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.     

Is Context-Based Choice due to Context-Dependent Preferences?

The rationalization of context-based choice is usually based on the assumption that preferences are context-dependent. In this paper, we show that context-based choice can be due to the characteristics of the choice procedure applied by the individual and not to the dependence of preferences (stochastic or deterministic) on the context. Our arguments are illustrated focusing on the much-studied dominated-alternative effects.     

Cumulative prospect theory's functional menagerie

Many different functional forms have been suggested for both the value function and probability weighting function of Cumulative Prospect Theory (Tversky and Kahneman, 1992). There are also many stochastic choice functions available. Since these three components only make predictions when considered in combination, this paper examines the complete pattern of 256 model variants that can be constructed from twenty functions. All these variants are fit to experimental data and their explanatory power assessed. Significant interaction effects are observed. The best model has a power value function, a risky weighting function due to Prelec (1998), and a Logit function. JEL Classification C52 · D81     

Reforming the European Common Agricultural Policy: From price & income support to risk management

Over the last 30 years, the European Union has significantly reformed its Common Agricultural Policy by introducing direct payments to farmers and reducing price support levels. While the European agricultural prices become more volatile, all economic models assessing these reforms remain static and ignore the risk dimensions. This paper develops an original stochastic computable general equilibrium model capturing the different sources of risk, farmers’ risk attitude and risk contingent markets. We find that the reduction of price support levels has modest market impacts but negative global welfare effects by exposing risk-averse European farmers to the world price volatility. This issue is not solved by the direct payments, which have negligible market and global welfare impacts through their wealth effects. On the other hand, we find that unbiased futures markets can solve this global welfare issue by allowing European farmers to transfer their price risks. Therefore, European policymakers should ensure well-functioning risk contingent markets rather than maintaining rigid intervention price levels.     

Even Risk-Averters may Love Risk

A decision maker bets on the outcomes of a sequence of coin-tossings. At the beginning of the game the decision maker can choose one of two coins to play the game. This initial choice is irreversible. The coins can be biased and the player is uncertain about the nature of one (or possibly both) coin(s). If the player is an expected-utility maximizer, her choice of the coin will depend on different elements: the nature of the game (namely, whether she can observe the outcomes of the previous tosses before making her next decision), her utility function, the prior distribution on the bias of the coin. We will show that even a risk averter might optimally choose a riskier coin when learning is allowed. We will express most of our results in the language of stochastic orderings, allowing comparisons that are valid for large classes of utility functions.     

The effect of incentive regulation on productive efficiency in telecommunications

Incentive regulation is now an important regulatory tool in the telecommunications industry in the United States. The issue explored here is whether incentive regulation has resulted in an increase in productive efficiency. After providing an overview of the nature of incentive regulation, one methodology for measuring the effects of incentive regulation on productive efficiency is reviewed. This methodology is data envelopment analysis (DEA) and allows for the measurement of both scale efficiency and technical efficiency of individual local exchange carriers (LECs). The results indicate that most LECs were technically efficient over the 1988–1998 period. Four LECs, however, consistently demonstrate scale inefficiency. In the aggregate, however, based on the DEA results there was no identifiable improvement in aggregate LECs' technical efficiency between 1988 and 1998. Subsequently, an alternative methodology, a stochastic frontier production function approach, is considered. The results from this methodology confirm that there was no change in technical efficiency over the period of study, something that incentive regulation was specifically designed to enhance.     

On the Cycle-Transitivity of the Dice Model

We introduce the notion of a dice model as a framework for describing a class of probabilistic relations. We investigate the transitivity of the probabilistic relation generated by a dice model and prove that it is a special type of cycle-transitivity that is situated between moderate stochastic transitivity or product-transitivity on the one side, and ukasiewicz-transitivity on the other side. Finally, it is shown that any probabilistic relation with rational elements on a three-dimensional space of alternatives which possesses this particular type of cycle-transitivity, can be represented by a dice model. The same does not hold in higher dimensions.     

