0.05 (Equation 13). The SPM is more "conservative" when it comes to signals with X j ≤ ξ.

Testing the SPM on the Paradoxes of Prospect Theory

The results of the algorithm of the SPM are promising. What does the SPM predict in those cases that Prospect Theory describes as "paradoxes?" Can the SPM 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."

4.1. The Certainty Effect Paradox [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.

4.1.1. Kahneman and Tversky's Findings [START_REF] Kahneman | Prospect Theory: An Analysis of Decision under Risk[END_REF] compared two prospects (Table 6).

Author Prospect X 1 p 1 X 2 p 2 Decision K-T 3 A 4,000 -0.8 0 .2 20% B 3,000 1 80%

Table 6: The SPM Depicting the Certainty Effect Paradox "B" provides a sure win of 3,000 whereas "A" has two different outcomes X A0 = 4,000 at p A0 = 0.8 and X A2 = 0 at p A2 = 0.2. Although the expected utility of "A" is EU A = 3,200 > EU B = 3,000, Kahneman and Tversky found that 80% of the individuals decided in favor of prospect "B." The 20% probability of "losing" apparently prevents people from choosing "A."

4.1.2. Testing the SPM I tested Case K-T 3 with the SPM. This works again in four steps. There are three signals.

"A" consists of two signals π 0 and one signal π 1 (X A2 ≤ ξ) whereas "B" consists of one signal π 1 . "A" provides ω A1 = 0.1 and ω A2 = 0.6; and "B" provides ω B1 = 0.875 (Table 7). Equation 1leads to P N = 0.525. The SPM predicts "B." For K-T 1, the SPM predicts the results Kahneman and Tversky empirically measured solving the certainty effect paradox. I analyze a general pattern with a certain alternative "B" compared to an uncertain alternative "A" with X A1 , X B1 ≠ 0. Table 8 contains the preferences of the individuals 0, the SPM predicts "B" as long as

X 1 γ 1 X 2 γ 2 X max ω 1 ω 2 A X A1 -p 1 0 1-p 1 |8 | | - c * |8 | | 2 * 8 GHI + .5 1 -c 2 + .5 B X B1 1 |8 | | |8 { | 2 * 8 GHI + .5 N=3 = 2 3 - c 6 + |8 { | -c * |8 | | 6 * 8 GHI = 2 - c 1 2 + |8 { | -|8 | | * c 2 * 8 GHI
8 { >
Expected Utility Theory predicts "B" for Expected Utility Theory and the SPM for 1," both decision models choose the respective alternative. middle, Expected Utility Theory switches to Alternative 0 while the SPM still picks the "safer" Alternative 1. Risk aversion is at a certain leve I analyze a general pattern with a certain alternative "B" compared to an uncertain alternative 0. Table 8 contains the preferences of the individuals P as long as (calculation in Appendix 2)

> 8 | * 2 * c & 1 15
Expected Utility Theory predicts "B" for 8 { > 8 | * c . Figure 7 shows the predictions of Expected Utility Theory and the SPM for K-T 3. In the areas "Alternative 0" and "Alternative 1," both decision models choose the respective alternative. Inside the "triangle area" in the middle, Expected Utility Theory switches to Alternative 0 while the SPM still picks the isk aversion is at a certain level inherent in the SPM algorithm.

sion of the Individual for K-T 3 With X B1 > 0 Depending on p contains more prospects solved by the SPM. Column 1 of Table 8 Column 9 ("D") shows the empirically measured decision. Column 15 contains the sum of the information values and below this the preferences Column 16 shows the prospect the SPM predicts. Overall, the SPM predicts the pretty well. I analyze a general pattern with a certain alternative "B" compared to an uncertain alternative P N . For X A1 , X B1 ≠

X 2 γ 2 X 3 γ 3 D X max ω 1 ω 2 2,
shows the predictions of In the areas "Alternative 0" and "Alternative Inside the "triangle area" in the middle, Expected Utility Theory switches to Alternative 0 while the SPM still picks the l inherent in the SPM algorithm.

> 0 Depending on p 1 of Table 8 names the authors Column 9 ("D") shows the empirically measured decision. Column 15 contains the sum of the information values and below this the preferences P N of the Overall, the SPM predicts the

The Reflection Effect

The Reflection effect is another paradox of Expected Utility Theory that Kahn [START_REF] Kahneman | Prospect Theory: An Analysis of Decision under Risk[END_REF] empirically measured. gains and risk-loving regarding prospects involving losses.

Kahneman and Tversky's Findings

In K-T 3', Kahneman and Tversky compared "loss" of -3,000. "A" provided X Author K-T 3'

The SPM Capable of Predicting the

How does the SPM perform? According to > 2,400 for K-T 3 and D as long as X SPM predicts here the reflection effect for X D1 < 0 depending on p 1 (Equation both decision models choose the respective alternative. In the "Triangle chooses "C" while EUT decides i

Figure 8: Decision of the Individual for K Table 18 in Appendix 1 shows shows three decision problems (K isolation effect paradox. Altogether, the SPM is again capable Expected Utility Theory. This is a side effect of the SPM when expla is another paradox of Expected Utility Theory that Kahn (1979) empirically measured. Individuals are risk-averse as to prospects involving loving regarding prospects involving losses.

Kahneman and Tversky's Findings neman and Tversky compared "C" and "D" (Table 10). " provided X 1 = -4,000 at p 1 = 0.8 and X 2 = 0 at p 2 = 0.2. 15, the SPM predicts "B" as long as X and D as long as X D1 > -2,400. Thus, the SPM predicts "B" and "C." The reflection effect paradox. Figure 8 shows the decision of the individual (Equation 15). In the areas "Alternative 0" and "Alternative 1," both decision models choose the respective alternative. In the "Triangle" area chooses "C" while EUT decides in favor of "D." Decision of the Individual for K-T 3' With X D1 < 0 Depending on p Appendix 1 shows more cases when the SPM solves the reflection effect. It also three decision problems (K-T 10, K-T 13, KT 13') where the SPM Altogether, the SPM is again capable of solving several This is a side effect of the SPM when expla , the SPM predicts "B" as long as X B1 Thus, the SPM predicts "B" and "C." The shows the decision of the individual In the areas "Alternative 0" and "Alternative 1," " area, the SPM still < 0 Depending on p 1 more cases when the SPM solves the reflection effect. It also T 13, KT 13') where the SPM solves also the several paradoxes of This is a side effect of the SPM when explaining the origin of 4000 1 EUT SPM preferences and reconciling economics with ancient rhetoric and modern communications research.

