Common ratio using delay

Size: px
Start display at page:

Download "Common ratio using delay"

Transcription

1 Theory Dec. (2010) 68: DOI /s Common ratio using delay Manel Baucells Franz H. Heukamp Published online: 4 January 2009 Springer Science+Business Media, LLC Abstract We present an experiment in which we add a common delay in a choice between two risky prospects. The results show that delay produces the same change in preferences as in the well-documented common ratio effect in risky lotteries. The added common delay acts as if the probabilities were divided by some common ratio. Moreover, we show that there is a strong magnitude effect, in the sense that the effect of delay depends on the magnitude of the outcome. The results are consistent with the recently introduced probability time trade-off (PTT) model by Baucells and Heukamp. We present a parameterization of the model based on the experimental results, showing that the value function exhibits increasing relative risk aversion, the weighting function is s-shaped, and the intrinsic discount rate is decreasing. Keywords Risk and time preferences Common ratio effect 1 Introduction Several authors have recognized the parallelism between the role of uncertainty and time in decision making (Rotter 1954; Mischel and Grusec 1967; Prelec and Loewenstein 1991; Quiggin and Horowitz 1995). However, most research on decision making over time and decision making under uncertainty has evolved independently. In the domain of decisions with delays, the model of discounted utility has been developed as the standard normative model albeit M. Baucells F. H. Heukamp (B) Department of Managerial Decision Sciences, IESE Business School, Avenida Pearson 21, 08034, Barcelona, Spain fheukamp@iese.edu M. Baucells mbaucells@iese.edu

2 150 M. Baucells, F. H. Heukamp with many documented deviations from it (Cruz and Muñoz 2004). Discounted utility has its equivalent normative model in the domain of risk, namely, expected utility and also many deviations from it (Wu et al. 2004). A well-known deviation from discounted utility is the common difference effect: When subjects are indifferent between a higher amount to be received later and the smaller amount to be received sooner then adding a common delay will make most subjects prefer the larger later amount (Bostic et al. 1990; Keren and Roelofsma 1995; Weber and Chapman 2005). The analogous effect in the domain of risk is the common ratio effect. When subjects are indifferent between a higher amount with lower probability and a lower amount with higher probability, then multiplying the probabilities with a common ratio will make most subjects prefer the higher amount (Kahneman and Tversky 1979). In the context of the common difference effect, Keren and Roelofsma (1995) studied the relation between delay and probability. They showed that the preference switch associated with the common difference effect can equally be observed when a common probability is applied to the delayed payoffs. In this article, we focus on the the common ratio effect and study what happens if a delay is added in a choice between two risky prospects. If the delay acts as an additional uncertainty, then we expect to observe the same results as in the common ratio effect. The experiment adds to the literature related to the time probability tradeoff. While our experiment shares some features with the experiments of Weber and Chapman (2005), it differs in important aspects of the experimental design. The results of our experiment establish a baseline of evidence that empirically relevant models about probability and time trade-off need to adhere to. The experiment involved 221 subjects and was carried out with an incentive compatible random device. Based on the experimental results, we fit a stochastic choice model through the parameterization of the probability time trade-off (PTT) model by Baucells and Heukamp (2007). 2 The common ratio using delay experiment 2.1 The common ratio effect The common ratio effect is a robust behavioral finding in decision-making under risk. Most subjects prefer, say, a sure e 300 gain to an 80% chance at e 400. However, this preference is reversed if the probabilities in both prospects are divided by a common ratio of, say, ten. If chance to gain the e 300 is 10% and the chance to gain the e 400 is 8%, then most subjects prefer the second prospect (Kahneman and Tversky 1979). In the experiment we test whether the same change in preferences can be observed if a common delay is added to the prospects. That is, instead of multiplying probabilities by a common factor of 1/10, we add a common delay of, say, 6 months. The resulting option is a sure e 300 gain to be received in 6 months, or an 80% chance at e 400 to be received in 6 months. We call this the common ratio using delay effect. If time is treated as if it were uncertain, then the delay of 6 months acts as a common probability factor that induces some subjects to switch preference towards the second option.

3 Common ratio using delay Design, incentives, and subjects Subjects were 221 participants of the MBA and EMBA programs of IESE Business School in Barcelona and Madrid. Participation in the experiment was voluntary and the experiment was self-administered through a spreadsheet. This spreadsheet was designed so that some tasks were answered by all subjects and others were randomly assigned to only some students. The goal was to test the common ratio effect and the common ratio using delay effect for different monetary amounts and delays. The total number of tasks was 25. To each student 14 tasks were presented in a first round and three additional ones in a second round 3 weeks later. Each task consisted of a choice between two prospects. A prospect was characterized by an amount x to be received at time t with probability p and otherwise zero. The stakes ranged from e 0.03 to e 300. The presentation of the tasks was randomized: The order of the tasks, within each task the presentation of alternatives 1 and 2, and the order of the attributes (x, t, p) were random. The choices used real incentives: three participants were chosen at random, and one of their preferred choices, also chosen at random, was played out with real delays and real incentives. Table 5 shows the design of the 25 tasks. 2.3 Results and discussion Table 1 shows the results for six of the tasks. In the high certainty treatment, Prospect 1involvese 9 for sure and Prospect 2 e 12 with an 80% chance. This choice is being made for delays of 0, 1, and 3 months. Similarly, in the low certainty treatment, Prospect 1 involves e 9 with a 10% chance and Prospect 2 offers e 12 with an 8% chance. Again, the delays are 0, 1, and 3 months. In the absence of delay (column t=now), we reproduce the common ratio effect: Most subjects prefer e 9 for sure in the high certainty treatment (58%) and, in violation of the independence axiom, most prefer the e 12 with an 8% chance in the low certainty treatment (78%). Consider now the high certainty treatment when the delay is added. The preference for Prospect 1 is reduced to the point that for a delay of 3 months, Prospect 2 is preferred by most of the subjects (57%). Therefore, we are able to reproduce the common Table 1 Proportion of subjects preferring the corresponding outcome for three different levels of delay. Boldface indicates results above 50% at p = 5% Delay of monetary reward t = now (%) t = 1 month (%) t = L3 months (%) High certainty 1. e 9forsure e 12 with Low certainty 1. e 9 with e 12 with

