A short step between democracy and dictatorship

When preferences are defined over two alternatives and societies are variable, the group formed by the relative majority rule, the unanimity rule, the dictatorial rules, and the strongly dictatorial rules is characterized in terms of five axioms: unanimity, reducibility, substitutability, exchangeability, and parity. This result is used to provide characterizations of each of these rules by postulating separating axioms, that is, an axiom and its negation. Such axioms identify traits specifically differentiating a type of rule from the other types. For instance, majority differs from strong dictatorship in the existence of a society for which collective indifference should be a less likely outcome than the strict preference of one alternative over the other. As a second example, the difference between majority and strong dictatorship can be traced back to the requirement that the likelihood of collective indifference diminishes with the size of society.     

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.     

On Preference and Freedom

We consider the role of preferences in the assessment of an agent's freedom, visualized as the opportunity for choice. After discussing several possible intuitive approaches to the problem, we explore an approach based on the notion of preference orderings that a reasonable person may possibly have. Using different sets of axioms, we characterize the rules for ranking opportunity sets in terms of freedom. We also show that certain axioms for ranking opportunity sets are incompatible.     

Resolute majority rules

We investigate resolute voting rules that always rank two alternatives strictly and avoid social indecision. Resolute majority rules differ from the standard majority rule in that whenever both alternatives win the same number of votes, a tie-breaking function is used to determine the outcome. We provide axiomatic characterizations of resolute majority rules or resolute majority rules with a quorum. Resoluteness axiom is used in all these results. The other axioms are weaker than those considered in the characterization of the majority rule by May (1952 Econometrica, 20:680–684). In particular, instead of May’s positive responsiveness, we consider a much weaker monotonicity axiom.     

How to reveal people’s preferences: Comparing time consistency and predictive power of multiple price list risk elicitation methods

The question of how to measure and classify people’s risk preferences is of substantial importance in the field of economics. Inspired by the multitude of ways used to elicit risk preferences, we conduct a holistic investigation of the most prevalent method, the multiple price list (MPL) and its derivations. In our experiment, we find that revealed preferences differ under various versions of MPLs as well as yield unstable results within a 30-minute time frame. We determine the most stable elicitation method with the highest forecast accuracy by using multiple measures of within-method consistency and by using behavior in two economically relevant games as benchmarks. A derivation of the well-known method by Holt and Laury (American Economic Review 92(5):1644–1655, 2002), where the highest payoff is varied instead of probabilities, emerges as the best MPL method in both dimensions. As we pinpoint each MPL characteristic’s effect on the revealed preference and its consistency, our results have implications for preference elicitation procedures in general.     

On the Representation of Beliefs by Probabilities

This paper explores two axiomatic structures of subjective expected utility assuming a finite state-space and state-dependent, connected, topological outcome-spaces. Building on the work of Karni and Schmeidler (1981) the analytical framework includes, in addition to the preference relation on acts, introspective preferences on hypothetical lotteries that are linked to the preference relation on acts by consistency axioms. The two models accommodate state-dependent preferences and yield subjective probabilities that correctly represent the decision-maker's beliefs. State-independent preferences are a special case.     

Ranking sets additively in decisional contexts: an axiomatic characterization

Ranking finite subsets of a given set X of elements is the formal object of analysis in this article. This problem has found a wide range of economic interpretations in the literature. The focus of the article is on the family of rankings that are additively representable. Existing characterizations are too complex and hard to grasp in decisional contexts. Furthermore, Fishburn (1996), Journal of Mathematical Psychology 40, 64–77 showed that the number of sufficient and necessary conditions that are needed to characterize such a family has no upper bound as the cardinality of X increases. In turn, this article proposes a way to overcome these difficulties and allows for the characterization of a meaningful (sub)family of additively representable rankings of sets by means of a few simple axioms. Pattanaik and Xu’s (1990), Recherches Economiques de Louvain 56, 383–390) characterization of the cardinality-based rule will be derived from our main result, and other new rules that stem from our general proposal are discussed and characterized in even simpler terms. In particular, we analyze restricted-cardinality based rules, where the set of “focal” elements is not given ex-ante; but brought out by the axioms.      

Stability and Efficiency of Partitions in Matching Problems

We define two versions of stability and efficiency of partitions and analyze their relationships for some matching rules. The stability and efficiency of a partition depends on the matching rule φ. The results are stated under various membership property rights axioms. It is shown that in a world where agents can freely exit from and enter coalitions, whenever the matching rule is individually rational and Pareto optimal, the set of φ-stable and φ-efficient partitions coincide and it is unique: the grand coalition. Then we define a weaker version of stability and efficiency, namely specific to a given preference profile and find some negative results for stable matching rules.     

Preferences Representable by a Lower Expectation: Some Characterizations

We propose two different characterizations for preference relations representable by lower (upper) expectations with the aim of removing either fair price or completeness requirements. Moreover, we give an explicit characterization for comparative degrees of belief on a finite algebra of events representable by lower probabilities.     

