The effect of the cognitive load on decision making under risk : does a higher cognitive load create the fourfold pattern of risk attitudes?

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The effect of the cognitive load on

decision making under risk:

Does a higher cognitive load create the fourfold pattern

of risk attitudes?

Faculty Economics and Business

Master Thesis

Economics

Specialization: Behavioural Economics and Game Theory

Renout Erik van der Wolf 5927641

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List of figures

Figure 1: The value function of prospect theory in 1979. 7 Figure 2: The weighting function of Kahneman and Tversky in 1979. 8 Figure 3: The weighting functions of Cumulative Prospect Theory. 9 Figure 4: Sensitivity to probabilities shown in the weighting function. 10 Figure 5: The subjective probability weighting function. 14

Figure 6: The pictures of the spinners. 15

Figure 7: Distributions of group Difficult (upper) and group Easy (lower) conditional on

the probability 21

Figure 8: Reflection of risk attitudes conditional on the low probability 0.1. 28 Figure 9: Reflection of risk attitudes conditional on the high probability 0.8. 29 Figure 10: Reflection of risk attitudes conditional on gains. 30 Figure 11: Reflection of risk attitudes conditional on losses. 31 Figure 12: Risk aversion within-participants group Difficult. 32 Figure 13: Risk aversion within-participants group Easy. 33

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List of tables

Table 1: The six Prospects. 14

Table 2: The four different orders. 18

Table 3: The difference between group Difficult and group Easy. 20 Table 4: Mean and median prices of group Difficult and group Easy. 21

Table 5: Risk attitude of group Difficult 23

Table 6: Risk attitude of group Easy. 24

Table 7: Critical values of the Wilcoxon Rank-Sum Test. 24 Table 8: Risk attitude of group Difficult, gains first, losses second. 25 Table 9: Risk attitude of group Difficult, losses first, gains second. 26 Table 10: Risk attitude of group Easy, gains first, losses second. 27 Table 11: Risk attitude of group Easy, losses first, gains second. 27

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1. Introduction

The standard Expected Utility Theory (EUT) plays a very important role in the economic theory of today. It assumes that people are fully rational, selfish and their preferences do not change (Kahneman, 2012). So people choose the risky or uncertain prospect with the highest expected utility. The person obtains the expected utility values by calculating the weighted sums by adding the utility values of outcomes multiplied by their respective probabilities (Mongin, 1997). More formally this can be written as the decision over the prospect (x1, p1; …; xn, pn) where xi is the outcome and pi is the probability with p1 + p2 + … + pn = 1 (Kahneman and Tversky, 1979). However, recent research shows that people’s decisions are not in accordance with EUT and preferences violate the axioms of EUT repeatedly (Kahneman and Tversky, 1979) (Mongin, 1997) (Kahneman, 2012), especially when the cognitive load is higher (Harbaugh, Krause, and Vesterlund, 2010).

In empirical studies starting in the 1950s it is shown that decision making of people under risk and uncertainty violates EUT consequently. Several patterns are extracted by these studies and new theories are developed. One of the most important and well-known theories is Prospect Theory (PT) by Daniel Kahneman and Amos Tversky developed in 1979 (Starmer, 2000). PT has two important assumptions. People are risk averse over gains and risk seeking over losses. People overweight low probabilities and underweight high probabilities (Harbaugh et al., 2010).

In 1992 Tversky and Kahneman emphasize the fourfold pattern of risk attitudes. More specifically PT predicts the following choice behavior of people when they face risky prospects:

“- risk-seeking over low-probability gains,

- risk-averse over high-probability gains, - risk-averse over low-probability losses and - risk-seeking over high-probability losses."

(Harbaugh et al., 2010 (p. 1))

For most people choices about risky or uncertain prospects are surely not everyday choices and one can therefore expect that people find it hard to make the choice they prefer. Therefore, one can wonder whether this fourfold pattern of risk attitudes in choice behavior is due to real preferences of people or due to systematical mistakes that people make when the cognitive load is higher.

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In line with this disquisition, the main objective of this thesis is to examine whether the choice behavior of people is different when they face a different cognitive load. Moreover it specifically examines whether the choices of people are closer to PT when the cognitive load is higher. Secondly, this thesis tests the fourfold pattern directly.

This thesis uses a price-based elicitation procedure to find the maximum willingness to pay for lotteries. In order to achieve this goal, this thesis uses an incentive compatible mechanism, which means that the best choice that people can make, is to truthfully reveal their preferences. The procedure that is used, is the Becker-DeGroot-Marschak (BDM) procedure, which is a frequently used incentive compatible mechanism in experimental economics (Bohm, Lindén, and Sonnegård, 1997). It is assumed that a price based elicitation procedure is experienced as relatively complex by most people (Harbaugh et al., 2010) and therefore the cognitive load of such decisions is relatively high. This thesis uses the same price-based elicitation method as Harbaugh et al. (2010) as the basis for this study. 40 people are asked to make choices about gains and losses with different probabilities. Every subject in this study has to choose over the same lotteries. However the cognitive load of the presented lotteries is different. For half of the subjects the price elicitation is made easier than for the other half of the subjects by giving them supporting information.

This thesis concludes that there is no difference in the decision-making of people that face a different cognitive load. In both groups, i.e. group Difficult and group Easy, the choices tend towards the fourfold pattern. It also finds evidence that choices reflect from gains to losses and from low to high probabilities. The results however do not show loss aversion.

In chapter 2 the relevant parts of the existing literature are summarized. Thereafter in chapter 3, there is an elaborate description of the experimental design. In chapter 4 the results of the experiment are presented followed by a discussion in chapter 5. Finally, the conclusions of this thesis can be found in chapter 6.

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2. Literature review

This chapter covers a summary of the relevant literature. In the first paragraph the theory of the dual self is explained. Thereafter the systematical mistakes EUT makes with respect to the preferences of people are explicated. Followed by the explanation of, and criticism on PT. PT assumes people have two phases when they make decisions under risk. Thereafter the value function of PT is demonstrated followed by a weighting function where the decision weight versus the stated probability ratio is shown. This weighting function shows that probabilities are often not taken linearly by people when they make risky decisions. Finally, the most important follow-up research and extensions on PT from a variety of authors is explicated.

2.1. Dual-process Theory

In the Dual-process Theory (DT) one distinguishes two types of thinking. The first type of thinking is the type that operates automatic, relatively effortless and quick, and people are unaware of using this type of thinking. This type of thinking Kahneman labels system 1. The second type of thinking is the one in which people choose consciously and the choice demands more effort. Such type of thinking is used in more difficult and complex situations or not everyday choices. This type of thinking Kahneman labels system 2. (Kahneman, 2012)

DT describes how people order and process all information they get in a manner which minimizes effort and optimizes performance. The brain does this by using heuristics via system 1. These heuristics also lead to systematic mistakes in the way people perceive several situations causing biases (Kahneman, 2012). These biases also arise in decision making under risk.