Including Coding into the SPM

As outlined above referring to Yaari's quote, every decision model has its own paradoxes.

There are some paradoxes of the SPM. These paradoxes, however, can be fixed by taking into account the information processing of signals.

"Coding" and the use of a "value function" are important parts of Prospect Theory. According to Prospect Theory, the individual uses an "editing phase." He or she applies a "value function" delivering the "true outcome" of a prospect.

The SPM works with signals. A signal might say one thing but actually have a different meaning. This idea goes back at least to Aristotle. He wrote around 340 B.C.: "For when the poet calls old age a reed, he produces understanding and recognition through the generic similarity; for both have lost their flower" (Aristotle 2004, p.235). Rhetoric calls this style "tropes." Burke (1945, p.503) names "irony, metaphor, metonymy, and synecdoche" the main tropes.

I use the term "Codes" to identify circumstances when a signal says one thing but actually means something else. Codes are based on the information processing of signals. They help the SPM work in more cases. So far, I have found three Codes. The three Codes concern lifetime income, symmetric choices, and simplifications.

Lifetime Income / The Allais Paradox

Allais (1953) found inconsistent decisions violating the substitution axiom of the Expected Utility Theory. He compared two prospects. "A" provided are sure outcome of 1,000,000. "B" provided 1,000,000 at 89%, 5,000,000 at 10%, and 0 at 1%. He found that most of the people chose "A" over "B" although the Expected Utility of "B" was higher than of "A." This is called the "Allais-Paradox."

The SPM and "Coding" Allais

I first analyze what the signals actually mean. In 1953, "1,000,000" meant "not having to work." "5,000,000" also meant "not having to work." "0" meant "having to work." This leads to Code 1: If a prospect involves a lifetime income, individuals tend not to differentiate between it and an n-fold of it with n ∈ N.

Testing the SPM on a "Coded" Allais

Then, I apply Code 1 to Allais (Table 11). There are four signals. Three of them promise the individual "not having to work = 0." One signal promises the individual "having to work = 1." Prospect k Sum X j γ A π 0 1,000k 1 ("not having to work") -1 0 B π 1 5,000k 1 ("not having to work") 0.10 0.55 B π 1 1,000k 1 ("not having to work") 0.89 0.945 B π 0 0 0 ("having to work") -0.01 0.495 N = 4 X max = 1 P N = 0.497 ∑ 1.99 Table 11: Applying the SPM to Allais Using Code 1 I again use the four phases of the SPM. First, I determine the types of the signals. Two signals are of type π 0 ("A" is better), two signals favor "B." Second, I determine the signs of the γ j . Signals of type π 0 receive a negative sign in their credibility. Third, I determine the information value of the signals using Equation 10. The sum of the information values of the four signals is 1.99 (Column 6). Fourth, I determine the preferences P N using Equation 1. P N = 0.497 < 0.5. The individual has preferences for "A", as Allais empirically found. With applying Code 1, the SPM solves the Allais Paradox.

Symmetric Choices

When analyzing more prospects, I found an interesting pattern that I call Code 2: If a prospect offers two symmetric choices ("win"/ "lose") with a zero outcome, and the credibility is similar of both prospects, this is regarded one signal by the SPM. People disregard components of a decision problem. Table 12 shows the decision problem K-T 4. In K-T 4, Expected Utility Theory chooses "E" (EU E = 800 > 750 = EU F ). [START_REF] Kahneman | Prospect Theory: An Analysis of Decision under Risk[END_REF] found that 65% of people chose "E." K-T 4 is easy to calculate in one's head.

When applying the SPM to K-T 4 (Table 14), the use of Code 2 is needed. K-T 4 has only two signals, not four. Why is this? Apparently, the individual concentrates on deciding between 4,000 at 0.2 and 3,000 at 0,25. The credibility (0.2 vs. 0.25) is so close together that the individual apparently frames the decision problem ("4,000/0") as one signal. With P N = 0.497, the SPM chooses "E" as empirically measured. I develop a general pattern for Code 2 prospects (Table 14).

Prospect

X 1 γ 1 X 2 γ 2 X max ω j A X A1 -p 1 0 1-p 1 |8 { | - c * |8 | | 2 * 8 GHI + .5 B X B1 p 2 0 -(1-p 2 ) |8 { | c B * |8 { | 2 * 8 GHI + .5 N=2 = 1 2 + c B * |8 { | -c * |8 | | 4 * 8 GHI ∑ = 1+ } ƒ * |~" ' | … } ' * |~• ' | B * ~€ •'
Table 14: The SPM and Symmetric Choices with Zero Outcomes (X B1 > X A1 )

Applying the SPM with Code 2, the individual prefers Alternative 1 ("B") for X A1 , X B1 ≠ 0 as long as (calculation see Appendix 2)

8 { > c * 8 | c B 16
Both models, the SPM using Code 2 and Expected Utility Theory, deliver in the same results. It seems interesting whether the use of Code 2 requires the ability to calculate an Expected Utility in one's head. Table 18 (Appendix 1) contains more prospects solved by the SPM using Code 2.

Simplifications

Appendix 1 also shows more prospects that deal with small differences in probabilities. Individuals do not seem to differentiate between "0.001" and "0.002" (Prospect K-T 8).