4 152 M. Baucells, F. H. Heukamp Table 2 Proportion of subjects preferring the corresponding sure outcome for two levels of delay and varying stakes Amount for sure Delay of monetary reward t = now (%) t = 3 months (%) e e e e ratio effect by adding a delay. The low certainty treatment with delay produces no surprises, as it reinforces the preference for the larger outcome. While Table 1 extracts the results for stakes of e 9 and e 12, respectively, a similar pattern holds for the other stakes (see Table 5). If a common delay is added to the two prospects of a task, then the preference for the sure prospect is always reduced. Indeed, with the exception of a e 300 prospect with a delay of 6 months, the preference for the risky prospect increases as the delay is increased. The delay seems to be perceived as additional uncertainty and therefore the sure prospect is not considered for sure anymore. As shown in Table 2, the reduction in preference for the sure prospect when adding delay ranges from a few percentage points (sure gains of e 300 or e 25) to a preference reversal (sure gains of e 9ore 3). Diverging from Weber and Chapman (2005), we show that added delay leads to similar results as dividing the probability by a common ratio. One explanation for this difference in results is our use of a simple design. We simply divide the probabilities in the high certainty case by the common ratio of 10. In contrast, Weber and Chapman (2005) use a more complicated Allais Paradox design. Also, we use relatively short delays of up to 12 months Weber and Chapman (2005) go up to 25 years that correspond to a realistic time of continuing interaction with the subjects as program participants at the business school and which excludes potential doubts about payments etc. Finally, in contrast with Weber and Chapman (2005), we offer real incentives. 3 A Model-based analysis 3.1 The PTT model Simple prospects of the form (x, t, p) are in the domain of applicability of the PTT Model axiomatized in Baucells and Heukamp (2007). The PTT model rests on the condition that additive changes in delays are perceived as multiplicative changes in probabilities, with a magnitude-dependent exchange rate between them. Specifically, it stipulates that an (x, t, p) prospect is evaluated as V (x, t, p) = w(pe r(x)t )v(x). (1) Here r(x) is an intrinsic discount rate function that can depend on the stakes, w is a probability weighting function and v(x) is a value function. The PTT model addresses

5 Common ratio using delay 153 Table 3 Proportion of subjects preferring the corresponding outcome for three different levels of probability (Keren and Roelofsma 1995, Table 1) Probability of monetary reward p = 1.0 (%) p = 0.9(%) p = 0.5(%) Imminent future A. 100 now B. 110 in 4 weeks Remote future C. 100 in 26 weeks D. 110 in 30 weeks All amounts are in Dutch Guldens. In 1995, 1 Gulden was equivalent to roughly $$0.6 only the trade-off between delay and probability. The shapes of r, w, and v are taken as given. From Eq. 1 we see that for a decision maker who follows the PTT model, a delay creates an additional subjective uncertainty in addition to the objective probability p. This also implies that in the PTT framework, the common ratio effect, i.e., dividing the probability p by some factor, is equivalent to the common delay effect, i.e., adding a delay to the current time t. This analogy has been suggested before by Prelec and Loewenstein (1991). The PTT model accommodates the experimental findings reported in this article and the ones by Keren and Roelofsma (1995) (see Table 3). Keren and Roelofsma (1995) conducted an experiment with simple prospects of the type (x, t, p) in which a common probability was added to delayed prospects. Their results demonstrated that the preference reversal observed in the common difference effect can equally be obtained by adding risk (Table 3). The PTT model is not the only way to account for preferences over triples (x, t, p). However, we now show that other forms are not possible to reconcile with the evidence we have presented here. For instance, following the logic of discounted expected utility, an intuitive formulation for valuation of a risky prospect with delay would be V (x, t, p) = f (t)w(p)v(x) (2) for given functions f, w, and v. Evaluating pairs of prospects, say A and B in Table 3, leads to the following evaluation (indices A and B refer to the attributes of the respective prospect): V (x A, t A, p A ) V (x B, t B, p B ) = f (t A )w(p A )v(x A ) f (t B )w(p B )v(x B ) For the experiments by Keren and Roelofsma (1995) (Table 3) the probability is the same for the two prospects, p = p A = p B. This yields V (x A, t A, p A ) V (x B, t B, p B ) = w(p)[ f (t A )v(x A ) f (t B )v(x B )] Thus, if prospect A is preferred to prospect B for p = 1 then this should also be the case for any other p. This is in contradiction with the change of preferences

6 154 M. Baucells, F. H. Heukamp in the experiments by Keren and Roelofsma (1995). This falsifies the formulation given in (2) as behaviorally plausible. More generally, any formulation of the type V (x, t, p) = w(p)v(x, t) is incompatible with the evidence of Table 3. Of course, the PTT model given in Eq. 1 not only is compatible with the results by Keren and Roelofsma (1995) but specifically predicts that an added common probability p will do the same as a common delay. In the case of a common delay for the two prospects (Table 1), the evaluation of V (x, t, p) = f (t)w(p)v(x) leads to V (x A, t A, p A ) V (x B, t B, p B ) = f (t)[w(p A )v(x A ) w(p B )v(x B )] Because the preference for prospect A or B should not depend on t, we again confirm that the formulation given in (2) is incompatible with the experimental results of Table 1. The PTT model is again not only compatible with the results reported in this article but predicts that an added common delay causes the same changes in preferences as reducing the probability by a common ratio. Together, the results of Keren and Roelofsma (1995) on common delay with risk and the ones reported here on common ratio with delay show that the probability and time dimensions cannot be separated in an empirically relevant representation of V (x, t, p). 3.2 Magnitude effects An additional view on the effects of the stakes can be obtained from Table 4. The table displays the percentage of subjects who prefer the sure gain for all the tasks in the high certainty treatment (14 out of the total 25 tasks shown in Table 5). The stakes of the risky prospect (Prospect 2) are always 4/3 of the stakes of the sure prospect (Prospect 1) and its probability (p 2 ) is always 80%. By way of example, the e 300 column shows the percentage of subjects that prefer e 300 for sure to e 400 with an 80% chance, for the different delays. In this two-way table, we observe the effect of delay (rows) and magnitude (columns). Let us consider these two effects separately. As discussed before, for any fixed amount (or column), the preference for the sure prospect decreases with the delay. In addition, the preference for the sure prospect decreases as the stakes are reduced. This magnitude effect can be explained in two Table 4 Percentage of subjects who prefer the sure prospect (Prospect 1) as a function of x 1 and t t\x 1 e300 (%) e25 (%) e9(%) e3 (%) e0.3 (%) e0.03 (%) The stakes of the risky prospect (Prospect 2) are always 4/3 of the stakes of the sure prospect and its probability (p 2 )isalways0.8

7 Common ratio using delay 155 Table 5 Task design and results (last two columns) of the experiment of common ratio with delay # x 1 [e] t 1 [months] p 1 [1] x 2 [e] t 2 [months] p 2 [1] N 1[%] 2[%] Task design Boldface indicates results above 50% at p = 5%. Columns 2 4 show the attributes (x 1, t 1, p 1 )ofprospect 1 and columns 5 7 the same attributes for Prospect 2. Columns 8 10 show the number of subjects who were presented with the task (N) and the percentages that preferred each prospect ways. It could be related to the shape of the value function of a subject. But if the value function were to exhibit constant relative risk aversion, then a multiplicative scaling of the payoffs would not alter the preferences (Pratt 1964) and the percentage of subjects choosing x for sure would not depend on x. This is not the pattern observed in the first row of Table 4. Hence, this first row alone rules out a power value function. The observed results rather indicate that subjects value function is consistent with increasing relative risk aversion. This same result was obtained in an experiment with real and similarly large stakes as ours by Holt and Laury (2002). Table 4 also shows the effect of time (row). Fixing a column, let us consider the effect of adding a delay. If discount rates were constant, then the decay rates of preference for the sure option should be the same, independent of the magnitude of outcomes.

