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.     

On the evaluation of solution concepts

It is proposed that solution concepts for games should be evaluated in a way that is analogous to the way a logic is evaluated by a model theory for the language. A solution concept defines a set of strategy profiles, as a logic defines a set of theorems. A model theoretic analysis for a game defines a class of models, which are abstract representations of particular plays of the game. Given an appropriate definition of a model, one can show that various solution concepts are characterized by intuitively natural classes of models in the same sense that the set of theorems of a logic is characterized by a class of models of the language. Sketches of characterization results of this kind are given for rationalizability, Nash equilibrium, and for a refinement of rationalizability —strong rationalizability — that has some features of an equilibrium concept. It is shown that strong rationalizability is equivalent to Nash equilibrium in perfect information games. Extensions of the model theoretic framework that represent belief revision and that permit the characterization of other solution concepts are explored informally.     

Alternating-Offer Bargaining and Common Knowledge of Rationality

This paper reconsiders Rubinstein's alternating-offer bargaining game with complete information. We define rationalizability and trembling- hand rationalizability (THR) for multi-stage games with observed actions. We show that rationalizability does not exclude perpetual disagreement or delay, but that THR implies a unique solution. Moreover, this unique solution is the unique subgame perfect equilibrium (SPE). Also, we reconsider an extension of Rubinstein's game where a smallest money unit is introduced: THR rules out the non-uniqueness of SPE in some particular case. Finally, we investigate the assumption of boundedly rational players. Perpetual disagreement is excluded, but not delay. Furthermore, we cannot use the asymmetric Nash bargaining solution as an approximation of the alternating-offer bargaining model once the players are boundedly rational ones.     

Comparing uncertainty aversion towards different sources

In this article, we discuss some aspects of Eliaz and Ok ’s (Games Econ Behav 56:61–86, 2006) choice theoretical foundations of incomplete preferences. Our aim is to clarify some aspects of their regularity condition for preorders, showing that, as far as rationalization of a choice correspondence alone is concerned, no further restriction is imposed by requiring the preorder to be regular. However, if one is also interested in capturing other observable aspects of the individual’s choice procedure, such as Eliaz and Ok’s notion of c-incomparability or the notion of behavioral indifference introduced in this paper, then the only option is to use a regular preorder. We also argue that their weak axiom of revealed non-inferiority (WARNI) is too strong a property if our aim is to characterize the rationalizability of a choice correspondence by a (possibly incomplete) preorder. Finally, as we have mentioned above, we introduce the notion of behavioral indifference and argue, not only that Eliaz and Ok’s notion of c-incomparability (observable incomparability) can be derived from it, but also that it has a wider range of applicability than their notion of observable incomparability.     

Comparison of the Polar Decision Rules for Various Types of Distributions

We focus on the dichotomous choice model, which goes back as far as Condorcet (1785; Essai sur l'application de l'analyse a la probabilité des décisions rendues a la pluralité des voix, Paris). A group of experts is required to select one of two alternatives, of which exactly one is regarded as correct. The alternatives may be related to a wide variety of areas. A decision rule translates the individual opinions of the members into a group decision. A decision rule is optimal if it maximizes the probability of the group to make a correct choice. In this paper we assume the correctness probabilities of the experts to be independent random variables, selected from some given distribution. Moreover, the ranking of the members in the team is (at least partly) known. Thus, one can follow rules based on this ranking. The polar different rules are the expert and the majority rules. The probabilities of the two polar rules being optimal were compared in a series of papers. The main purpose of this paper is to outline the results, providing exact formulas or estimates for these probabilities. We consider a variety of distributions and show that for all of these distributions the asymptotic behaviour of the probabilities of the two polar rules follows the same patterns.     

Oligarchy for Social Choice Correspondences and Strategy-Proofness

We study the existence of a group of individuals which has some decisive power for social choice correspondences that satisfy a monotonicity property which we call modified monotonicity. And we examine the relation between modified monotonicity and strategy-proofness of social choice correspondences according to the definition by Duggan and Schwartz (2000). We will show mainly the following two results. (1) Modified monotonicity implies the existence of an oligarchy. An oligarchy is a group of individuals such that it has some decisive power (semi-decisiveness), and at least one of the most preferred alternatives of every its member is always chosen by any social choice correspondence. (2) Strategy-proofness of social choice correspondences is equivalent to modified monotonicity.     