Kahneman and Tversky described this as "simplification." The analysis of these cases with the SPM starts again with the question "What is the actual information of the signals the individual received?" This leads to Code 3: If a prospect contains signals with small differences in credibility, individuals differentiate between credibility at a level they can process. [START_REF] Machina | Choice Under Uncertainty: Problems Solved and Unsolved[END_REF] showed that this is part of a general empirical pattern. Indifference curves "fan out." This fanning out can be explained by difficulties of the individual in processing small probabilities or high gains. Neither Expected Utility Theory nor the SPM depict the fanning out of the indifference curves completely. Analyzing the information processing of signals helps to understand why "fanning out" occurs.

6. The SPM Depicting "Emotions"

In the previous sections, I analyzed decision problems ("lotteries") from what [START_REF] Hausman | Preference, Value, Choice, and Welfare[END_REF] called "means-end reasoning." The SPM is also capable of processing other sources of the origin of preferences. [START_REF] Hausman | Preference, Value, Choice, and Welfare[END_REF] identified means-end reasoning, attribute-based valuation, emotional influence, and physiological needs.

Definition 10: [START_REF] Hausman | Preference, Value, Choice, and Welfare[END_REF] four sources of preferences are called categories of signals.

Definition 11: Preference formation may include all four sources of preferences.

Definition 12: The formation process of preferences that involves different categories of signals is called signal mixture.

6.1. A Decision Problem Without "Emotions"

I will now solve a decision problem that involves "signal mixture." Let's consider a hypothetical Hollywood producer who is trying to determine which script to make into a movie. Script "A" produces an outcome of X A1 = 200 at p A1 = 0.98 and X A2 = 0 at p A2 = 0.02. Script "B" produces a sure win of X B1 = 100. Expected Utility Theory clearly favors "A" (EU A = 196 > 100 = EU B ). I analyze the three signals (Table 15) using the SPM.

Prospect Signal Type 15: The SPM, Emotional Signals and Signal Mixture One signal is of type π 0 (X A1 = 200) that favors A (ω A1 = 0.010). Both other signals (X A2 = 0; X B0 = 100) are of type π 1 and favor "B." According to Equation 1, P N = 0.420. The producer prefers script "A" but decides to postpone making a decision until the next day because of an important celebrity-filled party this night.

Adding "Emotions" to the Decision Problem

Continuing with our hypothetical, the producer meets Channing Tatum who she adores for many years at the party. They talk about projects, including the scripts the producer is considering. Mr. Tatum says he strongly likes "B" better but provides no logical explanation for his preference. How does the decisional problem look like the next day? This is not an unusual situation in business life. The conversation the producer had with Mr. Tatum leads to an addition signal. This is a signal of type π 1 because it favors "B." It is a strong signal. Thus, ω 4 = 1. This signal swings the preferences to P N = 0.565. The CEO has now prefers "B." 6.3. Rational Behavior in Spite of "Emotions"

The SPM algorithm enables economics to process cases like this that are very close to reality and to integrate them into economic decision theory. Traditional Economic Decision Theory would rule the CEO's behavior irrational. Using the SPM, the behavior becomes rational.

The SPM and the Use of a Utility Function

What is the impact of a model of endogenous preferences on Economic Utility Theory? Does a theory that is based on constant preferences need to be totally rewritten? The answer is no. As outlined above, economic theory deals in many cases with recurrent consumer decisions that are already based on a great number of prior signals. The assumption of constant preferences makes sense in these cases.

7.1. Utility Under Uncertainty -The Use of the SPM What about cases when preferences accrue? Can these cases be integrated into traditional microeconomic theory? The concept which makes this possible has existed in microeconomic textbooks for decades. Varian (1993, p.217) presents a Cobb-Douglas utility function as an example that "might be used to examine choice under uncertainty" (u(c 1 ,c 2 ,π,1-π) = OE OE B … .

This works when consumption comprises two "states" (c 1 , c 2 ) and "probabilities of states" (π, 1-π). This approach can be easily applied using the SPM. In doing so, the utility depends on the P N . I implement the interaction between signals and preferences modeled in the Signal-Preference Model into Varian's utility function (Equation 17).

x ? , ? B , •, = • ? … ? B 17

The reception of signals influences the utility function and the indifference curves of the individual. The preference axioms (Varian 1992, pp.94ff) apply for states of constant information. They might not apply when comparing different states of information. Can this be applied in practice?

Empirical Findings

As outlined above, several studies measured the influence of food advertisements on the calorie intake of children. The studies found with near unanimity that food advertisements increase the calorie intake of children. [START_REF] Halford | Beyond-brand effect of Television (TV) food advertisements / commercials on calorie intake and food choice of 5-7-year-old children[END_REF], e.g., exposed children from five to seven years to different signals. The children were divided in two reference groups. One group was exposed to "food related advertisements." The reference group was exposed to "non food related advertisements." Afterwards, the eating behavior of both groups was measured. [START_REF] Halford | Beyond-brand effect of Television (TV) food advertisements / commercials on calorie intake and food choice of 5-7-year-old children[END_REF] found that the amount of food in kcal eaten in the session with "non-food adverts" is 545 kcal. The other session with "food adverts" shows an amount of 657 kcal.

Reference Both numbers are measured for normal weight children. For overweight and obese children the numbers are 594 kcal ("non-food adverts") and 684 kcal ("food adverts"). The empirical findings of [START_REF] Halford | Beyond-brand effect of Television (TV) food advertisements / commercials on calorie intake and food choice of 5-7-year-old children[END_REF] are depicted in Table 17. [START_REF] Halford | Beyond-brand effect of Television (TV) food advertisements / commercials on calorie intake and food choice of 5-7-year-old children[END_REF] found strong support for their hypothesis that exposure to food advertisements leads to and increased kcal intake of children. This context is in particular strong for "jellies" and "snack-a-jacks" (Appendix 1; Table 20).

Microeconomic Modeling

I model the case prior to the reception of the signal. I assume that the individual consumes two goods, x 1 and x 2 . Good x 1 is "food" and x 2 is "all other goods but food." The amount of calories (K) eaten by the individual is expressed by Equation 18. I standardize the amount of kcal per unit of good x 1 to κ 1 = 55.9 kcal per unit. Good x 2 has κ 2 = 0 kcal per unit.