8 156 M. Baucells, F. H. Heukamp However, what we observe is that the temporal discount rate is an increasing function of the magnitude of the payoffs. As the stakes increase, subjects may be more patient (Thaler 1981). In Table 4, this effect can be observed in the interaction between the effect of the delay, t, and the outcome size. The preference for the sure outcome is more stable with respect to a delay for high stakes (e.g. e 300) than for lower stakes (e.g. e 25 or even more for e 9). 3.3 A stochastic choice model Qualitatively, we have argued that the results of Tables 1 and 3 are consistent with the PTT model. This suggests that a parametric specification of the model can have some predictive value and provide additional insight. In the following, we estimate such a parametric model. For the three functions of the PTT model, we choose the following specifications. For the value function, we choose the expo-power form used in Holt and Laury (2002): v(x) = 1 exp( αx1 β ) α (3) As explained before, both Holt and Laury (2002) and our results indicate that a simple power form would not do justice to the data, which exhibits increasing relative risk aversion. With respect to the probability weighting function, we choose the form proposed by Prelec (1998). In Baucells and Heukamp (2007) we show that this function is particularly suited for our application, as its associated time discount function has a direct time acceleration interpretation. Hence, w(p) = exp( ( lnp) γ ) (4) Finally, regarding the intrinsic discount rate function, the only constraint we impose is that it should be non-increasing in order to capture the well-established absolute magnitude effect. We suggest a very simple one-parameter form: r(x) = R/ x (5) Of course, if x tends to zero, then the intrinsic discount rate tends to infinity. In summary, our parametric specification is: ( V (x, t, p) = w pe r(x)t) ( ( ) Rt γ ) 1 exp( αx 1 β v(x) = exp x lnp ) α which implies the estimation of four parameters: R, α, β, and γ. To estimate the parameters, we use the results of Task 1 20 presented in Table 5 (for which at each level of the stakes high and low certainty treatments are available). We assume that the logarithm of the odds of preferring Prospect 1 over Prospect 2 is linearly related to the relative difference in valuation: (6)

9 Common ratio using delay 157 Ln [ q / (1-q) ] ( V1 - V2 ) / (V1+V2) Fig. 1 Best fit line for the stochastic choice model based on the results from Tasks ( ) q ln = V (x 1, t 1, p 1 ) V (x 2, t 2, p 2 ) 1 q V (x 1, t 1, p 1 ) + V (x 2, t 2, p 2 ) (7) where q is the probability of choosing Prospect 1. Minimizing the sum of the squared errors, the best fit is obtained for the following values of parameters: R = 1.52,α = , β = 0.03, and γ = 0.7. Figure 1 shows the fit of the model. The γ of the weighting function matches closely values in the literature. The α of the expo-power value function corresponds to a comparatively small risk tolerance of around e 550. Our model is richer than that of Holt and Laury (2002), as the risk attitude of our decision maker is given by the combined effect of both w and v (Holt and Laury (2002) do not include probability weighting). Also, the PTT model captures two possible effects of payoff magnitude, one associated with v(x) and a second associated with r(x). Finally, a sub-proportional weighting function would explain simultaneously the common ratio effect and the common difference effect. 4 Summary and concluding remarks The experiment presented in this article showed that a common delay in simple prospects leads to the same changes in preferences as the common ratio effect. This adds to the experimental literature and proves that common ratio effect and common delay effect are intimately related. The PTT model predicts the results presented in this article and is also compatible with earlier work by Keren and Roelofsma (1995). The parameterization of the PTT model that we obtain leads to reasonable specifications of the weighting function and value function. We observe magnitude effects that can be explained by the intrinsic discount rate function of the PTT model.

10 158 M. Baucells, F. H. Heukamp References Baucells, M., & Heukamp, F. (2007). Probability and Time Trade-off. IESE Business School Working Paper. Bostic, R., Herrnstein, R., & Luce, R. (1990). The effect on the preference-reversal phenomenon of using choice indifferences. Journal of Economic Behavior and Organization, 13(2), Cruz, S., & Muñoz, M. J. (2004). An analysis of the anomalies in traditional discounting models. International Journal of Psychology and Psychological Therapy, 4(1), Holt, C., & Laury, S. (2002). Risk Aversion and incentive effects. American Economic Review, 92(5), Kahneman, D., & Tversky, A. (1979). Prospect theory: An analysis of decision under risk. Econometrica, 47(2), Keren, G., & Roelofsma, P. (1995). Immediacy and certainty in intertemporal choice. Organizational Behavior And Human Decision Processes, 63(3), Mischel, W., & Grusec, J. (1967). Waiting for rewards and punishments: Effects of time and probability in choice. Journal of Personality and Social Psychology, 5, Pratt, J. (1964). Risk aversion in the small and in the large. Econometrica, 32(1 2), Prelec, D. (1998). The Probability weighting function. Econometrica, 66(3), Prelec, D., & Loewenstein, G. (1991). Decision-making over time and under uncertainty A common approach. Management Science, 37(7), Quiggin, J., & Horowitz, J. (1995). Time And Risk. Journal of Risk And Uncertainty, 10(1), Rotter, J. B. (1954). Social learning and clinical psychology. New Jersey: Prentice Hall. Thaler, R. H. (1981). Some empirical-evidence On dynamic inconsistency. Economics Letters, 8(3), Weber, B. J., & Chapman, G. B. (2005). The combined effects of risk and time on choice: Does uncertainty eliminate the immediacy effect? Does delay eliminate the certainty effect? Organizational Behavior and Human Decision Processes, 96(2), Wu, G., Zhang, J., & Gonzalez, R. (2004). Decision under risk. In D. Koehler, N. Harvey (Eds.), Blackwell handbook of judgment and decision making (pp ). Oxford: Blackwell.

A Relationship between Risk and Time Preferences

A Relationship between Risk and Time Preferences A Relationship between Risk and Time Preferences Kota SAITO Department of Economics, Northwestern University kotasaito@northwestern.edu June 12, 2009 Abstract This paper investigates a general relationship

More information

Weighted temporal utility

Weighted temporal utility Econ Theory DOI 10.1007/s00199-017-1058-8 RESEARCH ARTICLE Weighted temporal utility Anke Gerber 1 Kirsten I. M. Rohde 2,3 Received: 7 June 2016 / Accepted: 25 May 2017 The Author(s) 2017. This article

More information

Quantum Decision Theory

Quantum Decision Theory Quantum Decision Theory V.I. Yukalov and D. Sornette Department of Management, Technology and Economics\ ETH Zürich Plan 1. Classical Decision Theory 1.1. Notations and definitions 1.2. Typical paradoxes

More information

Recursive Ambiguity and Machina s Examples

Recursive Ambiguity and Machina s Examples Recursive Ambiguity and Machina s Examples David Dillenberger Uzi Segal May 0, 0 Abstract Machina (009, 0) lists a number of situations where standard models of ambiguity aversion are unable to capture

More information

Homework #6 (10/18/2017)

Homework #6 (10/18/2017) Homework #6 (0/8/207). Let G be the set of compound gambles over a finite set of deterministic payoffs {a, a 2,...a n } R +. A decision maker s preference relation over compound gambles can be represented

