Reevaluating evidence on myopic loss aversion: aggregate patterns versus individual choices

Investors who are more willing to accept risks when evaluating their investments less frequently are said to exhibit myopic loss aversion (MLA). Several recent experimental studies found that, on average, subjects bet significantly higher amounts on a risky lottery when they observe only a cumulative outcome of several realizations of the lottery (long evaluation period). In this article, we reexamine these empirical findings by analyzing individual rather than aggregate choice patterns. The behavior of the majority of subjects is inconsistent with the hypothesis of MLA: they bet an intermediate fraction of their initial endowment and these bets, on average, are not significantly different across two treatments with short and long evaluation period. We discuss several alternative explanations of this finding, including the Fechner model of random errors and the financial asset pricing model.     

Inferring beliefs as subjectively imprecise probabilities

We propose a method for estimating subjective beliefs, viewed as a subjective probability distribution. The key insight is to characterize beliefs as a parameter to be estimated from observed choices in a well-defined experimental task and to estimate that parameter as a random coefficient. The experimental task consists of a series of standard lottery choices in which the subject is assumed to use conventional risk attitudes to select one lottery or the other and then a series of betting choices in which the subject is presented with a range of bookies offering odds on the outcome of some event that the subject has a belief over. Knowledge of the risk attitudes of subjects conditions the inferences about subjective beliefs. Maximum simulated likelihood methods are used to estimate a structural model in which subjects employ subjective beliefs to make bets. We present evidence that some subjective probabilities are indeed best characterized as probability distributions with non-zero variance.     

Tacit Coordination in Choice Between Certain Outcomes in Endogenously Determined Lotteries

Tacit coordination is studied in a class of games in which each of n = 20 players is required to choose between two courses of actions. The first action offers each player a fixed outcome whereas the second presents her the opportunity of participating in a lottery with probabilities that are determined endogenously. Across multiple iterations of the game and trial-to-trial changes in the composition of the lottery, we observe a remarkably good coordination on the aggregate but not individual level. We further observe systematic deviations from the Nash equilibrium solution that are accounted for quite well by a simple adaptive learning model.     

Theory and individual behavior of first-price auctions

First-price auction theory is extended to the case of heterogeneous bidders characterized byM-parameter log-concave utility functions. This model, and its specific two-parameter constant relative risk averse special case, is generally supported by the results of 47 experiments. The one-parameter special case that comprises most of the theoretical literature is not supported by the experiments. One anomaly for the two-parameter model is that too many of the subjects exhibit positive (or negative) intercepts in their linear estimated bid functions. Accordingly, we develop a specific three-parameter model, which introduces a utility of winning, and a threshold utility of surplus. The new model, tested directly by introducing lump-sum payments or charges for winning, is not falsified by the new experiments.     

Stochastic Choice and Consistency in Decision Making Under Risk: An Experimental Study

This paper reports the results of an experiment designed to uncover the stochastic structure of individual preferences over lotteries. Unlike previous experiments, which have presented subjects with pair-wise choices between lotteries, our design allowed subjects to choose between two lotteries or (virtually) any convex combination of the two lotteries. We interpret the mixtures of lotteries chosen by subjects as a measure of the stochastic structure of choice. We test between two alternative interpretations of stochastic choice: the random utility interpretation and the deterministic preferences interpretation. The main findings of the experiment are that the typical subject prefers mixtures of lotteries rather than the extremes of a linear lottery choice set. The distribution of choices does not change between a first and second asking of the same question. We argue that this provides support for the deterministic preferences interpretation over the random utility interpretation of stochastic choice. As a subsidiary result, we find a small proportion of subjects make choices that violate transitivity, but the level of intransitive choice falls significantly over time.     

Implementing and testing risk-preference-induction mechanisms in experimental sealed-bid auctions

Risk-preference-inducing lottery procedures can serve as valuable tools for experimental economists. However, questioning their effectiveness, experimenters may avoid them even when predictions and conclusions depend crucially on risk preferences. Here, I review risk-preference-induction attempts in sealed-bid auctions, discussing factors that promote or hinder success. Making the procedure very transparent and having subjects learn about it in simple environments promote success. Hysteresis resulting from switching between monetary payoffs and lottery procedures in one environment hinders success. Thus, lottery procedures appear sensitive to the implementation. However, implemented carefully, they can generate behavior consistent with the intended preferences.     