Κ(x 1 ,x 2 ) = κ 1 x 1 + κ 2 x 2 = 55.9 kcal * x 1 (18)

For simplicity I assume the prices of the goods (p 1 = p 2 = 1). The budget (m = 20) remains constant. Prior to the reception of the signal, the individual consumes 10 units of each good. So, the individual consumes Κ = 559 kcal. After the reception of the signal the individual consumes Κ = 667 kcal that is 12 units of x 1 and 8 units of x 2 (numbers rounded). When assuming the budget is exogenous, why does one group (no food advertisements) prefer the bundle (10,10), the other group (exposed to food advertisements) the bundle (12,8)?

Traditional Economic Explanations

The explanation attempts of traditional economic theory do not seem very convincing. x 1 could be an "experience good" that was identified [START_REF] Nelson | Information and Consumer Behavior[END_REF]. Under this hypothesis, food advertisements unveil the "true" preferences of the individuals. Since increasing calorie intake leads to obesity, it seems questionable that being overweight is the "true preference" of these children.

It could also be argued that the childrens' behavior would be different if there was a strong budget restriction. The success of long time advertising campaigns of companies contradicts this explanation. In Germany, there is a discussion about banning so-called "quengelware." It is merchandise that is positioned close to the registers of grocery stores and is targeted at customers with small children. Children badger ("quengeln") their parents to buy them the merchandise and parents often give-in to keep their children quiet.

Applying Bayesian learning in this case also seems difficult. It assumes that the child knows, in particular, the conditional probabilities of state j when receiving a signal. Moreover, the findings with Bayesian learning are difficult to integrate into traditional microeconomic theory. [START_REF] Lancaster | Consumer Demand: A New Approach[END_REF] theory of preferences for characteristics of goods doesn't seem to help either. The new utility function U 1 cuts the budget restriction at the point U 1 (12;8). This is the optimum decision if P N = 0.4 (rounded). So, [START_REF] Halford | Beyond-brand effect of Television (TV) food advertisements / commercials on calorie intake and food choice of 5-7-year-old children[END_REF] measured in their experiments a point on a new utility function U 1 (Equation 22).

x ? , ? B = ? .Ž * ? B

.‰

21

The key factor of how intensely the utility function reacts to new information is the amount of information that the individual had received in the past. The empirical results imply using the model that the child received four signals prior to the advertisement. There were two signals of the type π 0 "x 1 is better" and two signal of the type π 1 "x 2 is better." These signals created U 0 . The advertisement that [START_REF] Halford | Beyond-brand effect of Television (TV) food advertisements / commercials on calorie intake and food choice of 5-7-year-old children[END_REF] communicated was the fifth signal (x 1 ) shifting U 0 to U 1 .

How To Shape Preferences?

The testing of the SPM shows there is strong evidence that preferences are shaped as predicted by the model.

This brings up the question whether the model can be used in order to figure out how to influence preferences. Before one can shape or alter the preferences of individuals, one must first analyze the existing preferences of the individual.

• How stable are the existing preferences of the individual?

• On how many signals rest the existing signals of the individual?

• How credible were the signals the preferences rest on?

The SPM predicts that the more stable the preferences of the individual are, the more unshakeable those preferences are. Thus, when an individual receives more signals or when the signals an individual receives are very credible, the preferences of the individual become more difficult to change. Preferences that rest on personal experiences of an individual are particularly challenging to alter. Generally, preferences that do not rest on personal experience of an individual can be more easily altered.

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

• Will the individual perceive my signals?

• How many signals will I be able to transfer?

• How credible are my signals?

(1) The more signals the individual perceives, ceteris paribus, the more impact the influencer will have on the preferences of the individual;

(2) The more signals an influencer is able to transfer, the more the more impact, ceteris paribus, the influencer will have on the preferences of the individual;

(3) The more credible the influencer's signals are, ceteris paribus, the more influence those signals will have on the preferences of the individual; (4) In addition, signals that are "emotional" tend to exert greater influence on the preferences of the individual. Concepts, sometimes only buzzwords, like "authenticity," "sustainability," or "attitude towards life" can become important in influencing preferences.

Critique

As the model predicts, it is not so easy to alter existing preferences ("Semmelweis reflex"). This also concerns, indeed, preferences for preference models. It is easier to keep with the old instead of thinking into something new even though the old has flaws. Possible critique of the SPM may concern the procedure of developing a holistic approach, details of the model, or general considerations.

(1) The SPM also can be described as "holistic." It combines elements of economics, communications research, classical rhetoric, and even sales training. It lacks the dogmatic purity of each discipline. However, isn't a "holistic," "sustainable" approach that what everybody is looking for? (2) I can be said, the SPM doesn't contain a mechanism how the individual forgets information. In the model, information is not forgotten but rather only diluted by new information. However, this keeps the model simple, in particular, regarding every individual differs as to how information is forgotten. (3) It might said it is difficult to measure credibility. However, it is every day business in marketing research to measure credibility and develop credible information. (4) The "kink" in Figure 5 around the reference point might be critized. However, this kink helps to solve paradoxes Prospect Theory found. The kink might very well actually depict the behavior of individuals. (5) The function U' in 7.5. is not proven. With more empirical data U' might look different. This is true. However, this does not affect the general possibility to seamlessly integrate endogenous preferences into traditional economics as shown in Chapter 7. (6) It might be questioned whether it is ethical to enable people to influence preferences. The Homo Oeconomicus is totally "rational," of "free will," and unswayable. However, this sight is apparently a mirage as it is the concept of "complete information." Preferences of individuals are formed every day by the media, advertising agencies, politicians, "influencers,", friends etc. This happens anyway and this paper will not change this. If an individual doesn't have "complete information" he or she can at least have the information about how preferences form. The understanding of the accrual of preferences makes the individual more of a Homo Oeconomicus. Economic Theory might be complete when being able to integrate its lacking brick.