More information

This paper introduces time-tradeoff (TTO) sequences as a general tool to analyze intertemporal choice. We

This paper introduces time-tradeoff (TTO) sequences as a general tool to analyze intertemporal choice. We MANAGEMENT SCIENCE Vol. 56, No. 11, November 2010, pp. 2015 2030 issn 0025-1909 eissn 1526-5501 10 5611 2015 informs doi 10.1287/mnsc.1100.1219 2010 INFORMS Time-Tradeoff Sequences for Analyzing Discounting

More information

Comments on prospect theory

Comments on prospect theory Comments on prospect theory Abstract Ioanid Roşu This note presents a critique of prospect theory, and develops a model for comparison of two simple lotteries, i.e. of the form ( x 1, p1; x 2, p 2 ;...;

More information

Week of May 5, lecture 1: Expected utility theory

Week of May 5, lecture 1: Expected utility theory Microeconomics 3 Andreas Ortmann, Ph.D. Summer 2003 (420 2) 240 05 117 andreas.ortmann@cerge-ei.cz http://home.cerge-ei.cz/ortmann Week of May 5, lecture 1: Expected utility theory Key readings: MWG 6.A.,

More information

Prospect Theory: An Analysis of Decision Under Risk

Prospect Theory: An Analysis of Decision Under Risk Prospect Theory: An Analysis of Decision Under Risk Daniel Kahneman and Amos Tversky(1979) Econometrica, 47(2) Presented by Hirofumi Kurokawa(Osaka Univ.) 1 Introduction This paper shows that there are

More information

Recursive Ambiguity and Machina s Examples

Recursive Ambiguity and Machina s Examples Recursive Ambiguity and Machina s Examples David Dillenberger Uzi Segal January 9, 204 Abstract Machina (2009, 202) lists a number of situations where Choquet expected utility, as well as other known models

More information

The nature of utility is controversial. Whereas decision theory commonly assumes that utility is context

The nature of utility is controversial. Whereas decision theory commonly assumes that utility is context MANAGEMENT SCIENCE Vol. 59, No. 9, September 2013, pp. 2153 2169 ISSN 0025-1909 (print) ISSN 1526-5501 (online) http://dx.doi.org/10.1287/mnsc.1120.1690 2013 INFORMS Is There One Unifying Concept of Utility?

More information

On the Necessity of Using Lottery Qualities*

On the Necessity of Using Lottery Qualities* Abstract Working paper 04-03 June 2004 On the Necessity of Using Lottery Qualities* Yves Alarie and Georges Dionne HEC Montréal The aim of this paper is to propose a model of decision making for lotteries.

More information

Choice under Uncertainty

Choice under Uncertainty In the Name of God Sharif University of Technology Graduate School of Management and Economics Microeconomics 2 44706 (1394-95 2 nd term) Group 2 Dr. S. Farshad Fatemi Chapter 6: Choice under Uncertainty

More information

Projective Expected Utility

Projective Expected Utility Projective Expected Utility Pierfrancesco La Mura Department of Microeconomics and Information Systems Leipzig Graduate School of Management (HHL) April 24, 2006 1 Introduction John von Neumann (1903-1957)

More information

Uniform Sources of Uncertainty for Subjective Probabilities and

Uniform Sources of Uncertainty for Subjective Probabilities and Uniform Sources of Uncertainty for Subjective Probabilities and Ambiguity Mohammed Abdellaoui (joint with Aurélien Baillon and Peter Wakker) 1 Informal Central in this work will be the recent finding of

More information

Are Probabilities Used in Markets? 1

Are Probabilities Used in Markets? 1 Journal of Economic Theory 91, 8690 (2000) doi:10.1006jeth.1999.2590, available online at http:www.idealibrary.com on NOTES, COMMENTS, AND LETTERS TO THE EDITOR Are Probabilities Used in Markets? 1 Larry

More information

RECURSIVE AMBIGUITY AND MACHINA S EXAMPLES 1. INTRODUCTION

RECURSIVE AMBIGUITY AND MACHINA S EXAMPLES 1. INTRODUCTION INTERNATIONAL ECONOMIC REVIEW Vol. 56, No., February 05 RECURSIVE AMBIGUITY AND MACHINA S EXAMPLES BY DAVID DILLENBERGER AND UZI SEGAL University of Pennsylvania, U.S.A.; Boston College, U.S.A., and Warwick

More information

An Empirical Test of Gain-Loss Separability in Prospect Theory

An Empirical Test of Gain-Loss Separability in Prospect Theory An Empirical Test of Gain-Loss Separability in Prospect Theory George Wu Alex B. Markle November 26, 2007 Abstract We investigate a basic premise of prospect theory, that the valuation of gains and losses

More information

Optimal Cognitive Processes for Lotteries. by Yves Alarie and Georges Dionne Working Paper March 2001 ISSN :

Optimal Cognitive Processes for Lotteries. by Yves Alarie and Georges Dionne Working Paper March 2001 ISSN : Optimal Cognitive Processes for Lotteries by Yves Alarie and Georges Dionne Working Paper 01-02 March 2001 ISSN : 1206-3304 Financial support by CRSH (Canada) and FCAR (Québec) is acknowledged. Optimal

More information

Modelling Choice and Valuation in Decision Experiments. Graham Loomes, University of Warwick, UK.

Modelling Choice and Valuation in Decision Experiments. Graham Loomes, University of Warwick, UK. Modelling Choice and Valuation in Decision Experiments Graham Loomes, University of Warwick, UK. E-mail g.loomes@warwick.ac.uk December 2009 Abstract This paper develops a parsimonious descriptive model

More information

Certainty Equivalent Representation of Binary Gambles That Are Decomposed into Risky and Sure Parts

Certainty Equivalent Representation of Binary Gambles That Are Decomposed into Risky and Sure Parts Review of Economics & Finance Submitted on 28/Nov./2011 Article ID: 1923-7529-2012-02-65-11 Yutaka Matsushita Certainty Equivalent Representation of Binary Gambles That Are Decomposed into Risky and Sure

More information

Intertemporal Risk Aversion, Stationarity, and Discounting

Intertemporal Risk Aversion, Stationarity, and Discounting Traeger, CES ifo 10 p. 1 Intertemporal Risk Aversion, Stationarity, and Discounting Christian Traeger Department of Agricultural & Resource Economics, UC Berkeley Introduce a more general preference representation

More information

DECISIONS UNDER UNCERTAINTY

DECISIONS UNDER UNCERTAINTY August 18, 2003 Aanund Hylland: # DECISIONS UNDER UNCERTAINTY Standard theory and alternatives 1. Introduction Individual decision making under uncertainty can be characterized as follows: The decision

More information

Cautious Expected Utility and the Certainty Effect

Cautious Expected Utility and the Certainty Effect Cautious Expected Utility and the Certainty Effect Simone Cerreia-Vioglio David Dillenberger Pietro Ortoleva February 2014 Abstract Many violations of the Independence axiom of Expected Utility can be