Stochastic superiority

This paper introduces a definition of stochastic superiority. One random variable is stochastically superior to another whenever it stochastically dominates the other after the risk in each random variable has been optimally reduced. Stochastic superiority is implied by stochastic dominance, but the reverse is not true. Stochastic superiority allows more pairs of random alternatives to be ranked, and efficient sets to be smaller. A very strong sufficient condition for stochastic superiority is demonstrated to also be necessary when preferences are risk averse. This condition provides a relatively easy way to conduct stochastic superiority tests. As an alternative to “almost stochastic dominance,” stochastic superiority also provides a natural solution to the “left tail problem” that arises often when comparing random alternatives.

     

Spatial externalities and risk in interdependent security games

Individuals regularly invest in self-protection to reduce the risk of an adverse event. The effectiveness of self-protection often depends on the actions of other economic agents and can be modeled as a stochastic coordination game with multiple Pareto-ranked equilibria. We use lab experiments to analyze tacit coordination in stochastic games with two kinds of interdependencies in payoffs: “non-spatial” in which every agent’s action has an impact on the risk faced by every other agent, and “spatial” in which agents only impact the risk faced by their immediate neighbors. We also compare behavior in the stochastic games to deterministic versions of the same games. We find that coordination on the payoff-dominant equilibrium is significantly easier in the deterministic games than in the stochastic games and that spatial interdependencies lead to greater levels of coordination in the deterministic game but not in the stochastic game. The difficulty with coordination observed in the stochastic games has important implications for many real-world examples of interdependent security and also illustrates the importance of not relying on data from deterministic experiments to analyze behavior in settings with risk.     

Risk-induced discounting

We establish a direct connection between time preference and risk about an attribute (health) of the instantaneous utility function. In doing so, we derive a risk-induced discount function that corresponds to a normalized expectation of that attribute. We provide several results characterizing this risk-induced discount function depending on the stochastic properties of the risk, which we model as a discrete Markov process. When it is well-defined, which we refer to as full approximation, the risk-induced discount function coincides with exponential discounting if the Markov process is stationary. However, a slight perturbation of the beliefs can trigger time-inconsistent discounting. When considering non-stationary Markov processes, time-inconsistency also emerges in situations where individuals’ beliefs change in a non-anticipated fashion over time, as exemplified by quasi-hyperbolic discounting. Results are illustrated via several applications.     

Stochastic revealed preference and rationalizability

This article explores rationalizability issues for finite sets of observations of stochastic choice in the framework introduced by Bandyopadhyay et al. (Journal of Economic Theory, 84(1), 95–110, 1999). It is argued that a useful approach is to consider indirect preferences on budgets instead of direct preferences on commodity bundles. A new rationalizability condition for stochastic choices, “rationalizable in terms of stochastic orderings on the normalized price space” (rsop), is defined. rsop is satisfied if and only if there exists a solution to a linear feasibility problem. The existence of a solution also implies rationalizability in terms of stochastic orderings on the commodity space. Furthermore it is shown that the problem of finding sufficiency conditions for binary choice probabilities to be rationalizable bears similarities to the problem considered here.     

Robust Control in Water Management

Since surface water flows are often stochastic, there is a role for water reservoirs in protecting users against uncertainty. We assume uncertainty regarding the probability distribution for the stochastic variable. Thus the decision allows for a range of approximate models that could be true, and the problem can be solved using robust optimal control. This paper analyses the implications of a robust framework on resource management decisions, using the case of water as an illustration. Robust choices are compared with those of a benchmark stochastic model and the emergence of precautionary behaviour is discussed.     

Stochastic evolution of rationality

Following up on previous results by Falmagne, this paper investigates possible mechanisms explaining how preference relations are created and how they evolve over time. We postulate a preference relation which is initially empty and becomes increasingly intricate under the influence of a random environment delivering discrete tokens of information concerning the alternatives. The framework is that of a class of real-time stochastic processes having interlinked Markov and Poisson components. Specifically, the occurence of the tokens is governed by a Poisson process, while the succession of preference relations is a Markov process. In an example case, the preference relations are the various possible semiorders on the set of alternatives. Asymptotic results are obtained in the form of the limit probabilities of any semiorder. The arguments extend to a much more general situation including interval orders, biorders and partial orders. The results provide (up to a small number of parameters) complete quantitative predictions for panel data of a standard type, in which the same sample of subjects has been asked to compare the alternatives a number of times.     