Experimental payment protocols and the Bipolar Behaviorist

If someone claims that individuals behave as if they violate the independence axiom (IA) when making decisions over simple lotteries, it is invariably on the basis of experiments and theories that must assume the IA through the use of the random lottery incentive mechanism (RLIM). We refer to someone who holds this view as a Bipolar Behaviorist, exhibiting pessimism about the axiom when it comes to characterizing how individuals directly evaluate two lotteries in a binary choice task, but optimism about the axiom when it comes to characterizing how individuals evaluate multiple lotteries that make up the incentive structure for a multiple-task experiment. We reject the hypothesis about subject behavior underlying this stance: we find that preferences estimated with a model that assumes violations of the IA are significantly affected when one elicits choices with procedures that require the independence assumption, as compared to choices elicited with procedures that do not require the assumption. The upshot is that one cannot consistently estimate popular models that relax the IA using data from experiments that assume the validity of the RLIM.     

Money Does Not Induce Risk Neutral Behavior,but Binary Lotteries Do even Worse

If payoffs are tickets for binary lotteries, which involve only two money prizes, then rationality requires expected value maximization in tickets. This payoff scheme was increasingly used to induce risk neutrality in experiments. The experiment presented here involved lottery choice and evaluation tasks. One subject group was paid in binary lottery tickets, another directly in money. Significantly greater deviations from risk neutral behavior are observed with binary lottery payoffs. This discrepancy increases when subjects have easy access to the alternatives' expected values and mean absolute deviations. Behavioral regularities are observed at least as often as with direct money payoffs.     

Does exposure to unawareness affect risk preferences? A preliminary result

One fundamental assumption often made in the literature on unawareness is that risk preferences are invariant to changes of awareness. We study how exposure to unawareness affects choices under risk. Participants in our experiment choose repeatedly between varying sure outcomes and a lottery in three phases. All treatments are exactly identical in phase 1 and phase 3, but differ in phase 2. There are five different treatments pertaining to the lottery faced in phase 2: The control treatment (i.e., a standard lottery), the treatment with awareness of unawareness of lottery outcomes but known number of outcomes, the treatment with awareness of unawareness of outcomes but with unknown number of outcomes, the treatment with unawareness of unawareness of some outcomes, and the treatment with an ambiguous lottery. We study both whether behavior differs in phase 3 across treatments (between subjects effect) and whether differences of subjects’ behavior between phases 1 and phase 3 differ across treatments (within subject effects). We observe no significant treatment effects.     

A further exploration of the uncertainty effect

Individual valuation of a binary lottery at values less than the lottery’s worst outcome has been designated as the “uncertainty effect”. Our paper aims to explore the boundary conditions of the uncertainty effect by investigating a plausible underlying process and proposing two possible methods. First, we examine how providing an exogenous evaluation opportunity prior to judging the value of the lottery affects individuals’ judgments, and find that first valuing the worst outcome and then the lottery eliminates the uncertainty effect. Second, we explore whether introducing additional cognitive load dampens how far decision makers correct their initial evaluations, and find that additional cognitive load is able to eliminate the uncertainty effect.     

Even-chance lotteries in social choice theory

This paper discusses aspects of the theory of social choice when a nonempty choice set is to be determined for each situation, which consists of a feasible set of alternatives and a preference order for each voter on the set of nonempty subsets of alternatives. The individual preference assumptions include ordering properties and averaging conditions, the latter of which are motivated by the interpretation that subset A is preferred to subset B if and only if the individual prefers an even-chance lottery over the basic alternatives in A to an even-chance lottery over the basic alternatives in B. Corresponding to this interpretation, a choice set with two or more alternatives is resolved by an even-chance lottery over these alternatives. Thus, from the traditional no-lottery social choice theory viewpoint, ties are resolved by even-chance lotteries on the tied alternatives. Compared to the approach which allows all lotteries to compete along with the basic alternatives, the present approach is a contraction which allows only even-chance lotteries.After discussing individual preference axioms, the paper examines Pareto optimality for nonempty subsets of a feasible set in a social choice context with n voters. Aspects of simple-majority comparisons in the even-chance context follow, including an analysis of single-peaked preferences. The paper concludes with an Arrowian type impossibility theorem that is designed for the even-chance setting.     