Conclusion

The Signal-Preference Model (SPM) is designed to explain the origin of preferences. The SPM 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 model is capable of predicting which preferences of individuals are stable and which preferences can be possibly shifted by information. The SPM works in Yaari's [0,1] interval.

When testing the model on lotteries, several interesting outcomes can be seen. First, the SPM delivers the same results Expected Utility Theory does for symmetric choices. Second, the SPM is similar to Bayesian learning but is more conservative when it comes to low outcome signals. Third, the SPM predicts some anomalies of Prospect Theory like the "reflection effect," and the "certainty effect" better than traditional economic theory. Fourth, information processing of signals gives insight into coding and the fanning out of indifference curves. Fifth, the SPM can also process contradictory signals and "signal mixture," which are everyday cases in business life. Sixth, the SPM can be used to model microeconomic utility functions. Altogether, it is surprising that a model that promotes such a radically new approach to the concept of 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.

Allais, M. (1953). Le comportement de l'homme rationnel devant le risque: critique des postulates et axiomes de l'école Américaine. Econometrica 21(4), 503-546.

Aristotle (2004). The Art of Rhetoric. London: Penguin Books.

12. Appendix 1: Additional Tables

  (11) N is the total number of signals the individual received. N ∈ N 0 . (12) N π0 and N π1 are the numbers of the respective signals the individual received. N π0 ∈ N 0 , N π1 ∈ N 0 . N π0 + N π1 = N. (13) Each signal has a different ̅ for signal π 0 and ̅ for signal (14) The preferences of an individual P (15) If the P N < 0.5, the individual chooses (16) If the P N > 0.5, the individual chooses (17) If P N = 0.5, the individual is indifferent between the alternatives. The whole spectrum of Aristotle's interval" as a reference to Yaari's Dual Theory. 2.3.The Model An individual receives signals. The signals carry information values signal on the preferences of the individual? an individual.

Figure 1

 1 Figure 1 shows the decision of the individual depending on the preferences the individual decides in favor of Alternative 1. If Alternative 0. At P N = 0.5, the individual is indifferent between both alternatives.

Figure 1 : 1 Figure 1 Figure 2

 1112 Figure 1: The Decision of the Individual Depending on

Figure 2 :Figure 2

 22 Figure 2: Stability of Preferences Depending on N Received Prio Individual I has stable preferences. T receiving new signals of the type influences the preferences of the individual still has preferences for Alternative 0 but the preferences are weaker than before.

4 Figure 2 Figure 3 :

 423 Figure 2 shows how simple the model is. It portrays the impact of 18 new signals of type π 1 of the individuals react to the

  preferences are impacted more strongly if the new signals are again how simple the model is. An individual has preferences that rest on signals in the past with 13 completely credible signals π 0 and five completely credible = 0.277 prior to the reception of the new signals. preferences for Alternative 0. The individual receives 18 new signals of type how the preferences of the individual react depends on the credibility of the n : Stability of Preferences Depending on the Credibility γ of New Signals γ=1) move the preferences to P N+18 = 0.64. Nine signals swing the s to Alternative 1. Moderately credible signals (γ=0.75) move the preferences to = 0.58. Eleven signals swing the preferences to Alternative 1. Neutral N+18 = 0.51. 17 signals swing the preferences to Alternative 1. signals (γ=0.25) move the preferences to P N+18 = 0.45 of the individual remain in favor of Alternative 0. As so with totally noncredible move to P N+18 = 0.39. The individual still has preferences for signals do not swing preferences, because ω j (γ j=0 preferences. Th model depicts the findings of communications research that even noncredible information has an impact on individuals. preferences from one alternative to the other, however, requires at least one credible new

  preferences are impacted more strongly if the new signals are more credible. again how simple the model is. An individual has preferences that rest on a N completely credible . The individual has type π 1 . The intensity depends on the credibility of the new signals. of New Signals π 1 = 0.64. Nine signals swing the =0.75) move the preferences to Neutral signals (γ=0.50) = 0.51. 17 signals swing the preferences to Alternative 1. 45. The preferences noncredible signals 39. The individual still has preferences for (γ j=0 ) = 0.5 (Equation of communications n has an impact on individuals. Changing at least one credible new one alternative to the other is why the assumption of constant preferences makes sense in many signals in the past (

  < B : 8 , c = d = -c <ef gQhijkg e< Dlcm n = c <ef gQhijkg e< Dlcm n \ 9

Figure 4 :)

 4 Figure4: ω j (γ j ) according to Equation10Figures5 and 6show the inconsistencies in the function of ω j (|^_| ^`ab) for various that occurs

  max = 4,000 P N =0.525 Σω j = 1.575

Figure 7 :

 7 Figure 7: Decision of the Individual for

  Applied to Reflection Effect Prospects 3,200 < EU D = -3,000. % of the individuals chose "C."

  max = 4,000 P N =0.497 ("E") Σω j = 0.994

7. 5 .

 5 Applying the SPM I analyze[START_REF] Halford | Beyond-brand effect of Television (TV) food advertisements / commercials on calorie intake and food choice of 5-7-year-old children[END_REF] empirical findings using the SPM. I identify two alternatives. Alternative 0 is "high fat, high sugar food is good." Alternative 1 is "high fat, high sugar food is bad."[START_REF] Halford | Beyond-brand effect of Television (TV) food advertisements / commercials on calorie intake and food choice of 5-7-year-old children[END_REF] exposed one reference group to a signal of type π 0 with an information value ω 0 = 0. This signal influences the existing preferences of the individuals P N . I assume that the initial utility function of the individuals is Equation19. With the given budget restriction, it is U max = U 0 (10,10) = 10. The preferences of the individual are P N = 0.5. of the signals, the preferences of the individual changed according to Equation 5 with ω j+1 = 0 as the information value of the new signal.

  for two Alternatives and Two Signals (Equation11)c {E > & c | * -|8 { | |8 | | c |B * -|8 {B | |8 |B | 8 GHI For all X A1 ,X A2, X B1 , X B2 ≠ 0, it is c {E > c | * 8 { -8 | + c |B * 8 {B -