Friendship and Delinquency: Selection and Influence Processes in Early Adolescence

Positive association of relevant characteristics is a widespread pattern among adolescent friends. A positive association may be caused by the selection of similar others as friends and by the deselection of dissimilar ones, but also by influence processes where friends adjust their behavior to each other. Social control theory argues that adolescents select each other as friends based on delinquency. Differential association theory, on the other hand, argues that adolescent friends influence each other's delinquency levels. We employ new statistical methods for assessing the empirical evidence for either process while controlling for the other process. These methods are based on ‘actor‐oriented’ stochastic simulation models. We analyze longitudinal data on friendship networks and delinquent behavior collected in four waves of 544 students in 21 first‐grade classrooms of Dutch secondary schools. Results indicate that adolescents select others as friends who have a similar level of delinquency compared with their own level. Estimates of the social influence parameters are not significant. The results are consistent with social control theory but provide no support for differential association theory.     

Changes in multiplicative background risk and risk-taking behavior

This article analyzes the conditions under which any change in a multiplicative background risk induces a more cautious behavior. We give necessary and sufficient conditions under which any change in the multiplicative background risk with respect to the Nth-degree stochastic dominance raises local risk aversion. Surprisingly, decreasing relative risk aversion of any order up to N in the sense of Pratt (Econometrica 32:122–136, 1964) coupled with decreasing relative risk aversion in the sense of Ross (Econometrica 49:631–638, 1981) are sufficient to guarantee an increase in local risk aversion after any deterioration of the multiplicative background risk thanks to the Nth-degree stochastic dominance. We link our results concerning second-order stochastic dominance with the concept of multiplicative risk vulnerability.     

Stronger utility

Empirical research often requires a method how to convert a deterministic economic theory into an econometric model. A popular method is to add a random error term on the utility scale. This method, however, ignores stochastic dominance. A modification of this method is proposed to account for stochastic dominance. The modified model compares favorably to other existing models in terms of goodness of fit to experimental data. The modified model can rationalize the preference reversal phenomenon. An intuitive axiomatic characterization of the modified model is provided. Important microeconomic concept of risk aversion is well defined in the modified model.     

The stochastic component in choice and regression to the mean

In this article, we illustrate experimentally an important consequence of the stochastic component in choice behaviour which has not been acknowledged so far. Namely, its potential to produce ‘regression to the mean’ (RTM) effects. We employ a novel approach to individual choice under risk, based on repeated multiple-lottery choices (i.e. choices among many lotteries), to show how the high degree of stochastic variability present in individual decisions can distort crucially certain results through RTM effects. We demonstrate the point in the context of a social comparison experiment.     

Group cooperation under uncertainty

Previous research has shown an ‘interindividual-intergroup discontinuity effect’: intergroup interactions generally lead to less cooperative outcomes than interindividual interactions. We replicate the discontinuity effect in the deterministic prisoner’s dilemma, but find that groups are more cooperative than individuals in a stochastic version of the game. Three major factors that underlie the usual discontinuity effect are reduced in the stochastic environment: greed, fear, and persuasion power. Two group mechanisms are proposed to explain the reversed discontinuity effect: the motivation to avoid guilt and blame when making decisions that affect others’ welfare, and the social pressure to conform to certain norms when one is in a group setting.     

Decreasing higher-order absolute risk aversion and higher-degree stochastic dominance

Fishburn and Vickson (Stochastic dominance: an approach to decision-making under risk, Lexington Books, D.C. Heath and Company, Lexington, pp. 39–113, 1978) showed that, when applied to random alternatives with an equal mean, 3rd-degree and decreasing absolute risk aversion stochastic dominances represent equivalent rules. The present paper generalizes this result to higher degrees. Specifically, higher-degree stochastic dominance rules and common preference by all decision makers with decreasing higher-order absolute risk aversion are shown to coincide under appropriate constraints on the respective moments of the random variables to be compared.