More information

TIME-TRADEOFF SEQUENCES FOR ANALYZING DISCOUNTING AND TIME INCONSISTENCY

TIME-TRADEOFF SEQUENCES FOR ANALYZING DISCOUNTING AND TIME INCONSISTENCY TIME-TRADEOFF SEQUENCES FOR ANALYZING DISCOUNTING AND TIME INCONSISTENCY Arthur E. Attema a, Han Bleichrodt b, Kirsten I.M. Rohde b, Peter P. Wakker b a :Dept Health Policy & Management, Erasmus University,

More information

Some Remarks About the Probability Weighting Function. by Yves Alarie and Georges Dionne Working Paper December 1998 ISSN :

Some Remarks About the Probability Weighting Function. by Yves Alarie and Georges Dionne Working Paper December 1998 ISSN : Some Remarks About the Probability Weighting Function by Yves Alarie and Georges Dionne Working Paper 98-17 December 1998 ISSN : 1206-3304 The authors would like to thank the critical collaboration of

More information

Explaining the harmonic sequence paradox. by Ulrich Schmidt, and Alexander Zimper

Explaining the harmonic sequence paradox. by Ulrich Schmidt, and Alexander Zimper Explaining the harmonic sequence paradox by Ulrich Schmidt, and Alexander Zimper No. 1724 August 2011 Kiel Institute for the World Economy, Hindenburgufer 66, 24105 Kiel, Germany Kiel Working Paper No.

More information

A simple derivation of Prelec s probability weighting function

A simple derivation of Prelec s probability weighting function A simple derivation of Prelec s probability weighting function Ali al-nowaihi Sanjit Dhami June 2005 Abstract Since Kahneman and Tversky (1979), it has been generally recognized that decision makers overweight

More information

Glimcher Decision Making

Glimcher Decision Making Glimcher Decision Making Signal Detection Theory With Gaussian Assumption Without Gaussian Assumption Equivalent to Maximum Likelihood w/o Cost Function Newsome Dot Task QuickTime and a Video decompressor

More information

CERGE-EI. Back to the St. Petersburg Paradox? Pavlo Blavatskyy. WORKING PAPER SERIES (ISSN ) Electronic Version

CERGE-EI. Back to the St. Petersburg Paradox? Pavlo Blavatskyy. WORKING PAPER SERIES (ISSN ) Electronic Version Back to the St. Petersburg Paradox? Pavlo Blavatskyy CERGE-EI Charles University Center for Economic Research and Graduate Education Academy of Sciences of the Czech Republic Economics Institute WORKING

More information

Towards a Theory of Decision Making without Paradoxes

Towards a Theory of Decision Making without Paradoxes Towards a Theory of Decision Making without Paradoxes Roman V. Belavkin (R.Belavkin@mdx.ac.uk) School of Computing Science, Middlesex University London NW4 4BT, United Kingdom Abstract Human subjects often

More information

Canada Research Chair in Risk Management Working paper LOTTERY QUALITIES. Yves Alarie * and Georges Dionne * May 4, 2006

Canada Research Chair in Risk Management Working paper LOTTERY QUALITIES. Yves Alarie * and Georges Dionne * May 4, 2006 Canada Research Chair in Risk Management Working paper 06-07 LOTTERY QUALITIES Yves Alarie * and Georges Dionne * May 4, 2006 Abstract The aim of this paper is to propose a model of decision-making for

More information

Eliciting Gul s Theory of Disappointment Aversion by the Tradeoff Method 1 HAN BLEICHRODT. March 2007

Eliciting Gul s Theory of Disappointment Aversion by the Tradeoff Method 1 HAN BLEICHRODT. March 2007 Eliciting Gul s Theory of Disappointment Aversion by the Tradeoff Method 1 MOHAMMED ABDELLAOUI Maison de la Recherche de l ESTP, GRID, 30 avenue du Président Wilson, 94230 Cachan, France, abdellaoui@grid.ensam.estp.fr.

More information

Reduction Invariance and Prelec's Weighting Functions

Reduction Invariance and Prelec's Weighting Functions Journal of Mathematical Psychology 45, 167179 (2001) doi:10.1006jmps.1999.1301, available online at http:www.idealibrary.com on Reduction Invariance and Prelec's Weighting Functions R. Duncan Luce University

More information

Economic uncertainty principle? Alexander Harin

Economic uncertainty principle? Alexander Harin Economic uncertainty principle? Alexander Harin This preliminary paper presents a qualitative description of the economic principle of (hidden, latent) uncertainty. Mathematical expressions of principle,

More information

Evidence against prospect theories in gambles with positive, negative, and mixed consequences

Evidence against prospect theories in gambles with positive, negative, and mixed consequences Journal of Economic Psychology 27 (2006) 737 761 www.elsevier.com/locate/joep Evidence against prospect theories in gambles with positive, negative, and mixed consequences Michael H. Birnbaum * Department

More information

Great Expectations. Part I: On the Customizability of Generalized Expected Utility*

Great Expectations. Part I: On the Customizability of Generalized Expected Utility* Great Expectations. Part I: On the Customizability of Generalized Expected Utility* Francis C. Chu and Joseph Y. Halpern Department of Computer Science Cornell University Ithaca, NY 14853, U.S.A. Email:

More information

Endogenizing Prospect Theory s Reference Point. by Ulrich Schmidt and Horst Zank

Endogenizing Prospect Theory s Reference Point. by Ulrich Schmidt and Horst Zank Endogenizing Prospect Theory s Reference Point by Ulrich Schmidt and Horst Zank No. 1611 March 2010 Kiel Institute for the World Economy, Hindenburgufer 66, 24105 Kiel, Germany Kiel Working Paper No. 1611

More information

If individuals have to evaluate a sequence of lotteries, their judgment is influenced by the

If individuals have to evaluate a sequence of lotteries, their judgment is influenced by the Prospect Theory, Mental Accounting, and Differences in Aggregated and Segregated Evaluation of Lottery Portfolios Thomas Langer Martin Weber Universität Mannheim, Lehrstuhl für Bankbetriebslehre, L 5,

More information

Recitation 7: Uncertainty. Xincheng Qiu

Recitation 7: Uncertainty. Xincheng Qiu Econ 701A Fall 2018 University of Pennsylvania Recitation 7: Uncertainty Xincheng Qiu (qiux@sas.upenn.edu 1 Expected Utility Remark 1. Primitives: in the basic consumer theory, a preference relation is

More information

MATH 446/546 Homework 2: Due October 8th, 2014

MATH 446/546 Homework 2: Due October 8th, 2014 MATH 446/546 Homework 2: Due October 8th, 2014 Answer the following questions. Some of which come from Winston s text book. 1. We are going to invest $1,000 for a period of 6 months. Two potential investments

More information

Modelling Choice and Valuation in Decision Experiments. Graham Loomes, University of East Anglia, UK. May 2008.