A Note On Impossibility Theorems and Seniority Rules

We characterize seniority rules, also known as lexical dictatorships, under weak consistency constraints on the groups choice function. These constraints are base triple-acyclicity in the case of binary choices and rationalizability (although not rationality) in the case of choices between an arbitrary number of alternatives. Existing results on these weakened constraints remain silent on the treatment of the groups most junior individuals and therefore do not yield a complete characterization of seniority rules. We also impose a universal domain, binary strict Pareto optimality, binary Pareto indifference, binary independence of irrelevant alternatives, and the newly introduced condition of conflict resolution. The latter condition requires a social choice rules not to remain indecisive between alternatives for which individuals have conflicting preferences.JEL CLASSIFICATIONS: D63, D71This revised version was published online in May 2005 with a corrected article title.     

The Experiences of Frontline Staff Working with Children Seeking Asylum

The focus of this paper is welfare professionals’ accounts of their work with children who are seeking asylum. The empirical basis is a commissioned study of children seeking asylum in Wales. As well as qualitative research with children (which is not discussed in this paper), 62 professionals took part in interviews and focus groups. This sample included staff from social services, health, housing, education, police and the voluntary sector. Research findings are presented in relation to the experience of these frontline staff. We attempt to identify some of the sites of tension and the nature of the professional dilemmas, as well as discussing the potential for the exercise of discretion to be exercised. We conclude that there is very little room for manoeuvre within the asylum system for welfare professionals, but that there is evidence of questioning and even minor challenge of current policy from frontline staff. We discuss the extent to which the professional dilemmas raised by the asylum system are of a different order from those experienced throughout social welfare work.     

Comparison and choice

This paper develops the idea of a choice as a mapping of subsets of a set X into their respective subsets and the idea of the comparison, as a relation between elements of X, that is determined or revealed by a choice. It then studies how certain properties of a choice imply or are implied by certain properties, such as acyclicity, quasi-transitivity, pseudo-transitivity and transitivity, of the comparison revealed, finally giving a complete logical diagram of all the implications between these latter properties of the comparison.     

Aggregation theorems and multidimensional stochastic choice models

In many choice situations, the options are multidimensional. Numerous probabilistic models have been developed for such choices between multidimensional options and for the parallel choices determined by one or more components of such options. In this paper, it is assumed that a functional relation exists between the choice probabilities over the multidimensional options and the choice probabilities over the associated component unidimensional options. It is shown that if that function satisfies a marginalization property then it is essentially an arithmetic mean, and if the function satisfies a likelihood independence property then it is a weighted geometric mean. The results are related to those on the combination of expert opinion, and various probabilistic models in the choice literature are shown to have the geometric mean form.     

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.     

How can an expert system help in choosing the optimal decision?

We introduce a rationality principle for a preference relation on an arbitrary set of lotteries. Such a principle is a necessary and sufficient condition for the existence of an expected utility agreeing with . The same principle also guarantees a rational extension of the preference relation to any larger set of lotteries. When the extended relation is unique with respect to the alternatives under consideration, the decision maker does not need a numerical evaluation in order to make a choice. Such a rationality condition needs little information in order to be applied, and its verification amounts to solving a linear system.The present research is supported by the Research Contract of CNR (Research National Council) 1989 and 1990 Decision Models under uncertainty and risk, for expert systems with incomplete and revisable information.     

Can good news lead to a more pessimistic choice of action?

Adapting a definition introduced by Milgrom (1981) we say that a signal about the environment is good news relative to some initial beliefs if the posterior beliefs dominate the initial beliefs in the sense of first-order stochastic dominance (the assumption being that higher values of the parameter representing the environment mean better environments). We give an example where good news leads to the adoption of a more pessimistic course of action (we say that action a ₁, reveals greater pessimism than action a ₂, if it gives higher payoff in bad environments and lower payoff in good environments). We then give sufficient conditions for a signal not to induce a more pessimistic choice of action.A first version of this paper was written when the author was Heyworth Research Fellow at Nuffield College, Oxford, and presented at the Second Annual Congress of the European Economic Association (Copenhagen, August 1987). The author is grateful to an anonymous referee for helpful comments.     

Dyadic characteristics of guanxi and their consequences

Research on guanxi is conducted principally within the disciplines of anthropology, business studies and sociology. It typically takes the form of empirical case studies, applications of extrinsic theory and literature reviews cum trend reports. The present paper, on the other hand, provides an analysis of guanxi in consideration of its elemental relations, components and properties. Discussion indicates the limitations of treatments of guanxi in terms of trust, guanxi bases, tie‐strength and the conveyance of influence and information. Having established the characteristic features of guanxi discussion then turns to how it may be an option or choice of commitment for persons and groups in contemporary China, its form and role in marketized exchanges, and how the efficiency of guanxi may be characterized.     