The cognitive load plays an important role in DT because this can exacerbate the anomalies via system 1. People are able to overcome the heuristics of system 1 when they consciously use system 2 but this depends on the cognitive ability (Stanovich and West, 2008). More specifically, people can easier overcome system 1 when they face a more familiar task and therefore people will make less systematic errors (Harbaugh et al., 2010). Benjamin, Brown and Shapiro (2006) add that anomalies in the choice-making of people can be an expression of cognitive inability, rather than a real desire and thus the choice-making is not according with the real preferences of people. In other words, if people really understand the choice then they will have chosen otherwise, however their cognitive ability does not allow them to do so.

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of system 1. Preferences of people thus differ for the same problem only because the framing is different. Moreover people often do not consider alternative frames and are not aware of the effect of a certain frame when they make a decision. They also state that people do not want their decisions to be dependent on a frame. However they often do not know how to overcome the inconsistencies resulting from their decision making.

In this thesis two groups face a different cognitive load. For most people the decisions of this experiment are not easy or familiar and therefore DT can be important to explain the results. Moreover DT predicts that in the group with a higher cognitive load the behavioral anomalies exacerbate.

2.2. Systematical errors in Expected Utility Theory

In the economic theory of today and in the education of new economists EUT plays a central role. This theory helps us to understand a lot of economic behavior but it also comes with a lot of anomalies. These anomalies can be clarified by DT.

Already in 1953 Allais shows that when people choose between certain lotteries, then in some cases EUT systematically mispredicts human behavior. Prelec (1998) adds that these simple examples have the force and simplicity of classical arguments assuming that there in nonlinear utility. Thereby also explaining that it is understandable for everyone that the difference in the utility interval between 10 and 20 is larger than between 1010 and 1020.

Kahneman and Tversky (1979) emphasize some systematical errors that EUT makes in explaining the preferences of people with respect to decision making under risk. In their paper they label these flaws in the following effects.

The certainty effect: people overweight outcomes that are regarded certain.

The reflection effect: The preferences reverse when the prospect changes from a gain to a loss and are

thus the mirror image. This implicates that people are risk averse when they face positive prospects and risk seeking when they face negative prospects.

The isolation effect: People look at the components that prospects distinguish and do not consider the

part of the prospects that is similar.

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2.3. Prospect Theory and criticism

In 1979 Daniel Kahneman and Amos Tversky publish their first paper about PT, which is a mathematically-formulated descriptive model of decision making under risk. This new theory describes the empirical findings, concerning the choices that people make when they face different risky or uncertain prospects, better than EUT. In their first paper Kahneman and Tversky (1979) describe hypothetical choice problems where people each time choose between two different prospects. With PT Kahneman and Tversky (1979) overcome the anomalies in which EUT fails systematically. In 1992 Tversky and Kahneman extend their theory to a cumulative version which applies for both risky as uncertain prospects with any number of outcomes. This extension also improves PT by allowing different weighting functions for both gains and losses.

Tversky and Kahneman (1992) state that a clear pattern arises from their theory, which they call the fourfold pattern of risk attitudes. This pattern implies that people are risk seeking for small probabilities of gains, risk averse for moderate and high probabilities of gains, risk averse for small probabilities of losses and risk seeking for moderate and high probabilities of losses.

Holt and Laury (2002) however doubt the validity of research with hypothetical payments. They question the assumption that is crucial for the method of Kahneman and Tversky (1979), namely “that people often know how they would behave in actual situations of choice, and on the further assumption that subjects have no special reason to disguise their true preferences” (Kahneman and Tversky, 1979, p. 265). From this follows that they also question whether people can reflect real life choices in a lab experiment with hypothetical choices. Also in follow-up research Laury and Holt (2008) stress that one has to be reserved in using the conclusions of economic experiments with hypothetical incentives.

Harbaugh, Krause and Vesterlund (2002) find different results when they replicate the experiment of Kahneman and Tversky (1979) with real payments. Moreover they also question the robustness of the fourfold pattern of risk attitudes. They do find the fourfold pattern when they use a price based elicitation procedure but do not find the fourfold pattern when they use a choice based elicitation procedure. Therefore they doubt to which extend PT is really a general phenomenon. They also state that most of our real-life choices are more like the choice elicitation method than the price elicitation method. This implies that PT will not hold in most of our choices in real-life.

Levy and Levy (2002) doubt the methodology of Kahneman and Tversky. According to them it is not realistic when people only choose between two positive or two negative outcomes. These are namely alternatives that are very rare in capital markets. In their research they find support for PT

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when they use the same framework. When they however use their own "PSD framework" the results consequently contradict PT.

Nwogugu (2005) even argues that PT does not explain most of the aspects of decision making under risk. He states that both PT and EUT are rigid, simplistic and impractical models and that decision making and risk are both multi-dimensional issues. Therefore decision making under risk cannot be explained by PT (or EUT).

Nonetheless, PT is widely seen as the most important theory to explain decision making under risk. It is the best alternative for EUT and the most acknowledged descriptive model. Camerer (1998) states that PT can describe a lot of economic (field data) observations in different economic domains while keeping the model easy to use.

2.4. Two phases of Prospect Theory

PT assumes that people have two phases when they make choices about risky prospects. In the first phase (the framing phase) people make a more simple representation of the offered prospects, while in the second phase (evaluation phase) the simpler representation is used to choose the prospect with the highest value (Kahneman and Tversky, 1979). In DT the first phase is related to system 1, whereas the second phase is related to system 2.

Although there is no formal model for the framing phase, one knows people tend to have standard anomalies that transform the consisting prospects. Recall that phase 1 involves an automatic type of thinking which uses heuristics to ease our decision making. These anomalies, which are described extensively in Kahneman and Tversky (1979), are explicated below.

Coding: people look at gains and losses relevant to a neutral reference point rather than final

outcomes.

Combination: people combine the probabilities of prospects with the same outcome. Segregation: people segregate the riskless part of a prospect.

Cancellation: people do not take into account the part of the prospect that is shared by the offered

prospects.

Simplification dominance: people are rounding probabilities or outcomes, which also results in

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2.5. The Value Function

In 1979 Kahneman and Tversky develop a formal model for the second phase. In their papers Kahneman and Tversky (1979) and Tversky and Kahneman (1992) propose a value function v(x) rather than a utility function (see figure 1). The value function consists of three important components. 1. The value function is defined on changes in wealth or welfare from the reference point. This reference point can be the current asset state but can also be an expectation or aspiration level that differs from the status quo.

2. The value function is concave for gains (v’’(x)<0, for x>0) and convex for losses (v’’(x)>0, for x<0), and the value function is thus S-shaped. The valuation rule is a two-part cumulative functional for the latter paper.

3. The value function is steeper for losses than for gains. When x>y≥0 then v(y)+v(-y)>v(x)+v(-x) and v(-y)-v(-x)>v(x)-v(y).