Preferences and decision errors in the winner’s curse

The problem of asymmetric information causes a winner’s curse in many environments. Given many unsuccessful attempts to eliminate it, we hypothesize that some people ‘prefer’ the lotteries underlying the winner’s curse. Study 1 shows that after removing the hypothesized cause of error, asymmetric information, half the subjects still prefer winner’s curse lotteries, implying past efforts to de-bias the winner’s curse may have been more successful than previously recognized since subjects prefer these lotteries. Study 2 shows risk-seeking preferences only partially explain lottery preferences, while non-monetary sources of utility may explain the rest. Study 2 suggests lottery preferences are not independent of context, and offers methods to reduce the winner’s curse.

Axiomatization of a Preference for Most Probable Winner

In binary choice between discrete outcome lotteries, an individual may prefer lottery L₁ to lottery L₂ when the probability that L₁ delivers a better outcome than L₂ is higher than the probability that L₂ delivers a better outcome than L₁. Such a preference can be rationalized by three standard axioms (solvability, convexity and symmetry) and one less standard axiom (a fanning-in). A preference for the most probable winner can be represented by a skew-symmetric bilinear utility function. Such a utility function has the structure of a regret theory when lottery outcomes are perceived as ordinal and the assumption of regret aversion is replaced with a preference for a win. The empirical evidence supporting the proposed system of axioms is discussed.     

Inducing risk-neutral preferences: An examination in a controlled market environment

This article reports 15 first-price auction experiments, each with four bidders, designed to test Cedric Smith' (1961) hypothesis that risk-neutral behavior can be induced in subjects' decisions by paying them in lotteries on money that are linear in the outcome probabilities. We choose the first-price auction environment because of its relatively high success in surviving a large number of tests, which contrasts with the widely documented tendency of subjects to violate the expected utility axioms in making choices among gambles. In the first five experiments, subjects were experienced in first-price auctions with monetary rewards. We prescreened these subjects for exceptionally high bidding consistency with the constant relative risk-averse model. The results unyielded only weak support for the risk-neutralizing procedure (3 of 10 risk-averse cases became risk-neutral, but only 1 in 8 that were retested continued to exhibit risk-neutral behavior). We recruited 16 new subjects with no previous experience for four lottery-only auctions. Eight of the 16 subjects bid as if risk-neutral, but in a retest of 12 subjects only 2 remained consistently risk-neutralized. Finally we recruited 12 inexperienced subjects, and each subject bid against 3 robot bidders whose bidding strategies were known to the human bidder. We use this procedure to control for Nash expectations. These 12 subjects were run under both monetary and lottery reward conditions. Two of the 12 subjects bid as if risk-neutral in the lottery auction, but both of these subjects had shown risk-neutral behavior with monetary rewards. In conclusion, we find very weak support for the risk-neutralizing procedure. We caution other researchers to run calibration tests of the procedure in the particular context they are studying to assess its reliability.     

The influence of fear in decisions: Experimental evidence

This article studies decisions made under conditions of fear, when a catastrophic outcome is introduced in a lottery. It reports on experimental results and seeks to compare the predictions of the expected utility (EU) framework with those of a new axiomatic treatment of choice under uncertainty that takes explicit account of emotions such as fear (Chichilnisky 1996, 2000, 2002, 2009). Results provide evidence that fear influences the cognitive process of decision-making by leading some subjects to focus excessively on catastrophic events. Such heterogeneity in subjects’ behavior, while not consistent with EU-based functions, is fully consistent with the new type of utility function implied by the new axioms.     

Embedding effects: Stimulus representation and response mode

Thecontingent valuation (CV) methodology assigns prices to environmental amenities by asking people how much they would be willing to pay in order to preserve or acquire those amenities. If this measurement procedure is valid, then responses should be sensitive to relevant changes in the amenities being judged and insensitive to irrelevant changes. One apparent demonstration of inappropriate insensitivity is theembedding effect: the observation that people are apparently willing to pay the same amount of money for a good as for a minor subset of that good. This study examined the possibility that the source of this effect lies with each of two (potentially treatable) methodological problems: 1) subjects have difficulty using quantitative (dollar) response modes to express their values; and 2) subjects have difficulty absorbing the essential details of the CV scenarios describing those goods. The study found that 1) subjects showed considerable embedding both with a simple paired-comparison response mode and with a more demanding one requiring direct dollar estimates; 2) embedding was much reduced with the simpler response mode; 3) subjects' preferences with the two response modes were usually inconsistent; 4) when asked to describe the CV scenario that they had just heard, subjects often reported key task details inaccurately; and 5) there was less embedding when tasks were reinterpreted in terms of the questions subjects reported having answered (as opposed to what had actually been asked). These results are discussed in terms of the match between the questions that investigators would like to ask and the ones that subjects are capable of answering.     