Analysis of Intertemporal Choice: A New Framework and Experimental Results

This paper reports the results of a series of experiments examining intertemporal choice. The paper makes three contributions: First, it presents a new analytic device, the intertemporal choice triangle, which is analogous to the Marschak--Machina choice triangle used in the analysis of choice under risk. Second, we have developed a new experimental design based on the intertemporal choice triangle which allows subjects greater flexibility in making choices, and which allows the researcher to make more subtle inferences, than are possible with designs previously employed. Subjects are able to create their most-preferred outcome in each choice situation by choosing a constrained linear combination of two extreme options. Third, our results show that while subjects do not typically maximize present value, they are significantly influenced break by present value considerations. We refer to this finding as it present value-seeking behavior. We find only weak evidence of several previously documented intertemporal choice anomalies in our framework.     

“I Pay Enough Taxes Already!” Applying Economic Voting Models to Environmental Referendums*

Objectives. Models of economic voting have rarely been applied to referendum votes. We fill this gap by testing citizens' voting behavior on environmental policy in relation to their perception of the business cycle and general orientation toward politics. Thus, the study examines the personal, institutional, and economic determinants of vote choice on 36 environmental bills from 1983 to 2004 in Switzerland. Methods. We apply a logistic hierarchical model, where individual characteristics on Level 1 are nested within contextual determinants situated on Level 2. Results. We confirm the crucial importance of the individual‐level variables education, political affinity, car ownership, and urbanity. Classifying the electorate into five groups, using open‐ended survey questions about respondents' reasons for approval or dismissal of the bills, allows for finer hypotheses testing. We show that the individuals' positive perception of their personal current economic condition has a positive effect on the likelihood of supporting the proposals. In turn, we prove the negative, constraining effect of deteriorating macroeconomic conditions on approval rates. Conclusions. By applying economic voting models to referendum analyses we advance the understanding of citizens' vote choice on environmental ballots, we show the role of context, and we propose an original typology of voters' general orientation toward politics.     

‘q-Pareto-Scalar’ Two-Stage Extremization Model and its Reducibility to One-Stage Model

A two-stage sequential choice model is studied, the first stage being defined by q-Pareto multicriterial choice rule, and the second stage being defined by scalar extremization model. In this model, at the first stage the q-Pareto rule choses alternatives which are not only undominated in terms of Pareto comparison, but also includes into choice the alternatives which are dominated by no more than q alternatives. Since the choice set of the first-stage usually contains too many elements, obtained set is used as a presentation for the second stage constructed by a scalar extremization model. The properties of the model are studied as well as its representability to one-stage scalar extremization model.     

Implementation without rationality assumptions

Hurwicz (Social Choice and public decision making. Essays in honor of Kenneth J. Arrow, Cambridge University Press, Cambridge, 1986) was the first to study an approach to implementation theory based on choice functions instead of preference relations. We argue that the solution concept used by him, the generalized Nash equilibrium, is not really compatible with the idea that individual behavior is describable by a choice function. A new solution concept that better fits the choice function framework is then introduced. Using this, we investigate what behavioral assumptions are needed for the full characterizations of Nash implementable social choice correspondences to still hold. We will show that a condition known as Property α is central.     

Context dependence and consistency in dynamic choice under uncertainty: the case of anticipated regret

We examine if and to what extent choice dispositions can allow dependence on contexts and maintain consistency over time, in a dynamic environment under uncertainty. We focus on one of the context dependence properties, opportunity dependence because of being affected by anticipated regret, where the consequentialist choice framework is maintained. There are two sources of potential inconsistency: one is arrival of information, and the other is changing opportunities. First, we go over the general method of resolution of potential inconsistency, by taking any kinds of inconsistency as given constraints. Second, we characterize a class of choice dispositions that are consistent to information arrival, but may be inconsistent to changing opportunities. Finally, we consider the overall requirement of dynamic consistency and show that it necessarily implies each of consistency to information arrival and independence of choice opportunities. The last result states that the two kinds of potential inconsistency cannot “compensate” each other to recover dynamic consistency overall.     

On the (Sample) Condorcet Efficiency of Majority Rule: An alternative view of majority cycles and social homogeneity

The Condorcet efficiency of a social choice procedure is usually defined as the probability that this procedure coincides with the majority winner (or majority ordering) in random samples, given a majority winner exists (or given the majority ordering is transitive). Consequently, it is in effect a conditional probability that two sample statistics coincide, given certain side conditions. We raise a different issue of Condorcet efficiencies: What is the probability that a social choice procedure applied to a sample matches with the majority preferences of the population from which the sample was drawn? We investigate the canonical case where the sample statistic is itself also majority rule and the samples are drawn from real world distributions gathered from national election surveys in Germany, France, and the United States. We relate the results to the existing literature on majority cycles and social homogeneity. We find that these samples rarely display majority cycles, whereas the probability that a sample misrepresents the majority preferences of the underlying population varies dramatically and always exceeds the probability that the sample displays cyclic majority preferences. Social homogeneity plays a fundamental role in the type of Condorcet efficiency investigated here.