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2.6. The Weighting Function

Figure 2: The weighting function of Kahneman and Tversky in 1979 (source: Kahneman and Tversky, (1979)).

Gonzalez and Wu (1999) state that in empirical studies it is shown that probabilities are mostly not treated linearly by decision makers. The weighting function allows for a decision weight at the stated probabilities form 0 to 1 and therefore the probabilities can be weighted nonlinearly.

The weighting function shows us the ratio between the decision weight and the stated probability. A decision weight π(p) is demonstrated on the vertical axis and indicates how p affects the value of the prospect. This decision weight π(p) is a monotonic function of p, but π(p) is not a probability (Tversky and Kahneman, 1981). The other scale p is demonstrated on the horizontal axis and indicates the stated probability of the prospect.

From the representation of the weighting function of Kahneman and Tversky (1979), see figure 2, one can observe two important features. Firstly, people tend to overweight low probabilities and underweight high probabilities. Secondly, it also shows that π does not go to 0 or 1 in the end points, which implies the disregard of very low probabilities and the exaggeration of high probabilities. Gonzalez and Wu (1999) stress that the weighting function in this paper is not a subjective probability but a distortion of the given probability. Kahneman and Tversky (1979) state that these findings can explain why people on the one hand have insurance and on the other hand also gamble.

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(a) (b) (c)

Figure 3: The weighting functions of Cumulative Prospect Theory (source: Kahneman and Tversky, (1992)).

From the weighting functions of Tversky and Kahneman (1992), see figure 3, for both gains (a) and losses (b) one can see that these cumulative version does behave well at the end points. In figure 3 (c), both gains (W+_{) and losses (W}-_{) are combined in one figure. In this improved version the} weighting function is concave for low probabilities and convex for high probabilities and an inversed-S-shaped form is demonstrated (Gonzalez and Wu, 1999). Prelec (1998) adds that empirical findings suggest that the probability weighting function is characterized by four properties, namely regressive, asymmetric (fixed point at about 1/3), s-shaped and reflective.

Most studies use assumptions about the functional form. Wu and Gonzalez (1996) add to the literature by testing the weighting function directly. In this research concavity-convexity preference ladders are used to find the weighting function. Such a ladder arises from a series of questions where only one common consequence changes. For example the beginning of ladder 1 starts with the choice between R (0.05, $240) and S (0.07, $200). Thereafter both choices are added with 0.1 chance for $200 leading to the choice between R (0.05, $240; 0.1, $200) and S (0.17, $200). Wu and Gonzalez find that the weighting function is concave up to p < 0.40 and thereafter convex. In addition the tests show that the weighting function is significant nonlinear.

Also from a psychological point of view this form of the weighting function does make sense. Three features can explain the inverse-S-shaped form, namely diminishing sensitivity, discriminability and attractiveness. The first feature is straight forward. When one moves away from the reference point people become less sensitive to changes. In this context one refers to probability 0 (certainly will not happen) and 1 (certainly will happen) as reference points. Therefore the weighting function is

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steeper near the endpoints of the probability scale. The second feature refers to the sensitivity of a decision maker in the domain where the probability is not near the endpoints. As one can see in figure 4, w2 is not very sensitive to changes in the probability scale, while w1 is almost linear. Experts possess an almost linear weighting function (w1) in their domain of expertise. So with a familiar or easy task people’s decision weight does almost not differ from the stated probability. This means that the overweighting of small probabilities and the underweighting of high probabilities diminishes. Therefore the cognitive load will affect the fourfold pattern of risk attitudes via the sensibility to changes in the probability scale. The last feature just explains that the weight one assigns to a probability can differ per person and this principle can elevate the whole weighting function. (Gonzalez and Wu, 1999)

Figure 4: Sensitivity to probabilities shown in the weighting function (source: Gonzalez and Wu, (1999)).

2.7. Follow-up research on Prospect Theory

Harbaugh et al. (2002) examine the fourfold pattern directly with simple and real gambles. They have a choice elicitation task, where people choose between a gamble and its expected value and a price elicitation task where people price a gamble. In this price elicitation task subjects report their willingness to pay for gains and their willingness to pay to avoid for losses. The price elicitation design is replicated in the experiment of this thesis. In the choice elicitation task the preferences of people are not in accordance with of the fourfold pattern. However in the price elicitation task the preferences of people are in accordance with the fourfold pattern of PT. The fourfold pattern in the price elicitation task also arises when people make the choice elicitation task first and also after people have the possibility to make changes at the end of the experiment in their earlier made decisions.

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In follow-up research in 2010 of Harbaugh et al., they state that people are less familiar with the price elicitation task and therefore their decisions are more like PT predicts. This is because the cognitive load is higher and therefore, in line with the theory of dual selves, the heuristics used by system 1 lead to more systematical mistakes, and therefore also in phase 1 of PT, the systematical errors increase.

In another research of Harbaugh, Krause and Vesterlund (2002) it is shown that decision making under risk changes over life-time. Children choose the opposite way as the fourfold pattern and underweight small probabilities and overweight high probabilities (even 75% of the children choose a fair gamble when the probability of losing was 0.1 and 70% when the probability of gaining was 0.8). While as people get older and get in their mid-twenties, they do use the objective probabilities in the gain domain. However in the loss domain they still use subjective probabilities. More specifically, they underweight low probabilities and overweight high probabilities. The divergent results concerning the fourfold pattern assign Harbaugh et al. (2002) to a different elicitation method. Where most research asks participants to reveal their willingness to pay or to choose between two gambles, this research asks to choose between a lottery and its expected value.

In Holt and Laury (2002) a menu of paired lottery choices over gains, of which the first option is less variable than the second option, is shown to the participants. From this answers they can observe when the participants shift from the saver choice to the risky option. In this way they try to elicit the degree of risk aversion and they are able to find a functional form. In this experiment they find that there is in general a lot of risk aversion in the choices people make. Moreover they find that when the payoffs increase people choose more often the safe options and thus are more risk averse. Although this experiment is probably experiencing order and treatment effects (Harrison et al., 2005). Holt and Laury (2005) redo the research with a single payment condition and confirmed the findings of their first experiment. This result of increasing risk aversion when the payoff increases, is in accordance with the experiment with farmers in Bangladesh from Binswanger (1980) where the stakes even rise to their average monthly income.

In the research of Binswanger (1980) a higher wealth slightly reduces the risk aversion, however not significantly. Nevertheless this higher wealth may reflect the higher reference point of these farmers, which plays an important role in PT.

In an experiment of exchange economies of two goods with several rounds involving losses it is found that people are risk seeking in the loss domain. Although people do become less risk seeking when they become more experienced with the task (Myagkov and Plott, 1997). It is possible that this result is related to the DT and people’s biases decrease because people become more familiar with the

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Laury and Holt (2005) and (2008) argue that people are not risk seeking in the loss domain as PT predicts. They find that people are risk neutral when they face choices over losses in all cases where incentives are real or hypothetical, low or high. However they still state that the decreased risk aversion in the loss region reflects the choice-behavior of people in the direction of PT. Also here an increase in risk aversion is detected. When the payoff scale increases 15x, then the loss aversion increases in the loss domain.

