Risky decisions on gains and losses with or without control of the value-function

 

 

 

Abstract

 

 

The general pattern of decision-making under risk has been disclosed, inter alia, in Kahneman and Tversky’s Prospect Theory: an analysis of decision under risk, published in Econometrica in March 1979. Individuals have been proven to behave statistically as risk-averse in the gain domain and risk-seekers in the losses. The purpose of the current experiment is to implement the Binary Lottery Procedure (BLP) to test people’s behaviors when outcome are generated differently. In other words, positing participants’ behaviors as consistent to Prospect Theory’s elicitation, we are going to see that manipulating the value-function has an effect on decision-making. When results are not expected, this effect needs to be balanced taking into account what can be due to a failure of the method or what is attributable to the weighting of probabilities. Within the experiment, we have been able to modify the hypothesis of the utility-function. Through the BLP, we manipulated this function to change the basic assumption of risk-neutrality when responding to the BLP tasks. In practice, we manipulated the value-function of three different groups: one having a linear function (risk-neutrality), another one having a concave function (risk-aversion) and the last one having an S-shape function (risk-seeking in the losses and risk-aversion in the gains).

 

On top of that, we aim to analyze more in depth some novel lotteries called nested and overlapping. We seek to what extent introducing the slightest incentive can make people change their preferences. As a matter of fact, results were significant. Both between-subjects analysis and within-subjects analysis trigger good interpretations from probability weighting perspective and manipulation through the BLP perspective. 

 

Keywords: Prospect Theory, Binary Lottery Procedure, Multiple Price List, Nested lotteries, Overlapping lotteries, Decision-making under risk, risk classification, Manipulation of risk preferences, Probability weighting. 

 

Introduction

 

 

Choices have to be made with their part of uncertainty and/or risk. Dilemma emerges when there are risks, but also when the result can be of the greatest value. Basically, if two investments have the same expected return, the one with the lower risk will be preferred by someone who is risk-averse. A risk-taking person will focus his attention on the greater possible outcome. The counterpart: the riskier investment needs to have a higher expected return in order to give an incentive for a risk-averse investor to select it. What is the process involved in decision-making that triggers risk-taking even if information and consequences are not enough well-measured, or known? Why most of the people behave like Kahneman and Tversky described: risk-averse in gains and risk-takers in losses? Is it still true when you modify their utility-function and you intend to inject a risk-neutral behavior with a linear value function, or a risk-averse behavior as a basic assumption thanks to the concavity of this function, or a risk-seeking behavior through the convexity of the curve?

 

When they published their paper in Econometrica in 1979, Daniel Kahneman and Amos Tversky introduced Prospect Theory as an analysis of decision under risk compared to a choice between prospects or gambles. They infer through their experimental research that people are risk-averse in the gain domain and risk-takers in the losses. The aim of this research project is to implement a new condition in the value-function. Controlling the value-function by the Binary Lottery Procedure will consider a linear function (control #1); a concave function (control #2) and an S-shape function (control #3). In the wake of Prospect Theory’s behavioral description, the goal is to analyze what is due to behavior inducing and what is due to outcome weighting, as far as people’s decision-making is concerned, and after having established the shape of the value-function.

 

It is stated that an event is uncertain when it is just a possibility among others and the final outcome is not yet known. Uncertainty affects economic behavior in the sense that people have to make decisions right now, not knowing, or partially knowing, what will happen in the future. Uncertainty can embody two forms. First, the risk when one has an imperfect knowledge of the outcome but has a perfect knowledge of the possibilities. And second, the proper uncertainty where one has both an imperfect knowledge of the outcomes and on their distribution. This notion of uncertainty enables to consider irrationality in the wake of decision-making in economics. On this precise point, psychology plays an important part: Kahneman and Tversky’s Prospect Theory brought some psychological factors into economics. This theory enabled to unshackle from the theoretical basis of expected utility theory; that is to say, to emancipate from what is supposed to happen for decisions under uncertainty (purely theoretical); and to lead the way to a more descriptive approach of what actually happens when those decisions (under risk) are at stake. With prospect theory, decisions are not taken in the wake of pure rationality anymore (Montier, 2002).

 

In order to test how people behave when they have been induced with a specific utility-function which is supposed to manipulate their risk-taking behavior, subjects’ preferences were controlled using the Binary Lottery Procedure developed first by Roth and Malouf (1979) and developed later by Berg, Dickhaut and O’Brien (1986); Prasnikar (2000) and Berg, Dickhaut and Rietz (2006). This procedure will be explained in the development of the theoretical part and also recalled in the results section. In order to compare preferences exhibited during different parts, the experiment consists in deriving a profile of risk-aversion and to seek to what extent people deflect from this pattern. This analysis embodies the within-subjects analysis and provide a good support to test the method implemented through the BLP. The between-subjects analysis, that comes previously, contributes to a consolidation of the method by measuring differences among groups.

 

 

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Method:

 

Sample:

 

Participants were recruited from the L.E.E.P. (Laboratoire d’Économie Expérimentale de Paris) website database. The experiment was conducted in two days with a total of 6 sessions, 3 per day. Each session lasts about 35 minutes. We had 3 groups: linear, concave and S-shape. On the first day, we ran 3 sessions in this order: linear group (16 people), concave group (17 people) and S-shape group (18 people). On the second day, we proceeded as following: linear group (18 people), linear group again (20 people) and S-shape group (20 people). On the overall, we had 109 participants (age: M=31.21; SD=13.93), composed by 74 females and 35 males. Statistics on the sample are as following:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Group 1 (linear) can be considered as a control group because in the BLP tasks, we introduced a linear value function, corresponding to a risk-neutral pattern. Comparisons will then be made within-subjects over monetary treatment and BLP treatment and between subjects in the wake of groups’ comparison. At the end of the experiment we collected the following information: age, gender, professional status (employed, unemployed, retired or student) and number of studies’ years accomplished.

 

 

 

 

 

Task design:

 

The experiment is divided into 4 parts, with 40 questions asking to choose between lotteries on the overall[1].

 

• Part 1 consists in a preference elicitation task, thanks to the Holt & Laury method. 10 pairs of lotteries with fixed outcomes: Lottery A: 2€ and 1.60€ and Lottery B: 3.85€ and 0.10€ and down going probabilities[2].

 

• Part 2 asks the preference between pairs of lotteries within 9 questions. This part is a monetary treatment involving gains.

 

• Part 3 asks preferences between pairs of lotteries within 15 questions (on the overall). This part is a BLP treatment involving gains, in which we implemented 6 questions of nested and overlapping lotteries.

 

• Part 4 asks preferences between pairs of lotteries within 6 questions. This last part is both a monetary treatment (3 questions) and a BLP treatment (3 questions) involving losses.

 

According to Holt and Laury’s method, we seek the prospect from which there is a change in the preferences[3]. Thanks to this preliminary part, we are able to classify one’s preferences pattern of risk aversion. This will enable to perform within-subjects comparisons and seek internal consistency between parts. In other words, we look for risk-aversion sensitiveness in the first part, and we investigate if the same or corresponding pattern can be found in further results, involving next parts.

 

 

 

[1] The broad experimental design is displayed in Appendix A: Useful Material

 

[2] See Section 3 for down going probabilities explanation

 

[3] See Table 2 in Section 3 for risk classification

 

 

 

 

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