Modelling Choice and Valuation in Decision Experiments. Graham Loomes, University of East Anglia, UK.  May 2008. Modelling Choice and Valuation in Decision Experiments Graham Loomes, University of East Anglia, UK. E-mail g.loomes@uea.ac.uk May 2008 Abstract This paper develops a parsimonious descriptive model of

More information

Cautious Expected Utility and the Certainty Effect

Cautious Expected Utility and the Certainty Effect Cautious Expected Utility and the Certainty Effect Simone Cerreia-Vioglio David Dillenberger Pietro Ortoleva August 2014 Abstract Many violations of the Independence axiom of Expected Utility can be traced

More information

An Experimental Investigation of Violations of Transitivity. in Choice under Uncertainty

An Experimental Investigation of Violations of Transitivity. in Choice under Uncertainty An Experimental Investigation of Violations of Transitivity in Choice under Uncertainty 1 Michael H. Birnbaum Department of Psychology California State University, Fullerton Ulrich Schmidt Department of

More information

Stochastic Utility Theorem

Stochastic Utility Theorem Institute for Empirical Research in Economics University of Zurich Working Paper Series ISSN 44-0459 Working Paper No. Stochastic Utility Theorem Pavlo R. Blavatskyy Januar 007 Stochastic Utility Theorem

More information

Allais Paradox. The set of prizes is X = {$0, $1, 000, 000, $5, 000, 000}.

Allais Paradox. The set of prizes is X = {$0, $1, 000, 000, $5, 000, 000}. 1 Allais Paradox The set of prizes is X = {$0, $1, 000, 000, $5, 000, 000}. Which probability do you prefer: p 1 = (0.00, 1.00, 0.00) or p 2 = (0.01, 0.89, 0.10)? Which probability do you prefer: p 3 =

More information

Problem Set 4 - Solution Hints

Problem Set 4 - Solution Hints ETH Zurich D-MTEC Chair of Risk & Insurance Economics (Prof. Mimra) Exercise Class Spring 206 Anastasia Sycheva Contact: asycheva@ethz.ch Office Hour: on appointment Zürichbergstrasse 8 / ZUE, Room F2

More information

Dragon-kings. Quantum Decision Theory with Prospect Interference and Entanglement. Financial Crisis Observatory.

Dragon-kings. Quantum Decision Theory with Prospect Interference and Entanglement. Financial Crisis Observatory. Quantum Decision Theory with Prospect Interference and Entanglement Didier Sornette (ETH Zurich) Dragon-kings (with V.I. Yukalov + PhD M. Favre and T. Kovalenko) Professor of Entrepreneurial Risks at ETH

More information

Evidence against Rank-Dependent Utility Theories: Tests of Cumulative Independence, Interval Independence, Stochastic Dominance, and Transitivity

Evidence against Rank-Dependent Utility Theories: Tests of Cumulative Independence, Interval Independence, Stochastic Dominance, and Transitivity Organizational Behavior and Human Decision Processes Vol. 77, No. 1, January, pp. 44 83, 1999 Article ID obhd.1998.2816, available online at http://www.idealibrary.com on Evidence against Rank-Dependent

More information

DEPARTMENT OF ECONOMICS A NOTE ON THE LOEWENSTEIN-PRELEC THEORY OF INTERTEMPORAL CHOICE

DEPARTMENT OF ECONOMICS A NOTE ON THE LOEWENSTEIN-PRELEC THEORY OF INTERTEMPORAL CHOICE DEPARTMENT OF ECONOMICS A NOTE ON THE LOEWENSTEIN-PRELEC THEORY OF INTERTEMPORAL CHOICE Ali al-nowaihi, University of Leicester, UK Sanjit Dhami, University of Leicester, UK Working Paper No. 05/18 July

More information

Full Surplus Extraction and Costless Information Revelation in Dynamic Environments. Shunya NODA (University of Tokyo)

Full Surplus Extraction and Costless Information Revelation in Dynamic Environments. Shunya NODA (University of Tokyo) Full Surplus Extraction and Costless Information Revelation in Dynamic Environments Shunya NODA (University of Tokyo) Outline 1. Introduction. Two-Period Example 3. Three-Period Example 4. Model 5. Main

More information

Expected Utility Framework

Expected Utility Framework Expected Utility Framework Preferences We want to examine the behavior of an individual, called a player, who must choose from among a set of outcomes. Let X be the (finite) set of outcomes with common

More information

A Truth-Serum for Non-Bayesians: Correcting Proper Scoring Rules for Risk Attitudes 1

A Truth-Serum for Non-Bayesians: Correcting Proper Scoring Rules for Risk Attitudes 1 A Truth-Serum for Non-Bayesians: Correcting Proper Scoring Rules for Risk Attitudes 1 Theo Offerman a, Joep Sonnemans a, Gijs van de Kuilen a, & Peter P. Wakker b a: CREED, Dept. of Economics, University

More information

3 Intertemporal Risk Aversion

3 Intertemporal Risk Aversion 3 Intertemporal Risk Aversion 3. Axiomatic Characterization This section characterizes the invariant quantity found in proposition 2 axiomatically. The axiomatic characterization below is for a decision

More information

Game Theory without Decision-Theoretic Paradoxes

Game Theory without Decision-Theoretic Paradoxes Game Theory without Decision-Theoretic Paradoxes Pierfrancesco La Mura Department of Economics and Information Systems HHL - Leipzig Graduate School of Management Jahnallee 59, 04109 Leipzig (Germany)

More information

Ambiguity Framed. Mark Schneider, Jonathan Leland, and Nathaniel T. Wilcox

Ambiguity Framed. Mark Schneider, Jonathan Leland, and Nathaniel T. Wilcox Ambiguity Framed Mark Schneider, Jonathan Leland, and Nathaniel T. Wilcox In his exposition of subjective expected utility theory, Savage (1954) proposed that the Allais paradox could be reduced if it

More information

Measurable Ambiguity. with Wolfgang Pesendorfer. August 2009

Measurable Ambiguity. with Wolfgang Pesendorfer. August 2009 Measurable Ambiguity with Wolfgang Pesendorfer August 2009 A Few Definitions A Lottery is a (cumulative) probability distribution over monetary prizes. It is a probabilistic description of the DMs uncertain

More information

Squeezing Every Ounce of Information from An Experiment: Adaptive Design Optimization

Squeezing Every Ounce of Information from An Experiment: Adaptive Design Optimization Squeezing Every Ounce of Information from An Experiment: Adaptive Design Optimization Jay Myung Department of Psychology Ohio State University UCI Department of Cognitive Sciences Colloquium (May 21, 2014)

More information

Probabilistic Subjective Expected Utility. Pavlo R. Blavatskyy

Probabilistic Subjective Expected Utility. Pavlo R. Blavatskyy Probabilistic Subjective Expected Utility Pavlo R. Blavatskyy Institute of Public Finance University of Innsbruck Universitaetsstrasse 15 A-6020 Innsbruck Austria Phone: +43 (0) 512 507 71 56 Fax: +43

More information

An Experimental Investigation of Violations of Transitivity in Choice under Uncertainty

An Experimental Investigation of Violations of Transitivity in Choice under Uncertainty 1 An Experimental Investigation of Violations of Transitivity in Choice under Uncertainty by Michael H. Birnbaum and Ulrich Schmidt No. 1396 January 2008 2 Kiel Institute for the World Economy Duesternbrooker

More information

AUSI expected utility: An anticipated utility theory of relative disappointment aversion