In research of Harbaugh et al. (2002) subjects choose both lower mean and median prices for gains than for similar losses, implying that losses loom larger than gains, and the value function is thus steeper for losses. This is also confirmed by neuro-economic research, showing greater brain activity after losses than after gains reflecting a stronger emotional response (Gehring and Willoughby, 2002).

With respect to the reflection effect Laury and Holt (2005) and (2008) find via the modal choice pattern that the reflection effect decreases extremely (from 26 percent to 13 percent) when they use real payments instead of hypothetical payments. Also when the payoffs are much higher, in this research by a factor 15x, the reflection rates reduce even more because people tend to be more risk averse. Harbaugh et al. (2002) show that the reflection effect does hold true for adults, but until 20 year olds the weighting function for gains is different than for losses. In Follow-up research in 2010 they find results for the reflection effect consistent with PT. On the one hand they find reflection between gains and losses conditional on a high or low probability prospect. On the other hand they find reflection between high and low probability prospects conditional on a gain or a loss.

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3. Experimental design

This chapter is organized in the following manner. At first the lotteries that are presented to the participants are explained. Thereafter the BDM price elicitation procedure is described accompanied by an explanation for what reasons this procedure is incentive compatible. Followed by some general information about the subject instructions and a description of the circumstances in which the participants participate in this experiment. Thirdly, the between-subject design and the within-subject design are discussed and it is explained how this design supports the objectives of this thesis. After that the four different treatments that participants can face are explicated. Finally a clarification of the statistical tests is given.

3.1. The presentation of the lotteries

The experiment is designed to test whether people make different decisions when they face risky prospects in situations with a different cognitive load. To attain such a situation half of the participants is supported with extra information in order to make their decision easier. In addition, this thesis wants to test the fourfold pattern of risk attitudes directly for both groups and all different treatments. There is also a within-subject design for the reflection effect and risk aversion.

The risky prospects are represented by simple lotteries for gains and losses with different probabilities, i.e. 10%, 40% and 80%. These are the same six prospects as Harbaugh et al. (2010). All participants choose over the same prospects, which are shown in Table 1. The reason these probabilities are chosen, is that the difference between the objective probability and the weighted probability is the largest where the objective probability is 0.1 and 0.8. The objective probability 0.4 is on the point these two functions approximately cross (Harbaugh et al., 2010). These findings can for example be verified by the subjective probability weighting function from Tversky and Kahneman (1992) which is shown in figure 5, with the objective probability p on the horizontal axis and the subjective probability w(p) on the vertical axis. The line W+_{shows the weighting function for gains} and the line W- shows the weighting function for losses.

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Table 1: The six Prospects.

Prospect number Probability Payoff Expected Value Predicted FFP of risk attitude 1 0.1 + €20 €2 Seeking 2 0.4 + €20 €8 Neutral 3 0.8 + €20 €16 Averse 4 0.1 - €20 - €2 Averse 5 0.4 - €20 - €8 Neutral 6 0.8 - €20 -€ 16 Seeking

(Source: Harbaugh et al. (2010))

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Rad

90% kans op 0 euro verlies 10% kans op 20 euro verlies

Rad

kans op 0 euro verlies kans op 20 euro verlies

The lotteries are presented by pictures of spinners, where the red surface represents the chance of a gain or loss and the blue surface represents the chance of no gain or no loss. Figure 6 (a) and 6 (b) are examples of spinners with a chance of a loss and a chance of no loss.

(a) (b)

Figure 6: The pictures of the spinners.

To attain the situation where half of the participants face a different cognitive load than the other half, there are two different groups a participant can be selected for. In the one group the participant faces just the picture of the spinner (figure 6a), hereafter group Difficult. In the other group the participant faces the same picture of the spinner and moreover the participant is supported with extra information, by mentioning the percentages of the probabilities explicitly (figure 6b), hereafter group Easy.

Thus this experiment assumes that in the latter case the participants have to make a decision with a lower cognitive load because in the first case the participant has to estimate the probability while in the latter case the probability is given.

3.2. The BDM method for price elicitation

To elicit the preferences op people this experiment uses a price elicitation procedure, which reveals the maximum willingness to pay of the participants. In the case of this experiment it means that participants have to reveal their maximum willingness to pay, to play a lottery over a gain. Or that they have to reveal their maximum willingness to pay, to avoid playing a lottery over a loss.

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strategy is to reveal real preferences (Noussair, Charles, Stephane Robin, and Bernard Ruffieux, 2004). In this experiment the BDM procedure is implemented as follows. After a participant reveals her maximum willingness to pay, then a random price between €0 and €22 is drawn. In the case of a gain the participant will play the lottery if her willingness to pay is higher than the random price. In the case of a loss the participant will avoid playing the lottery if her willingness to pay is higher than the random price. Because of this random price, a participant is always at least as well off, or better off, when she reveals her true maximum willingness to pay with respect to any other answer. If she reveals a higher price, there is a possibility that she will pay too much. On the other hand, if she reveals a lower price, there is a possibility that she does not play a lottery over gains while she personally wants to play the lottery or she does play a lottery over losses while she personally wants to avoid the lottery.

3.3. The instructions

The instructions are based on the instructions of Harbaugh et al. (2010) and are translated in Dutch. The instructions can be found in Appendix A. The four different instructions are very similar but differ only in the test of understanding and choice form or the sequence.

The participants make their decisions after reading the instructions. The subject instructions are handed to the participants on paper or online.

In the subject instructions it is explained to the participants that of all participants 2 will earn real money. This choice is made because paying all participants is financially not achievable. For these 2 participants only one decision will be randomly assigned for their payoff. This is because this experiment wants to elicit the maximum willingness to pay for a specific prospect and not a set of prospects. Hereby making it impossible for subjects to hedge in anyway. Also from Laury (2005) one knows that paying all choices or randomly paying one choice will give approximately the same decisions by participants. Therefore the decision for a random-choice payment method is valid.

The subject instructions also explain that there is no right or wrong answer and that the answers are not public. In the subject instructions the BDM procedure is explained for both gains and losses, to ensure they understand that the best they can do, is to truthfully reveal their maximum willingness to pay. The instructions (for both gains and losses) also include an extended example, a test of understanding, and the actual choice form. All subjects carry out their experiment by themselves on different times. The participants are all acquaintances, friends and family.

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3.4. Between-subject design and within-subject design

This thesis chooses a between-subject design to examine the difference between group Difficult and group Easy. The reason for a between-subject design is, that it is expected that participants will be influenced by the first task they face in such a way that the groups do not differ anymore. Such order and treatment effects will arise especially when a participant does the easy task first and later on the difficult task. In such a situation the probabilities are stated explicitly in the first task and in the second task the participant has to estimate the probability herself. However she already knows the exact probability from the first task and therefore the second task does not differ from the first. So to be sure the different tasks will not influence each other, and to focus as much as possible on the effect of the cognitive load, the between-subject design fits this experiment better.