Table 1 :

 1 can be integrated into the model as signals. The SPM is based on the empirical results of Communications Research over the past decades.3. Testing the ModelProposing such a radical new model raises the question of how such a model performs in the framework of the existing economic models. Does it put economics upside down? Is it merely a bothersome impurity in economic theory? Or, does the model fit into economic theory? This would be surprising because all attempts to implement a theory of endogenous preferences didn't make it into mainstream economics in the past. If a model of endogenous preferences could compete with traditional economic decision theory it would be breaking news.Therefore, this paper analyzes how the new algorithm performs as a decision model in comparison to Expected Utility Theory, Bayesian learning, and Prospect Theory. It additionally shows how to work with contradictory signals and "signal mixture."3.1. Transformation of Lottery Outcomes into the Yaari Interval

		Utility	Bayes' Theory	Prospect Theory	Information Cascades	SPM
	New information?	No	Yes	Yes	Yes	Yes
	New information leads to?	---	New proba-bility of state	New probabi-lity of state	Signal	Signal
	New information influences?	---	Probability of states	Probability of states	Probability of states	Preferences
	Preferences	Constant	Constant	Constant; value function	Constant	Endogenous
	Emotions, needs	Not part of the model	Not part of the model	Partly analy-zed ("coding")	Not part of the model	Provide signals

Methodological Differences between Economic Decision Models

The SPM, Bayes' Theory, Prospect Theory, and Bikhchandani's et al. information cascades recognize the existence of new information. In the SPM, new information is transferred as a "signal" that provides an "information value" with a "credibility" not a new "probability of state." New information influences directly the preferences of the individual. Thus, preferences are endogenous what is different to the other models. "Emotions" and "needs"

Table 2 :

 2 Expected Utility of Two Alternatives A and B

	The Expected Utility of Alternative "A" is 210. The Expected Utility of "B" is 220. The risk
	neutral individual decides in favor of "B." As a general pattern, the individual chooses "B" as
	long as	8 {B > 8 |B	c * 8 | -8 { c B	11

Table 3 :

 3 Solving the Decision Problem with Applying the SPM

Table 4 :

 4 Probabilities of States Influenced by New Information (Bayes)The new "state" III moves EU B from 220 to 198. The risk neutral individual decides now in favor of "A" according to Bayes. As a general pattern, the individual decides in favor of "A" using Bayes if (calculations see Appendix 2)

Table 7 :

 7 Solving Kahnemans and Tversky's Prospect with the SPM

	Prospect

Table 9

 9

		contains more prospects
	of the experiment. Column 9 ("D") shows the empirically measured decision. Column 15
	contains the sum of the information values and below this the preferences
	individual. Column 16 shows
	certainty effect paradox pretty
	Author Prospect	X 1	γ 1
	K-T 1	A	2,5k -.66
		B	2,4k	1
	K-T 5	A	3	.5
		B	1	-1
	Jen 1	A	30	.5
		B	1	1
	Yaari 1	A	.4	.8
		B	.3	-1
	Lindsay	A	49	1
		B	200	-.25

Table 9 :

 9

The SPM Applied to Certainty Effect Prospects In Jen 1, X B1 is a "lose." The SPM chooses

Table 10 :

 10 The SPM Applied to Reflection Effect Prospects Expected Utility Theory would choose Kahneman and Tversky found empirically Individuals are risk loving when it comes to losses.

Table 12 :

 12 The SPM Applied to Symmetric Choice

	Author	Prospect	X 1	p 1	X 2	p 2	EU	Decision	SPM
	K-T 4	E	4,000 0.20	0	0.80	X	65%	X
		F	3,000 0.25	0	0.75		35%

Table 13 :

 13 Solving K-T 4 with the SPM

Table 16 :

 16 Table 16 shows all signals and the information values. The SPM, Emotional Signals and Signal Mixture

	Prospect Signal Type	X j	Credibility Information Value
	A	π 0	200	0.98	0.010
	A	π 1	0	-0.02	0.501
	B	π 1	100	-1	0.750
	Channing	Emotion			1
		N = 4	X max = 200	P N = 0.565	∑ = 2.261

Table 17 :

 17 Kcal Intake Measured by[START_REF] Halford | Beyond-brand effect of Television (TV) food advertisements / commercials on calorie intake and food choice of 5-7-year-old children[END_REF]

	Group	A	B
	Signals Received	Non-Food Advertisements	Food Advertisements
	Kcal Intake after Signals Normal Weight Children	544.7	656.9
	Kcal Intake after Signals Overweight / Obese Children	594.9	683.6
	Kcal Intake All Children	559.0	667.1

Table 18 :

 18 The SPM Solving Kahneman's and Twersky's Remaining Prospects Column 1 names the authors of the experiment, Column 2 lists the names of the prospects. Comlums 3-8 list the outcomes (X 1 , X 2 , X 3 ) of the prospects and the credibility (γ 1 , γ 2 , γ 3 ). The credibility is the probability of the states with positive signs for signals of type π 0 and * > -