Rules of behavior and expected utility theory. Compatibility versus dependence

Conclusions We have seen that many decision rules which are intuitively and/or empirically supported and compatible with MEU, are compatible with it but not dependent on it.There are of course rules of behavior which are implied in MEU and also depend on it like this:If the hope of winning any of the prizes in a lottery motivates you to buy a ticket, and if you win half the amount of the highest prize, you should play double or nothing with your prize.Suppose you would prefer a one in a million chance of winning $2 million to a two in a million chance of winning $1 million, but your first choice is not available so you buy a ticket for $1 million. If you win, you should play 50–50 double or nothing with your prize. Generalize: put x in the place of $1 million and p in the place of 1/1 000000, and test yourself against this principle (Pf = preferred to): (p, 2x)Pf(2p, x) (0.5, 2x)Pf(1, x).See Friedmann and Savage (1968).In the real world lotteries are multiprize, i.e., composite games of elements like these. The same applies: If you would not have preferred the highest prize exchanged for a higher probability of some lower prize, then winning a lower prize would put you in the market for some simple bet like above. If you stand up to this test, you are a unique person because, as we know, such bets are not made.While in the process of finishing the final draft, I got hold of (Samuelson, 1983). He expresses grave doubts as to what he calls the dogma of Expected Utility maximizing. In a somewhat apologetic way, he preserves some formulations deriving behavior from EUM because, as he states in a general way, they do not depend on that particular dogma. More specifically: many models incompatible with EUM imply risk aversion, which would result also from maximizing the expectation of a concave utility function,In view of the authoritarian disposition of some of the strongest defenders of EUM and of Samuelson's (well deserved) authority and his leading role in the school of EUM theory, his open expression of doubt may well mark the beginning of the last chapter in the history of the rise and fall of the most powerful school that has so far been active in 20th century decision theory.     

An Experimental Investigation of the Disparity Between WTA and WTP for Lotteries

In this paper we experimentally investigate the disparity between willingness-to-accept (WTA) and willingness-to-pay (WTP) for risky lotteries. The direction of the income effect is reversed by endowing subjects with the highest price of a lottery when asking the WTP question. Our results show that the income effect is too small to be the only source of the disparity. Since the disparity concentrates on a subsample of subjects, parametric and nonparametric tests of the WTA-WTP ratio may lead to contradictory results. The disparity is significantly reduced when background risk is introduced. That is, putting subjects always into a risky position could improve the contingent valuation method, which is often concerned with the assessment of risky situations such as health risks, automobile safety, etc.      

2012年江西省福利彩票彩民购彩行为特征调查报告

为了解江西省福彩彩民购彩行为特征及彩民群体成瘾倾向,本文采用横断面研究方法,使用自编福彩彩民购彩行为调查表和购彩成瘾自评问卷,在江西全省11个设区市400个福利彩票投注站随机收集4396名购彩者的资料,分析彩民一般人口统计学资料、彩民购彩行为特征、彩民对彩票机构的态度以及彩民成瘾倾向特点。结果显示,中年、已婚、受教育程度低和月收入低的男性更易购彩成瘾。购彩频率、购彩金额和每天花费时间均是购彩成瘾的重要表现,购彩成瘾倾向与彩龄无关。因此,江西省目前福利彩票行业发展健康,但彩票购买者中约2%有病态赌博倾向,需要引起高度重视。     

Lotteries in the real world

Observed patterns of lottery play suggest that many players believe they can improve their chance of winning by adjusting their bets according to which numbers have won in recent drawings, or in response to their dreams or other portents. This skill orientation is encouraged by state lottery advertising, which tends to be misleading in other respects as well. Patterns of lottery play and the content of lottery commercials provide readily available illustrations of psychological tendencies in risky decision-making that have been documented in laboratory experiments.This article is based on an informal presentation the authors gave at the Fifth International Conference on the Foundation and Application of Utility, Risk, and Decisions Theories at Duke University, June 11, 1990.