There are four different ways in which this thesis examines the difference between group Difficult and group Easy. The first three tests use the Mann-Whitney Test. At first the clustered differences with the corresponding expected value for gains and losses of both groups are compared hereby examining whether the locations of the willingness to pay for lotteries are the same. This test will allow us to know whether the risk aversion in both groups is the same. Secondly, the clustered absolute differences with the corresponding expected value for gains and losses of both groups are compared hereby examining whether the deviation from the expected value of both groups is the same. The third test clusters the differences with the expected value conditional on the probability. In this way one can observe whether one group chooses more like PT. PT predicts a willingness to pay that is higher than the expected value for probability 0.1, the same for probability 0.4 and lower for probability 0.8. These tests examine whether the locations of the willingness to pay are the same at these critical probabilities. Finally the mean and median prices of both groups are shown. These can also give an indication of the location of both groups at the critical probabilities.

Thereafter this thesis examines whether the willingness to pay is different from the expected value. In order to do so, this thesis uses the Wilcoxon Rank-Sum Test and a Sign Test for paired observations of the willingness to pay and the corresponding expected value. In this way this thesis wants to find the risk attitudes at the critical probabilities. Also the mean and median prices are reported. These can give extra information of the risk attitude regarding the comparison of risk aversion in the gain and loss domain as well the existence of the reflection effect.

Next via a within-subject design this thesis tests for the reflection and risk aversion for gains and losses. At first all possible reflections subject to a gain or loss and subject to a low or high probability are demonstrated. Thereafter it is shown how much participants have a higher risk aversion

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3.5. The four different orders

In total 40 people participate in this experiment. The participants are evenly divided over the four different treatments, which means that every treatment contains 10 participants. The treatments are further clarified in table 2. In the experiment every participant is randomly selected to one of the two groups. Group Difficult only sees the standard spinners (picture 6a) , whereas group Easy is moreover supported with the explicit percentages of the probabilities (picture 6b).

To further prevent for order - or treatment effects entering the results via a loss frame or a gain frame half of the group will make the choices about gains first and thereafter the choices about losses, and vice versa. In this way there is a different sequence of choices about prospects that involve losses and choices of prospects that involve gains for different participants.

Summarizing the four orders that participants can face leads to the following table 2.

Table 2: The four different orders.

Group Difficult Treatment 1: (gains first, losses second) Treatment 2: (losses first, gains second) Expected value Probability Change in wealth Expected value Probability Change in wealth €2 0.1 + €20 ‐ €2 0.1 ‐ €20 €8 0.4 + €20 ‐ €8 0.4 ‐ €20 €16 0.8 + €20 ‐ €16 0.8 ‐ €20 ‐ €2 0.1 ‐ €20 €2 0.1 + €20 ‐ €8 0.4 ‐ €20 €8 0.4 + €20 ‐ €16 0.8 ‐ €20 €16 0.8 + €20 Group Easy Treatment 3: (gains first, losses second) Treatment 4: (losses first, gains second) Expected value Probability Change in wealth Expected value Probability Change in wealth €2 0.1 + €20 ‐ €2 0.1 ‐ €20 €8 0.4 + €20 ‐ €8 0.4 ‐ €20 €16 0.8 + €20 ‐ €16 0.8 ‐ €20 ‐ €2 0.1 ‐ €20 €2 0.1 + €20 ‐ €8 0.4 ‐ €20 €8 0.4 + €20 ‐ €16 0.8 ‐ €20 €16 0.8 + €20

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4. Results

In chapter 4 the results arising out of the experiment are presented. At first the results concerning the effect of the cognitive load are shown. The Mann-Whitney Test is used to examine whether the prices given by the participants of group Difficult and group Easy are the same in three different manners. Also the mean and median prices are compared and a graphical analyses of the distribution is shown. In the second paragraph the risk attitudes of both groups and all the 4 treatments are presented. The Wilcoxon-Rank Sum Test and the Sign Test are used to find whether participants choose differently from the expected value. Thereafter the results concerning the reflection effect are shown. Finally the results show whether participants are more risk averse in the gain domain or in the loss domain.

4.1. The effect of the cognitive load

In order to find the effect of the cognitive load this thesis uses the Whitney Test. The Mann-Whitney Test is a non-parametric test in which the test is only based on the order of the observations of the two samples. In this way one wants to determine whether the population locations are the same. (Keller, 2012)

In Table 3 the difference between group Difficult and group Easy is tested in three different ways. Also the relevant means and standard deviations are demonstrated in Table 3.

For the first tests (1 and 2) the differences of the willingness to pay with the expected value for each participant are clustered for the gain and loss domain. To examine the difference between group Easy and group Difficult there is a Mann-Whitney Test which tests whether the locations of these clustered values are the same. The p-value of test 1 shows that the willingness to pay for gains in group Easy is significantly lower than the willingness to pay for gains in group Difficult. This reflects that group Difficult is more risk averse in the gain domain. The risk aversion does not differ between group Difficult and group Easy in the loss domain.

The second tests (3 and 4) also use the clustered differences of the willingness to pay with the corresponding expected value for the gain and loss domain. However now it uses the absolute values of the differences. In this way this thesis is able to find whether the one group deviates more from the expected value than the other. Via the Mann-Whitney Test it is found that there is no difference between the groups in the gain as well in the loss domain.

The last tests (5, 6 and 7) examine the difference between the groups conditional on the probability. In PT one expects a higher willingness to pay for the low probability 0.1 and a lower

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willingness to pay for the high probability 0.8. For probability 0.4 it is expected to be the same as the expected value. The p-values of the Mann-Whitney Test demonstrate that the willingness to pay in both groups is the same for all probabilities. Therefore there is no reason to assume that the different cognitive load has led to a pattern that is more like the fourfold pattern of PT.

In all seven tests the standard deviation of group Difficult is higher than the standard deviation of group Easy which indicates that the data points of group Difficult are spread out over a wider range of values.

Table 3: The difference between group Difficult and group Easy. Mean difference with the

expected value

Standard deviation p-value Mann-Whitney Test Group

Difficult

Group Easy Group Difficult Group Easy 1. Gains 1,85 - 3,85 10,2129 6,0123 0,0734 2. Losses - 1,025 - 0,725 7,4018 6,3912 0,6818 3. Gains absolute difference 3,025 4,85 6,9485 3,9809 1 4. Losses absolute difference 3,725 3,925 5,5706 4,8731 0,4238 5. Probability 0.1 2,7875 2,1 5,5268 3,1639 0,6384 6. Probability 0.4 1 - 1,3 5,9245 3,8324 0,4472 7. Probability 0.8 - 2,9625 - 5,375 6,2651 6,0143 0,4180

Notes. 40 participants, 20 per group. The Mann-Whitney Test is used to test whether the population locations are the same. 1 and 2 compare the clustered differences with the expected value for gains and losses of both groups. 3 and 4 test compare the clustered absolute differences with the expected value for gains and losses of both groups. 5, 6 and 7 compare the clustered differences with the expected value conditional on the probability.