AUSI expected utility: An anticipated utility theory of relative disappointment aversion Journal of Economic Behavior & Organization Vol. 37 (1998) 277±290 AUSI expected utility: An anticipated utility theory of relative disappointment aversion Simon Grant *, Atsushi Kajii Australian National

More information

Overbidding in First-Price Auctions: Risk Aversion vs. Probability Weighting Function

Overbidding in First-Price Auctions: Risk Aversion vs. Probability Weighting Function Overbidding in First-Price Auctions: Risk Aversion vs. Probability Weighting Function Olivier Armantier Nicolas Treich January 2008 Abstract There is a long standing debate about whether or not risk aversion

More information

Agrowing body of qualitative evidence shows that loss aversion, a phenomenon formalized in prospect

Agrowing body of qualitative evidence shows that loss aversion, a phenomenon formalized in prospect MANAGEMENT SCIENCE Vol. 53, No. 10, October 2007, pp. 1659 1674 issn 0025-1909 eissn 1526-5501 07 5310 1659 informs doi 10.1287/mnsc.1070.0711 2007 INFORMS Loss Aversion Under Prospect Theory: A Parameter-Free

More information

RUNNING HEAD: COMPUTATIONAL MODEL OF DECISION WEIGHTS. A computational model of the attention process used to generate decision weights

RUNNING HEAD: COMPUTATIONAL MODEL OF DECISION WEIGHTS. A computational model of the attention process used to generate decision weights Computational model of decision weights 1 RUNNING HEAD: COMPUTATIONAL MODEL OF DECISION WEIGHTS A computational model of the attention process used to generate decision weights Joseph G. Johnson Miami

More information

Large Sharpening Intertemporal Prospect Theory

Large Sharpening Intertemporal Prospect Theory Applied Mathematical Sciences, Vol. 1, 2007, no. 34, 1695-1701 Large Sharpening Intertemporal Prospect Theory Pushpa Rathie Department of Statistics, University of Brasilia 70910-900 Brasilia DF, Brazil

More information

The Improbability of a General, Rational and Descriptively Adequate Theory of Decision Under Risk. Graham Loomes, University of East Anglia, UK.

The Improbability of a General, Rational and Descriptively Adequate Theory of Decision Under Risk. Graham Loomes, University of East Anglia, UK. NB: This is an early version of a paper which subsequently evolved into Modeling Choice and Valuation in Decision Experiments, due to appear in the Psychological Review in 2010 or 2011. In the course of

More information

Econometric Causality

Econometric Causality Econometric (2008) International Statistical Review, 76(1):1-27 James J. Heckman Spencer/INET Conference University of Chicago Econometric The econometric approach to causality develops explicit models

More information

ECO 317 Economics of Uncertainty Fall Term 2009 Notes for lectures 3. Risk Aversion

ECO 317 Economics of Uncertainty Fall Term 2009 Notes for lectures 3. Risk Aversion Reminders ECO 317 Economics of Uncertainty Fall Term 009 Notes for lectures 3. Risk Aversion On the space of lotteries L that offer a finite number of consequences (C 1, C,... C n ) with probabilities

More information

Empirical evaluation of third-generation prospect theory

Empirical evaluation of third-generation prospect theory Theory Dec. DOI 10.1007/s18-017-9607-y Empirical evaluation of third-generation prospect theory Michael H. Birnbaum 1 Springer Science+Business Media New York 2017 Abstract Third generation prospect theory

More information

An Axiomatic Model of Reference Dependence under Uncertainty. Yosuke Hashidate

An Axiomatic Model of Reference Dependence under Uncertainty. Yosuke Hashidate An Axiomatic Model of Reference Dependence under Uncertainty Yosuke Hashidate Abstract This paper presents a behavioral characteization of a reference-dependent choice under uncertainty in the Anscombe-Aumann

More information

A note on the connection between the Tsallis thermodynamics and cumulative prospect theory

A note on the connection between the Tsallis thermodynamics and cumulative prospect theory A note on the connection between the Tsallis thermodynamics and cumulative prospect theory Abstract: This note presents eplicitly a strong connection between the Tsallis thermodynamics and the so-called

More information

The Expected Utility Model

The Expected Utility Model 1 The Expected Utility Model Before addressing any decision problem under uncertainty, it is necessary to build a preference functional that evaluates the level of satisfaction of the decision maker who

More information

Psychology and Economics (Lecture 3)

Psychology and Economics (Lecture 3) Psychology and Economics (Lecture 3) Xavier Gabaix February 10, 2003 1 Discussion of traditional objections In the real world people would get it right Answer: there are many non-repeated interactions,

More information

Ambiguity Aversion: An Axiomatic Approach Using Second Order Probabilities

Ambiguity Aversion: An Axiomatic Approach Using Second Order Probabilities Ambiguity Aversion: An Axiomatic Approach Using Second Order Probabilities William S. Neilson Department of Economics University of Tennessee Knoxville, TN 37996-0550 wneilson@utk.edu April 1993 Abstract

More information

Incremental Preference Elicitation for Decision Making Under Risk with the Rank-Dependent Utility Model

Incremental Preference Elicitation for Decision Making Under Risk with the Rank-Dependent Utility Model Incremental Preference Elicitation for Decision Making Under Risk with the Rank-Dependent Utility Model Patrice Perny Sorbonne Universités UPMC Univ Paris 06 CNRS, LIP6 UMR 7606 Paris, France Paolo Viappiani

More information

Compound Invariance Implies Prospect Theory for Simple Prospects

Compound Invariance Implies Prospect Theory for Simple Prospects Compound Invariance Implies Prospect Theory for Simple Prospects Han Bleichrodt a, Amit Kothiyal b, Drazen Prelec c, & Peter P. Wakker d March, 2013 a, d: School of Economics, Erasmus University, P.O.

More information

Cautious Expected Utility and the Certainty Effect

Cautious Expected Utility and the Certainty Effect Cautious Expected Utility and the Certainty Effect Simone Cerreia-Vioglio David Dillenberger Pietro Ortoleva May 2013 Abstract One of the most prominently observed behavioral patterns in decision making

More information

Economics 201B Economic Theory (Spring 2017) Bargaining. Topics: the axiomatic approach (OR 15) and the strategic approach (OR 7).

