Lottery Dependent Utility: a Reexamination

In order to accommodate empirically observed violations of the independence axiom of expected utility theory Becker and Sarin (1987) proposed their model of lottery dependent utility in which the utility of an outcome may depend on the lottery being evaluated. Although this dependence is intuitively very appealing and provides a simple functional form of the resulting decision criterion, lottery dependent utility has been nearly completely neglected in the recent literature on decision making under risk. The goal of this paper is to revive the lottery dependent utility model. Therefore, we derive first a sound axiomatic foundation of lottery dependent utility. Secondly, we develop a discontinuous variant of the model which can accommodate boundary effects and may lead to a lexicographic non-expected utility model. Both analyses are accompanied by considering some functional specifications which are in accordance with recent experimental results and may have significant applications in business and management science.     

On a lottery pricing anomaly: Time tells the tale

This article identifies a lottery pricing anomaly, which I call the “r=x anomaly,” that is present in past pricing experiments—namely, a tendency for subjects to announce that their minimum selling price for some binary lottery is the greater of the two lottery prizes. The study shows that the anomaly is inconsistent with two theoretical explanations for another well-known pricing anomaly (preference reversal) and experimentally replicates these inconsistencies. The new experiment also measures the time subjects spend making their pricing decisions. These decision-time measurements suggest that ther=x anomaly may be a decision-cost effect.     

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.     

An Analysis of the Distribution of Combinations Chosen by UK National Lottery Players

This paper is concerned with the behaviour of lottery players when they get to choose their own numbers. Most lotto players do not pick combinations at random, but prefer more idiosyncratic techniques when they fill in the play grid. This is highlighted when the actual distribution of combinations for a single draw in the UK National Lottery is examined. A new model of gambler choice is developed and specified, and the resulting distribution of combinations fitted to the empirical data. Various implications of the model are discussed, such as the expected value of lotto tickets for different types of player.     

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.     

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。     

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.     

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.     

State Conducted Lotteries: History, Problems, and Promises

Lotteries have played an important role in American finance through much of this Nation's history. This paper begins with an account of the abuses that led to the prohibition of the privately run lottery during the nineteenth century. It then goes on to analyze the promise and performance of the state run lotteries that have been created during the last decade. The paper argues that the lotteries have failed to fulfill the promises of their proponents, either in raising revenue or in fighting organized crime, and that they constitute a regressive and inefficient form of taxation. It also argues that the promotion of gambling serves to tarnish the image of state government.     

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.     

Expected utility without utility

This paper advances an interpretation of Von Neumann-Morgenstern's expected utility model for preferences over lotteries which does not require the notion of a cardinal utility over prizes and can be phrased entirely in the language of probability. According to it, the expected utility of a lottery can be read as the probability that this lottery outperforms another given independent lottery. The implications of this interpretation for some topics and models in decision theory are considered.     

The price for information about probabilities and its relation with risk and ambiguity

In this article, ambiguity attitude is measured through the maximum price a decision maker is willing to pay to know the probability of an event. Two problems are examined in which the decision maker faces an act: in one case, buying information implies playing a lottery, while, in the other case, buying information gives also the option to avoid playing the lottery. In both decision settings, relying on the Choquet expected utility model, we study how the decision maker??s risk and ambiguity attitudes affect the reservation price for ambiguity resolution. These effects are analyzed for different levels of ambiguity of the act. Operating instructions for the elicitation of the reservation price for ambiguity resolution in an experimental setting are provided at the end of the article.     

Ellsberg paradox: Ambiguity and complexity aversions compared

We present a simple model where preferences with complexity aversion, rather than ambiguity aversion, resolve the Ellsberg paradox. We test our theory using laboratory experiments where subjects choose among lotteries that “range” from a simple risky lottery, through risky but more complex lotteries, to one similar to Ellsberg’s ambiguity urn. Our model ranks lotteries according to their complexity and makes different—at times contrasting—predictions than most models of ambiguity in response to manipulations of prizes. The results support that complexity aversion preferences play an important and separate role from beliefs with ambiguity aversion in explaining behavior under uncertainty.     

Are Event-Splitting Effects Actually Boundary Effects?

An event-splitting effect (ESE) occurs when an event, which yields a positive outcome in one lottery but zero under another, is separated into two sub-events and this increases the relative attractiveness of the former lottery. ESEs are attributed to either (1) a preference for more positive outcomes in lotteries, or (2) an aversion to more zero outcomes. An experiment is reported which replicates ESEs whilst controlling for explanation (2). This favours explanation (1), but a lack of generality in replication suggests previous ESEs to be partially due to (2). Implications are discussed for a related choice phenomena, decision theory, and real-world decision-making.     

Bayesian decisions with ambiguous belief aversion

This study provides an empirical perspective on the effect of ambiguous environmental risk information on lottery preferences using a sample of 646 adults. The learning process follows a Bayesian expected utility model in terms of the overall magnitude and sign of the weights that respondents place on the risk information. Significant ambiguous belief aversion that is consistent with the Ellsberg paradox is also evident. The extent of this aversion increases with the size of the risk spread, but at a decreasing rate. These results are consistent with both probability-based and preference-based models of ambiguous probabilities. The findings also indicate the presence of cognitive limitations in the processing of risk information, but lead to rejection of more extreme models in which individuals respond in alarmist fashion or do not learn at all.     

Anticipating Likely Consequences of Lottery‐Based Affirmative Action*

Objectives. To better understand the consequences of whole or partial reliance on test scores as a screening mechanism for college or university admissions or for job placement or promotion. Methods. We introduce a simple hurdles/threshold model to study one particular mechanism that has been recently proposed to generate a “compromise” between race‐normed or gender‐normed standards for acceptance, on the one hand, and the decision to select those with the highest score regardless of race or gender, on the other—a method we call lottery‐based rules with minimum thresholds of acceptance. Results. We show the factors that determine how close acceptance rates for the disadvantaged group under lottery‐based methods will be to the acceptance rates under either race‐normal or pretest‐score‐based mechanisms. Conclusions. We argue that the likely consequences of using this method are not nearly as attractive as they might first appear to reformers.     

The Lottery and Income Inequality in the States*

Objective. Since the early 1970s, income inequality in the United States has increased dramatically. We examine the impact of state lotteries on income inequality in the American states from 1976–1995. Methods. We use cross‐sectional time‐series data to evaluate the effect of lotteries as well as those of other state tax policies, redistributive programs, and demographic factors on income inequality. Results. We find that state lotteries foster income concentration. Ceteris paribus, states with lotteries have higher levels of income inequality than those states without a lottery. We also find that additional demographic and policy factors have an impact on income inequality in the states. Conclusions. One of the most important policy‐oriented determinants of income inequality is the lottery and a significant portion of the increase in income inequality over our two‐decade time period is attributable to the increasing prevalence and popularity of state lotteries.     

(Sub) Optimality and (non) optimal satisficing in risky decision experiments

We implement a risky choice experiment based on one-dimensional choice variables and risk neutrality induced via binary lottery incentives. Each participant confronts many parameter constellations with varying optimal payoffs. We assess (sub)optimality, as well as (non)optimal satisficing by eliciting aspirations in addition to choices. Treatments differ in the probability that a binary random event, which are payoff—but not optimal choice—relevant is experimentally induced and whether participants choose portfolios directly or via satisficing, i.e., by forming aspirations and checking for satisficing before making their choice. By incentivizing aspiration formation, we can test satisficing, and in cases of satisficing, determine whether it is optimal.     

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.