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In table 4 the mean and median prices of group Difficult and group Easy are shown. On the left one can find the six different prospects, in the middle the mean prices of both groups are presented and on the right the median prices of both groups can be found. In the gain domain both mean and median prices are higher for group Difficult than for group Easy. This shows that the risk aversion in the gain domain is higher in group Difficult. In relation to the expected value the mean and median prices show no pattern at all. The group that is closer to the expected value varies continually. This confirms the outcomes of the Mann-Whitney Test at table 3 number 3 and 4 that neither of the groups deviates more from the expected value and number 5, 6 and 7 that neither of the groups has a pattern which is more like the fourfold pattern of risk attitudes of PT.

Table 4: Mean and median prices of group Difficult and group Easy.

Notes. 40 participants, 20 per group.

In figure 7 the distributions of both groups are demonstrated. On the horizontal axis the willingness to pay of participants is placed. On the vertical axis the number of participants corresponding to that willingness to pay is placed. The upper graphs belong to group Difficult and the lower graphs belong to group Easy. The expected values starting from the left are 2, 8 and 16.

Prospect Mean reported price Median reported price

Description EV Price group

Difficult Price group Easy Price group Difficult Price group Easy 1. p = 0.1 €2 €3,6875 €2,5 €2,125 €2 Gain + €20 2. p = 0.4 €8 €8,75 €6,8 €8 €7 3. p = 0.8 €16 €15,4125 €12,85 €16 €13,5 4. p = 0.1 - €2 - €3,1 - €3,6 - €2 - €3 Loss - €20 5. p = 0.4 - €8 - €8,25 -€7,9 - €8,5 - €8 6. p = 0.8 - €16 - €13,625 - €13,775 - €15,5 - €15

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a) probability 0.1 b) probability 0.4 c) probability 0.8

Figure 7: Distributions of group Difficult (upper) and group Easy (lower) conditional on the probability.

Notes. 40 participants, 20 per group. The number of participants with a certain willingness to pay conditional on the probability.

Figure 7 adds to the statistical analyses by making the sample locations visual. One can obeserve that there are no distinct differences between group Difficult and group Easy. Therefore also via the graphical analyses there is no evidence that the one group has a pattern that is more like PT than the other group. Although it is visible that the data of group Difficult is spread out over a wider range of values indicating the larger standard deviation.

4.2. Risk attitudes

To examine the risk attitudes this thesis uses two non-parametric tests for paired observations. The Wilcoxon Rank-Sum Test is only based on the order of the observations of the two samples. It wants to test whether the population locations are the same. In the Sign Test the differences for each pair of observations are calculated. This test will only use the sign of the differences and gives no value to the magnitude of these differences. (Keller, 2012)

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In all reported tables about risk attitudes below, participants are classified as risk seeking if they want to pay more than the expected value, neutral if they pay the same as the expected value and risk averse if they pay less than the expected value for gains for a p-value < 0,1. For losses this is vice versa for a p-value < 0,1.

Table 5: Risk attitude of group Difficult.

Description EV Price p-value Attitude Price P-value Attitude

1. p = 0.1 €2 €3,6875 0,1124 Neutral €2,125 0,1096 Neutral Gain + €20 2. p = 0.4 €8 €8,75 0,5892 Neutral €8 0,5962 Neutral 3. p = 0.8 €16 €15,4125 1,0000 Neutral €16 1,0000 Neutral 4. p = 0.1 - €2 - €3,1 0,4180 Neutral - €2 0,4412 Neutral Loss - €20 5. p = 0.4 - €8 - €8,25 0,2802 Neutral - €8,5 0,1586 Neutral 6. p = 0.8 - €16 - €13,625 0,1770 Neutral - €15,5 0,1970 Neutral

Notes. 20 participants. The Wilcoxon Rank-Sum Test tests whether the mean reported prices are the same as the expected value. The Sign Test tests whether the median reported prices are the same as the expected value. The risk attitude is averse/seeking for a p-value < 0,1 otherwise the risk attitude is neutral.

In table 5 the risk attitudes of the participants in group Difficult are shown. One can see that the mean prices of prospect 1, prospect 4 and prospect 6 differ quite a lot in the way PT predicts. However these differences are not significantly according to the Wilcoxon Rank-Sum Test. Prospects 2 and 5 are similar to the expected value supporting PT. Prospect 3 is also almost the same as its expected value in contrast with the expectation of PT. Summarizing the results of the mean reported prices one can observe that the results of group Difficult tend towards the pattern of PT. Also the willingness to pay reflects from the gain domain to the loss domain. However all the results are not significant.

The median prices are all very close to the expected value and when performing a sign Test there is also no evidence that the prices of the participants differ from the expected value. These results indicate that the participants choose the same as the expected value.

The mean prices for gains are all higher than for similar sized losses. These results reflect a higher risk aversion in the gain domain, which contradicts the existing literature and the existence of loss aversion. For median prices the results concerning risk aversion are mixed reflecting no difference in the gain or loss domain.

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Table 6: Risk attitude of group Easy.

Description EV Price p-value Attitude Price P-value Attitude

1. p = 0.1 €2 €2,5 0,4180 Neutral €2 0,4066 Neutral Gain + €20 2. p = 0.4 €8 €6,8 0,1770 Neutral €7 0,2262 Neutral 3. p = 0.8 €16 €12,85 0,0028 Averse €13,5 0,0076 Averse 4. p = 0.1 - €2 - €3,6 0,0000 Averse - €3 0,0000 Averse Loss - €20 5. p = 0.4 - €8 -€7,9 0,2802 Neutral - €8 0,5962 Neutral 6. p = 0.8 - €16 - €13,775 0,0308 Seeking - €15 0,0456 Seeking Notes. 20 participants. The Wilcoxon Rank-Sum Test tests whether the mean reported prices are the

same as the expected value. The Sign Test tests whether the median reported prices are the same as the expected value. The risk attitude is averse/seeking for a p-value < 0,1 otherwise the risk attitude is neutral.

In table 6 the risk attitudes of the participants in group Easy are shown. The mean reported prices of prospects 3, 4 and 6 differ significantly with the Wilcoxon Rank-Sum Test as well as the median reported prices differ significantly with the Sign Test. All in the way PT predicts. Also prospects 2 and 5 support PT by being approximately the expected value. Only prospect 1 does not support the expectation of PT and is the same as its expected value. Summarizing the results there is evidence that the risk attitudes in group Easy are as PT predicts. Moreover the willingness to pay reflects from the gain domain to the loss domain.

In group Easy the mean and median prices for gains are lower than for losses. This reflects more risk aversion in the loss domain. Therefore in this group there is loss aversion.

Table 7: Critical values of the Wilcoxon Rank-Sum Test.