	Author Prospect	X 1	γ 1	X 2	γ 2	X 3 γ 3	D X max	ω 1	ω 2	ω 3 N	Σω. P N	SPM
	K-T 2	C	2,500	.33	0	.67			83 2.5k	.335		2 .998	X
	Code2	D	2,400	.34	0	.66			17 2.5k	.663			.499
	K-T 4'	C	-4,000	-.2	0	.8			42	4k	.60		2 1.006
	Code2	D	-3,000	.25	0	-.75			58	4k	.41			.503	X
	K-T 6	C	3	.05					67	3	.475		2 .992	X
	Code2	D	1	.1					33	3	.517			.496
	K-T 7	A	6,000	.45	0	-.55			14	6k	.28	.78	4 2.225
		B	3,000	-.9	0	.1			86	6k	.73	.45		.556	X
	K-T 7'	A	-6,000 -.45	0	.55			92	6k	.73	.23	4 1.775	X
		B	-3,000	.9	0	-.1			8	6k	.28	.55		.444
	K-T 8	C	6,000 .001	0 -.999			73	6k	.4995		2 1.000 IND
	Code2	D	3,000 -.002 0	.998			27	6k	.5005			.500 IND
	K-T 8'	E	-6,000 -.001 0	.999			30	6k	.5005		2 1.000 IND
	Code2	F	-3k	.002	0 -.998			70	6k	.4995			.500 IND
	K-T 10	A	4k	.2	0	-.05	0 -.75		4k	.4	.53	.88 5 2.519
	Isolation effect	B	3k	-.25	0	.75				4k	.59	.13		.504	X
	K-T 11	A	1k	-.5	0	-5			16	1k	.25	.75	3 1.75
	Reflection effect	B	500	1					84	1k	.75			.583	X
	K-T 12	C	-1k	.5	0	-.5			69	1k	.75	.25	3 1.25	X
	Reflection effect	D	-500	1					31	1k	.25			.417
	K-T 13	A	6k	.25	0	-.25	0	-.5 18	6k	.38	.63	.75 6 3.13
	Isolation effect	B	4k	-.25 2k -.25	0	.5 82	6k	.58	.54	.25	.52	X
	K-T 13'	C	-6k	-.25	0	.25	0	.5 70	6k	.63	.38	.25 6 2.88	X
	Isolation effect	D	-4k	.25 -2k -.25	0	-.5 30	6k	.42	.46	.75	.48
	K-T 14	G	5k	.001	0 -.999			72	5k	0.4995 .9995	3 1.499	X
	Reflection effect	H	5	-1					28	5k	.000			.4997
	K-T 14'	I	-5k	-.001 0	.999			17	5k	.5005 .0005	3 1.501
	Reflection effect	J	-5	1					83	5k	1		X	.5003	X

negative signs for signals of type π 1 . Column 9 ("D") shows the empirically measured decision. Column 10 contains the maximum outcome (X max ). Column 11-13 shows the information values of the signals ω j . Column 14 contains the number of signals involved. Column 15 contains the sum of the information values and below the preferences P N of the individual. If P N > 0.5, the individual prefers Alternative 1. If P N < 0.5, the individual prefers Alternative 0. At P N = 0.5 the individual is indifferent. Column 16 shows the prospect the SPM predicts. For K-T 10, K-T 13 and K-T 13', the SPM solves the isolation effect paradox. , < 0.5 * 0.5 * 1 + ̅ + * 0.5 * 1 + ̅ + * * 0.5 * 1 + ̅ + * > 0.5

13.5. A General Pattern for Bayes (Equation 13) A General Pattern for the SPM (Equation 14)


M Di Giacomo

B Ducoudret

P Baret

J-C Deroy

THE TEST BENCH FOR THE POWER AMPLIFIERS OF THE SPIRAL-2 SC LINAC

The high current driver accelerator of the SPIRAL 2 project uses independently phased SC resonators working at 88 MHz. Solid state power amplifiers equipped with circulators are foreseen to drive the cavities with widely ranging conditions of beam loading. These power devices are developed by industrial companies and a test bench has been studied and manufactured to test the prototypes, to commission all the units before their installation on the accelerator and to be used to test repaired modules. Even if designed to be used at 88 MHz, the test bench can be used at higher frequencies too. The poster describes the test bench as well as the results on the first amplifiers bought for the cryomodule power tests.

BEAM LOADING AND POWER REQUIREMENTS

The Spiral 2 driver [START_REF] Junquera | The Spiral2 project, Construction progress and recent developments on the sc linac driver[END_REF] will accelerate ion beams ranging from few tenths of uA to several mA, corresponding to a wide range of beam-loading. A fixed coupler is foreseen for the SC cavities for reliability reasons, with 4.5E5 and 1.2E6 nominal Q loaded factors for the low and high beta families. These values correspond to overall optimal matching conditions at maximum beam loading.

Beam dynamics simulations [START_REF] Jl Biarrotte | Configuration de base di Linac Supraconducteur V2.0, Internal SP2 report[END_REF] at maximum deuteron current give the amount of beam loading of each cavity as shown in Figure 1 . Taking into account feedback margins and losses in the lines and circulators, 10 and 20 kW amplifiers are required for the two families.

These amplifiers have to stand high reflected power. Low intensity beam operation (negligible beam loading) typically requires 25% of the nominal power, as shown in Figure 2 where the amount of power required for the power tests of the cryomodule prototypes at different field levels is plot. This RF power being totally reflected, we chose to use a 10 kW circulator behind the amplifier.

POWER AMPLIFIERS FM MARKET

One of the reasons for which 88 MHz was chosen as the operating frequency for Spiral 2 is the possibility to take profit of the power equipment industrially developed for the FM market.

Solid state amplifiers are more and more used in FM application, offering higher flexibility then tube ones. Nevertheless, 20 kW and CW (continuous wave) operating mode into high mismatched load are not standard applications and both items required some development to be achieved.

Standard devices are air cooled. Water cooling reduces the dimension of the amplifier and increases the life time.

TESTS BENCH

A 20 kW test bench was then developed to study prototypes built by industrial companies and to achieve the experience to define the final requirements for the linac amplifiers. A 50 ohm load in parallel to a quarter wave line equipped with a sliding short acts as variable VSWR device.

Figure 4 : mechanicals details

To be used at 20 kW, the device is manufactured with a 3 1/8" transmission line and air cooled.

A PT 100 temperature sensor monitors the temperature at the short circuit contacts to protect the device. The Tee block is machined in solid copper while the 50 ohm resistor is a standard coaxial load, dimensioned for 25 kW.

The phase shifter is an industrial device from Mega Industries Inc, able to produce a 250° phase rotation at 88 MHz.

The computer control uses a graphic interface developed with LabView and USB, GPIB and compact field point cards interface the motors commands and position indicators, to read temperatures, and to interface the synthesizer and other instrumentation.