Economics 201B Economic Theory (Spring 2017) Bargaining. Topics: the axiomatic approach (OR 15) and the strategic approach (OR 7). Economics 201B Economic Theory (Spring 2017) Bargaining Topics: the axiomatic approach (OR 15) and the strategic approach (OR 7). The axiomatic approach (OR 15) Nash s (1950) work is the starting point

More information

Foundations for Prospect Theory Through Probability Midpoint Consistency

Foundations for Prospect Theory Through Probability Midpoint Consistency Foundations for Prospect Theory Through Probability Midpoint Consistency by Katarzyna Werner and Horst Zank 1 Economics, School of Social Sciences, The University of Manchester, United Kingdom. 16 March

More information

Relative Benefit Equilibrating Bargaining Solution and the Ordinal Interpretation of Gauthier s Arbitration Scheme

Relative Benefit Equilibrating Bargaining Solution and the Ordinal Interpretation of Gauthier s Arbitration Scheme Relative Benefit Equilibrating Bargaining Solution and the Ordinal Interpretation of Gauthier s Arbitration Scheme Mantas Radzvilas July 2017 Abstract In 1986 David Gauthier proposed an arbitration scheme

More information

Uncertainty & Decision

Uncertainty & Decision Uncertainty & Decision von Neumann Morgenstern s Theorem Stéphane Airiau & Umberto Grandi ILLC - University of Amsterdam Stéphane Airiau & Umberto Grandi (ILLC) - Uncertainty & Decision von Neumann Morgenstern

More information

Asset Pricing. Chapter III. Making Choice in Risky Situations. June 20, 2006

Asset Pricing. Chapter III. Making Choice in Risky Situations. June 20, 2006 Chapter III. Making Choice in Risky Situations June 20, 2006 A future risky cash flow is modelled as a random variable State-by-state dominance =>incomplete ranking «riskier» Table 3.1: Asset Payoffs ($)

More information

A theory of robust experiments for choice under uncertainty

A theory of robust experiments for choice under uncertainty A theory of robust experiments for choice under uncertainty S. Grant a,, J. Kline b, I. Meneghel a, J. Quiggin b, R. Tourky a a Australian National University b The University of Queensland Abstract Thought

More information

THE PARADOXES OF ALLAIS, STOCHASTIC DOMINANCE, AND

THE PARADOXES OF ALLAIS, STOCHASTIC DOMINANCE, AND This is the penultimate (1997) version of the chapter as it was to appear in the Festschrift Volume honoring Ward Edwards, scheduled for publication in 1998. The chapter was published in 1999 and should

More information

A Note On Comparative Probability

A Note On Comparative Probability A Note On Comparative Probability Nick Haverkamp and Moritz Schulz Penultimate draft. Please quote from the published version (Erkenntnis 2012). Abstract A possible event always seems to be more probable

More information

Transitive Regret. Sushil Bikhchandani and Uzi Segal. October 24, Abstract

Transitive Regret. Sushil Bikhchandani and Uzi Segal. October 24, Abstract Transitive Regret Sushil Bikhchandani and Uzi Segal October 24, 2009 Abstract Preferences may arise from regret, i.e., from comparisons with alternatives forgone by the decision maker. We ask whether regret-based

More information

On the Optimality of Likelihood Ratio Test for Prospect Theory Based Binary Hypothesis Testing

On the Optimality of Likelihood Ratio Test for Prospect Theory Based Binary Hypothesis Testing 1 On the Optimality of Likelihood Ratio Test for Prospect Theory Based Binary Hypothesis Testing Sinan Gezici, Senior Member, IEEE, and Pramod K. Varshney, Life Fellow, IEEE Abstract In this letter, the

More information

arxiv: v1 [q-fin.mf] 25 Dec 2015

arxiv: v1 [q-fin.mf] 25 Dec 2015 Risk Aversion in the Small and in the Large under Rank-Dependent Utility arxiv:52.08037v [q-fin.mf] 25 Dec 205 Louis R. Eeckhoudt IESEG School of Management Catholic University of Lille and CORE Louis.Eeckhoudt@fucam.ac.be

More information

Almost essential: Consumption and Uncertainty Probability Distributions MICROECONOMICS

Almost essential: Consumption and Uncertainty Probability Distributions MICROECONOMICS Prerequisites Almost essential: Consumption and Uncertainty Probability Distributions RISK MICROECONOMICS Principles and Analysis Frank Cowell July 2017 1 Risk and uncertainty In dealing with uncertainty

More information

Weak* Axiom of Independence and the Non-Expected Utility Theory

Weak* Axiom of Independence and the Non-Expected Utility Theory Review of Economic Analysis 4 (01) 67-75 1973-3909/01067 Weak* Axiom of Independence and the Non-Expected Utility Theory TAPAN BISWAS University of Hull 1 Introduction The axiomatic foundation of the expected

More information

Quantum Probability in Cognition. Ryan Weiss 11/28/2018

Quantum Probability in Cognition. Ryan Weiss 11/28/2018 Quantum Probability in Cognition Ryan Weiss 11/28/2018 Overview Introduction Classical vs Quantum Probability Brain Information Processing Decision Making Conclusion Introduction Quantum probability in

More information

Choice under uncertainty

Choice under uncertainty Choice under uncertainty Expected utility theory The agent chooses among a set of risky alternatives (lotteries) Description of risky alternatives (lotteries) a lottery L = a random variable on a set of

More information

Understanding the Reference Effect

Understanding the Reference Effect Understanding the Reference Effect Yusufcan Masatlioglu Neslihan Uler University of Michigan Abstract This paper explores how a reference point affects individual preferences. While reference-dependence

More information

A revealed reference point for prospect theory

A revealed reference point for prospect theory Econ Theory https://doi.org/10.1007/s00199-017-1096-2 RESEARCH ARTICLE Katarzyna M. Werner 1 Horst Zank 2 Received: 14 November 2016 / Accepted: 19 December 2017 The Author(s) 2018. This article is an

More information

Parametric weighting functions

Parametric weighting functions Journal of Economic Theory 144 (2009) 1102 1118 www.elsevier.com/locate/jet Parametric weighting functions Enrico Diecidue a, Ulrich Schmidt b,c, Horst Zank d, a Decision Sciences Area, INSEAD, Fontainebleau,

More information

Dynamic Decision Making When Risk Perception Depends on Past Experience

Dynamic Decision Making When Risk Perception Depends on Past Experience Dynamic Decision Making When Risk Perception Depends on Past Experience M. Cohen fi, J. Etner, and M. Jeleva Keywords: Dynamic decision making Past experience Rank dependent utility model Recursive model

More information

Meaningfulness and the Possible Psychophysical Laws

Meaningfulness and the Possible Psychophysical Laws Meaningfulness and the Possible Psychophysical Laws Perceived Risk Pollatsek and Tversky (1970) (a, p, b), where a, b, and p are real numbers and 0 < p < 1 stands for the simple gamble of receiving a dollars

More information

Considering the Pasadena Paradox

Considering the Pasadena Paradox MPRA Munich Personal RePEc Archive Considering the Pasadena Paradox Robert William Vivian University of the Witwatersrand June 2006 Online at http://mpra.ub.uni-muenchen.de/5232/ MPRA Paper No. 5232, posted

More information

1 Uncertainty. These notes correspond to chapter 2 of Jehle and Reny.

1 Uncertainty. These notes correspond to chapter 2 of Jehle and Reny. These notes correspond to chapter of Jehle and Reny. Uncertainty Until now we have considered our consumer s making decisions in a world with perfect certainty. However, we can extend the consumer theory

More information

Intertemporal Risk Aversion, Stationarity and Discounting

Intertemporal Risk Aversion, Stationarity and Discounting Intertemporal Risk Aversion, Stationarity and Discounting Job Market Paper, November 2007 Christian P. TRAEGER Department of Agricultural & Resource Economics, UC Berkeley Department of Economics, UC Berkeley

More information