One-tail α = 0.025 α = 0.05 Two-tail α = 0.05 α = 0.10 n2 ↓/n1 → 10 10 TL = 79 TL = 83 TU = 131 TU = 127 (Source: Keller, (2012))

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Test, which is shown in table 7. In tables 8, 9, 10 and 11 the rank values, TL and TU, are shown for the expected value of the prospect and the willingness to pay of the participants. If the value is lower than 79 or 83 then the location lies significantly more to the left for α = 0.05 and α = 0.10 respectively. If the value is higher than 131 or 127 then the location lies significantly more to the right for α = 0.05 and α = 0.10 respectively.

In general the sequence of gains and losses does not affect the results. The only result that changes is the risk aversion in the loss domain. When the choices about losses are second then the risk aversion rises. Hereafter the risk attitudes of all treatments are discussed separately.

Table 8: Risk attitude of group Difficult, gains first, losses second.

Prospect Mean reported price Median

reported price

Description EV Price Rank values Attitude

EV Participants 1. p = 0.1 €2 €3,975 85 125 Neutral €2,625 Gain + €20 2. p = 0.4 €8 €7,7 115 95 Neutral €7,5 3. p = 0.8 €16 €14,175 120 90 Neutral €14,375 4. p = 0.1 - €2 - €3,6 90 120 Neutral - €2,75 Loss - €20 5. p = 0.4 - €8 - €8,6 90 120 Neutral - €9,5 6. p = 0.8 - €16 - €13,65 110 100 Neutral -€14,25

Notes. 10 participants. The Wilcoxon Rank-Sum Test tests whether the mean reported prices are the same as the expected value. The Rank values are used because the number of participants is too small to calculate the p-value. TL is 79 and 83 for α = 0.05 and α = 0.10 respectively. TU is 131 and 127 for

α = 0.05 and α = 0.10 respectively.

In table 8 the risk attitudes of treatment 1 are demonstrated. As PT predicts the mean and median prices of prospects 1, 3, 4 and 6 are divergent from the expected value. However these deviations are not significant according to the Wilcoxon Rank-Sum Test. The mean and median prices also reflect from the gain domain to the loss domain. Overall these risk attitudes tend towards PT.

For similar sized gains and losses there is no clear pattern whether the participants are willing to pay more for gains or losses. Therefore there is no difference in risk aversion between the gain domain and the loss domain.

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Table 9: Risk attitude of group Difficult, losses first, gains second.

reported price

EV Participants 1. p = 0.1 €2 €3,4 95 115 Neutral €2 Gain + €20 2. p = 0.4 €8 €9,8 85 125 Neutral €9 3. p = 0.8 €16 €16,65 90 120 Neutral €16,75 4. p = 0.1 - €2 - €2,6 105 105 Neutral - €2 Loss - €20 5. p = 0.4 - €8 - €7,9 100 110 Neutral - €8 6. p = 0.8 - €16 - €13,65 125 85 Neutral - €14,25

In table 9 the risk attitudes of treatment 2 are shown. Prospects 1, 2 and 6 do differ substantially from the expected value. However these are all not significant changes according to the Wilcoxon Rank-Sum Test. According to PT prospect 2 shall be the same as the expected value but here it diverges a lot from the expected value however not significantly. PT does predict that prospect 1 and 6 are different from its expected value. Prospect 3 is even higher than its expected value indicating that these subjects are more leaning towards risk seeking which contradicts PT. Prospect 5 is almost the same as the present value as is predicted by PT. The risk attitudes in the gain domain are therefore not in line with PT. In the loss domain the risk attitudes tend towards PT but not significantly. There is no evidence for the reflection effect.

Surprisingly, when looking at the mean prices then the participants in this treatment do pay substantially more for gains than losses. For median prices this tendency is also found in 2/3 of the prospects. This means that people are more risk averse in the gain domain.

Table 10 presents the risk attitudes of the participants of treatment 3. The mean and median reported prices of prospects 1,3,4 and 6 are all substantially different from its expected value as PT predicts. However prospect 1 does not differ significantly according to the Wilcoxon Rank-Sum Test. The other prospects do differ significantly according to the Wilcoxon Rank-Sum Test for respectively α=0,10, α=0,05 and α=0,10. Prospects 2 and 5 are almost the same as its expected value as predicted by PT. Therefore there is strong support for the risk attitudes to be the way as PT predicts. There is also support for the reflection effect.

The mean and median reported prices for gains are all lower than the ones for similar sized losses except for the median prices with probability 0.4 where the participants pay the same. This means that there is evidence that people are loss averse.

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Table 10: Risk attitude of group Easy, gains first, losses second.

reported price

EV Participants 1. p = 0.1 €2 €3,1 85 125 Neutral €3,5 Gain + €20 2. p = 0.4 €8 €7,2 110 100 Neutral €7,5 3. p = 0.8 €16 €13,6 130 80 Averse* €13,5 4. p = 0.1 - €2 - €4,5 60 150 Averse** - €4 Loss - €20 5. p = 0.4 - €8 - €8,3 115 95 Neutral - €7,5 6. p = 0.8 - €16 - €14,5 130 80 Seeking* - €15 *significant at two-tailed test for α=0,10. ** significant at two-tailed test for α=0,05.

In Table 11 the risk attitudes of treatment 4 can be found. Prospects 3 and 6 differ a lot from their expected value. However only prospect 3 differs significantly according to the Wilcoxon Rank-Sum Test for α=0,05. Prospects 1,2, 4 and 5 are very close to their expected value. According to PT this is only expected for prospects 2 and 5. According to PT prospects 1 and 4 are in the contrary to the results expected to be priced higher by the participants. There is no evidence for the reflection effect.

For both reported mean and median prices the participants are willing to pay a lot more for losses than for gains. This demonstrates the existence of loss aversion.

Table 11: Risk attitude of group Easy, losses first, gains second.

reported price

EV Participants 1. p = 0.1 €2 €1,9 110 100 Neutral € 2 Gain + €20 2. p = 0.4 €8 €6,4 125 85 Neutral € 7 3. p = 0.8 €16 €12,1 135 75 Averse* € 13,5 4. p = 0.1 - €2 - €2,7 85 125 Neutral - € 2,5 Loss - €20 5. p = 0.4 - €8 - €7,5 105 105 Neutral - € 8 6. p = 0.8 - €16 - €13,05 120 90 Neutral - € 15,5 * significant at two-tailed test for α=0,05.

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4.3. Reflection effect within-participants

The binomial test is used to test for the reflection effect. The risk attitude conditional on a low probability, high probability, gain or loss has three possible risk attitudes and therefore nine different combinations. Therefore if the participants choose randomly the chance for each combination is (1/9). With a binomial test this thesis examines whether there are more people in a particular cell.

a) group Difficult b) group Easy

Figure 8: Reflection of risk attitudes conditional on the low probability 0.1.