Figure 5 shows the whole tests bench with the variable VSWR device in front, the phase shifter behind, the computer control in the background. The 20 kW amplifier and circulator are also visible.

AND 20 KW PROTOTYPES

Our first prototyping efforts during the design study phase concerned 1 kW amplifiers, based on four, 300 watt elementary modules combined together. Each module was equipped with a 500 watt circulator but the amplifier could only sustain 50% of reflected power due to thermal dissipation.

Figure 6: air-cooled 1 kW rack with and without circulators (@ ECRESO)

Other tests on standard 1 kW amplifiers equipped with an external circulator showed that this solution is more flexible and less expensive at 88 MHz. It implies no need to oversize the output stage components and the combiners to sustain high reflected power and it leads to more compact systems.

kW amplifier

Availability of new more powerful MosFets and water cooling gave recently the possibility to have 3 kW compact racks based on the scheme of Figure 7.

The single RF pallet contains two SD2942 push-pull Mosfets, combined by a Wilkinson lumped circuit and able to deliver up to 800 W in class C operation. Four of these pallets are combined by a 4 way, Wilkinson strip-line circuit. The RF pallets and the 4way combiners are water cooled. The rack includes a 300 W preamplifier whose output power is limited to avoid over driving of the final stages.

Two power supplies bias the 4 pallets with independent readings of the four voltages (48V) and currents (<20A). The driver can be biased via any of the two units, that allowing operation, at reduced power, even when one power supply fails. The power supplies are equipped with their own funs, which let the rack be operated stand alone.

Significant mechanical optimisation led to the availability of a 3 kW rack weighting less than 30 kg, which we consider as a weigh goal for easy maintenance.

kW and 20 kW amplifier

Combining four of these racks gives a compact 10 kW amplifier that can be contained in a 650x1000x1900 cabinet. In air hybrid 3dB combiners are used for highest efficiency.

The cabinet also contains a 3 W driver, the control logic, the output directional coupler, the mains switches, the watercooling distribution and a fun for complementary aircooling. Two similar cabinets are combined to produce a 20 kW amplifier. The present 20 kW combiner is oversized and test with a smaller one still have to be performed.

TEST RESULTS

Test bench

The test bench has been used up to 15 kW at maximum VSWR, and up to 20 kW at lower mismatching levels. More tests will be performed as soon as the 20 kW circulator is available. The response of the variable VSWR device fits quite well the expected curve as shown in figure 11

Amplifiers

The 3 kW racks are set to give 2.8 kW and stand 10% of reflected power. Efficiency of the single pallet depends on the working point. Using Vd=48V and Vg=0.8V it is around 78%. Combination of the four stages reduces this value to 74% for the 3 kW rack. The splitters and combiners are balanced at ± 0.1 dB as well as the driver outputs while no special care (unless bias figures) is taken for the 3 kW racks by the moment. Figure 12 shows the maximum and minimum responses of the two sets of racks of the 20kW amplifier; the rack contribution is therefore well balanced at maximum power only. Harmonics are well below 35 dB at the 10 kW output and even less after the 20 kW combiner. Long time tests have been performed on matched and mismatched loads, to monitor the output power stability and overall reliability. Both the 10 and 20 kW amplifiers reach nominal power and grant 1% stability during a 24 hours test. A few troubles on the power supplies and two Mosfet failures append during the first few weeks of tests. The most of these problems arrived while we were searching for the maximum level of reflected power the amplifier could stand at a given phase. This could mean that the rack protections are not reliable at any phase yet. Figure 13 shows the reflected power monitored by each rack at constant (1.5) VSVR vs the position of the phase shifter: the sum of the monitored values is not constant which clearly indicates a measurement problem. Nevertheless more measurements will be done in the next weeks. Figure 13: reflected power on the 4 racks, @ 10 kW output power, VSWR =1.5.

CONCLUSION

The test bench for the amplifiers and other RF power devices of the Spiral 2 SC Linac is ready and let us commission the first three power amplifiers required by the incoming cryomodule power tests.

A compact, water cooled, high efficiency, and easy to maintain 10 kW amplifier which achieved the required parameters have been developed by an industrial company of the FM market Useful experience has been acquired on the critical elements of solid state amplifiers which will help in the preparation of the call for tender for the serial production.

Figure 1 :

 1 Figure 1: Beam loading along the SC linac cavities for a deuteron beam of 5 mA.

Figure 2 :

 2 Figure 2: Power requirements for the power test of the cryomodule prototypes

Figure 3 :

 3 Figure 3: Test bench scheme Figure 3 shows the functional scheme of the tests bench.

Figure 5 :

 5 Figure 5: Test bench installation

Figure 7 :

 7 Figure 7: Schematics of the 3 kW rack.

Figure 8 :

 8 Figure 8: water cooled 3 kW rack Mains presence, temperature threshold, reflected and driving powers, external authorisations are interlocked by a PLC. Pallets parameters, input signal level, output direct and reverse powers, cooling plate temperature are monitored on the front face and available through a RG 485 link with a Jbus protocol.

Figure 9 :

 9 Figure 9: 10 kW cabinet and 6 and 10 kW hybrid combiners.

Figure 10 :

 10 Figure 10: 20 kW combiner

Figure 11

 11 Figure 11: variable VSWR device response (88 MHz)

Figure 12 :

 12 Figure 12: response scatter of the 3 kW racks

Proceedings of SRF2007, Peking Univ., Beijing, China

Proceedings of SRF2007, Peking Univ., Beijing, China

WEP: Poster Session II

ACKNOWLEDGEMENTS

The authors would like to thank, in particular, Y. Merrer of the LPC -Caen Laboratory for mechanical design of the variable VSWR device and P. Toussaint and the Ganil workshop group for its manufacture and assembly, They are also grateful to D. Allal and L. Menager of the Ganil accelerator division RF group for their participation to test bench assembling, and to Ti Ruan of the Synchrotron Soleil for useful discussions on solid state amplifiers.