Notes. 40 Participants, 20 per group. The number of participants that have a certain risk attitude are displayed on the vertical axis.7/20 and 8/20 have the predicted risk attitude.

In figure 8 the reflection of risk attitudes is shown conditional on the low probability 0.1. The number of participants is displayed on the vertical axis. The losses are displayed on the horizontal axis and the gains are displayed on the axis going in depth. PT expects that people are risk seeking for low probability gains and risk averse for low probability losses.

For both groups one observes an incomparably high bar for the expected reflection of risk attitudes. Via the binomial test one finds that in group Difficult 7/20 (0,004) and in group Easy 8/20 (0,001) of the participants are both risk seeking for gains and risk averse for losses.

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Figure 9: Reflection of risk attitudes conditional on the high probability 0.8.

In figure 9 the reflection of risk attitudes conditional on the high probability 0.8 is presented. The number of participants is displayed on the vertical axis. The losses are displayed on the horizontal axis and the gains are displayed on the axis going in depth. PT expects that people are risk averse for high probability gains and risk seeking for high probability losses.

Also in these bar charts one observes the highest bars in the predicted cell by PT. Also here only these reflections are significantly large. Via the binomial test one finds that in group Difficult 6/20 (0,0184) participants are in the expected cell and in group Easy even 11/20 (0,000) participants are risk averse over gains and risk seeking for losses.

Therefore also conditional on the high probability 0.8 there is evidence for the reflection effect.

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Figure 10: Reflection of risk attitudes conditional on gains.

Notes. 40 Participants, 20 per group. The number of participants that have a certain risk attitude are displayed on the vertical axis. 4/20 and 5/20 have the predicted risk attitude.

In figure 10 the representation of the risk attitudes conditional on gains is presented. The number of participants is displayed on the vertical axis. The high probability 0.8 is labeled on the horizontal axis and the small probability 0.1 is displayed on the axis going in depth. PT predicts that most people will be at the cell which is risk seeking over small probabilities and risk averse over high probabilities.

In group Difficult half of the participants is risk seeking over small probabilities. However over large probabilities the participants choose differently. The attitude Seeking-Averse is chosen 4/20 and the attitude Seeking-Seeking is chosen 5/20 and thereby the latter is the only significant risk attitude (0,0632) via the binomial test.

In group Easy 14/20 are risk averse when they face high probabilities. However in this group the attitude at the low probability is mixed. Seeking-Averse has 5/20, Neutral-Averse has 4/20 and Averse-Averse has 5/20. Therefore Seeking-Averse and Averse-Averse are both significantly different (0,0632) via the binomial test.

So in both groups there is a tendency towards the reflection of risk attitudes of PT, however there is no convincing evidence.

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Figure 11: Reflection of risk attitudes conditional on losses.

In figure 11 the risk attitudes conditional on losses are displayed. The number of participants is displayed on the vertical axis. Again the high probability 0.8 is labeled on the horizontal axis and the small probability 0.1 is displayed on the axis going in depth. The risk attitude PT predicts is risk averse over small probabilities and risk seeking over high probabilities.

In group Difficult 5/20 participants choose this risk attitude Averse-Seeking and this is the only significant cell (0,0632) via the binomial test. In group Easy exactly half of the participants 10/20 choose the risk attitude predicted by PT and this result is significant (0,000) via the binomial test.

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4.4. Risk aversion within-participants

In this paragraph the participants that pay more for losses than for gains conditional on the probability are displayed as losses. This reflects the number of participants that is loss averse for that particular probability. The participants that pay more for gains than for similar losses are displayed as gains. This reflects the number of participants that are more risk averse in the gain domain. Participants that pay the same for similar gains and losses are displayed as neutral because their risk aversion is the same for gains and losses for that particular probability. PT predicts that losses loom larger than gains and people shall thus pay more for similar losses.

From figure 12 one can observe that in group Difficult the most striking finding is that almost no one wants to pay more for losses. Therefore there is no evidence for loss aversion at all. Moreover a large number of participants pay more for gains than losses suggesting that gains loom larger than losses. These results contradict the loss aversion of PT completely

Figure 12: Risk aversion within-participants group Difficult.

Notes. 20 participants. The number of participants that are more risk averse for gains, neutral or losses conditional on the probability.

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Figure 13 shows that in group Easy losses do loom larger than gains for probabilities 0.1 and 0.4. However also here a lot of people, although fewer, do treat gains and losses the same for these probabilities and are neutral. For probability 0.8 the participants are close to evenly divided. These findings tend to give some support for the loss aversion in PT. However there is no strong evidence.

Figure 13: Risk aversion within-participants group Easy.

Notes. 20 participants. The number of participants that are more risk averse for gains, neutral or losses conditional on the probability.

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5. Discussion

The main question of this thesis is whether the choice behavior of people is different when they face a different cognitive load. Moreover it specifically examines whether the choices of people are closer to PT when the cognitive load is higher. Based on current literature one expects group Easy to choose more like the expected value. DT expects group Difficult to choose more like PT because the higher cognitive load exacerbates the behavioral anomalies. With the Mann-Whitney Test this thesis finds that group Difficult is more risk averse in the gain domain than group Easy. In the loss domain there is no difference. In contrast with the existing literature both groups deviate evenly from the expected value. Also when one looks at the sample locations subject to the critical probabilities (10%, 40% and 80%) there is no difference. Moreover the comparison of the mean and median prices, and the graphical reproduction of the distribution at the critical probabilities concur with the findings of the Mann-Whitney Test. Therefore the results of this thesis find no evidence that the cognitive load exacerbates the behavioral anomalies leading to the fourfold pattern. The different cognitive load has not influenced the choice behavior.

With the Wilcoxon-Rank Sum Tests this thesis examines the fourfold pattern directly. By examining the risk attitudes of both groups, it is suggested that the choices of group Easy deviate more from the expected value towards PT than the choices of group Difficult. In group Difficult for none of the high or low probability prospects a significant difference from the expected value is observed. Although for the mean prices 5/6 prospects, except high probability gains, of this group tend towards the expectation of PT away from the expected value. In group Easy all except one prospect are significantly different from the expected value confirming PT for both mean and median prices. Only the low probability for gains is the same as the expected value. These results thus also suggest that overall there is a tendency towards PT. In Harbaugh et al. (2010) the choices of people differ substantially from their expected value for low and high probabilities. They conclude that their results are very much in line with the fourfold pattern. So this thesis confirms the results concerning the risk attitudes of Harbaugh et al. (2010).

However during the implementation of this experiment, it is obvious that the participants find the BDM procedure very difficult. It is possible that this has a large effect on the results because the different task of the two groups is not experienced as more difficult/easy by the participants. In that case every participant faces the same cognitive load and there is no difference between group Easy and group Difficult. However in all tests between the two groups, the standard deviation of group Difficult is higher than the standard deviation of group Easy which can suggest that the cognitive load in group Difficult is higher.

The effect of the cognitive load on decision making under risk : does a higher cognitive load create the fourfold pattern of risk attitudes?