A challenge to the compound lottery axiom: A two-stage normative structure and comparison to other theories

This paper examines preferences among uncertain prospects when the decision maker is uneasy about his assignment of subjective probabilities. It proposes a two-stage lottery framework for the analysis of such prospects, where the first stage represents an assessment of the vagueness (ambiguity) in defining the problem's randomness and the second stage represents an assessment of the problem for each hypothesized randomness condition. Standard axioms of rationality are prescribed for each stage, including weak ordering, continuity, and strong independence. The Reduction of Compound Lotteries' axiom is weakened, however, so that the two lottery stages have consistent, but not collapsible, preference structures. The paper derives a representation theorem from the primitive preference axioms, and the theorem asserts that preference-consistent decisions are made as if the decision maker is maximizing a modified expected utility functional. This representation and its implications are compared to alternative decision models. Criteria for assigning the relative empirical power of the alternative models are suggested.     

The reasonable man — a social choice approach

Most legal systems rely heavily on the notion of the reasonable man. Here an attempt is made to analyze the reasonable man in a social choice model. The main argument is that if the reasonable man satisfies a certain set of axioms, he essentially coincides with one of the individuals, both in terms of his preferences and in terms of his expectations.     

Choice procedure consistent with similarity relations

We deal with the approach, initiated by Rubinstein, which assumes that people, when evaluating pairs of lotteries, use similarity relations. We interpret these relations as a way of modelling the imperfect powers of discrimination of the human mind and study the relationship between preferences and similarities. The class of both preferences and similarities that we deal with is larger than that considered by Rubinstein. The extension is made because we do not want to restrict ourselves to lottery spaces. Thus, under the above interpretation of a similarity, we find that some of the axioms imposed by Rubinstein are not justified if we want to consider other fields of choice theory. We show that any preference consistent with a pair of similarities is monotone on a subset of the choice space. We establish the implication upon the similarities of the requirement of making indifferent alternatives with a component which is zero. Furthermore, we show that Rubinstein's general results can also be obtained in this larger class of both preferences and similarity relations.The nontransitiveness of indifference must be recognized and explained on any theory of choice and the only explanation that seems to work is based on the imperfect powers of discrimination of the human mind whereby inequality becomes recognizable only when of sufficient magnitude.     

Guilt and shame: an axiomatic analysis

Using the machinery of Game Theory, this article analyzes how shame and guilt affect preferences. Based on abundant psychological literature, we posit that the preference ordering of someone who can feel shame (or guilt) must satisfy a number of axioms and prove that it can be represented by a particular utility function. Understanding how shame and guilt work is important to explain why people respect social norms and exhibit prosocial behavior, many times contrary to their material interest.     

Conditional expected utility

Let \({\mathcal {E}}\) be a class of events. Conditionally Expected Utility decision makers are decision makers whose conditional preferences \(\succsim _{E}\), \(E\in {\mathcal {E}}\), satisfy the axioms of Subjective Expected Utility (SEU) theory. We extend the notion of unconditional preference that is conditionally EU to unconditional preferences that are not necessarily SEU. We study a subclass of these preferences, namely those that satisfy dynamic consistency. We give a representation theorem, and show that these preferences are Invariant Bi-separable in the sense of Ghirardato et al. (Journal of Economic Theory 118:133–173, 2004). We also show that these preferences have only a trivial overlap with the class of Choquet Expected Utility preferences, but there are plenty of preferences of the \(\alpha \)-Maxmin Expected Utility type that satisfy our assumptions. We identify several concrete settings where our results could be applied. Finally, we consider the special case where the unconditional preference is itself SEU, and compare our results with those of Fishburn (Econometrica 41:1–25, 1973).     

On the existence of fair matching algorithms

We analyze the Gale-Shapley matching problem within the context of Rawlsian justice. Defining a fair matching algorithm by a set of 4 axioms (Gender Indifference, Peer Indifference, Maximin Optimality, and Stability), we show that not all preference profiles admit a fair matching algorithm, the reason being that even this set of minimal axioms is too strong in a sense. Because of conflict between Stability and Maximin Optimality, even the algorithm which generates the mutual agreement match, paradoxically, has no chance to be fair.We then relax the definition of fairness (by giving preference to Stability over Maximin Optimality) and again find that some preference profiles admit a fair matching algorithm, while others still do not, but the mutual agreement algorithm now is fair under this definition.The paper then develops a test, which determines, for a given preference profile, whether a fair algorithm exists or not.     

Strategy-proofness,tops-only,and the uniform rule

In the division problem with single-peaked preferences, an allocation rule is strategy-proof for same tops if no one can gain by reporting a false preference relation having the true peak. This new condition is so weak that it is implied by strategy-proofness and tops-only. We show that the uniform rule is the only rule satisfying this mild property under efficiency and envy-freeness. We then analyze how largely the preference domain can be extended with admitting a rule satisfying the three axioms, and show that the single-plateaued domain is the unique such maximal domain.     

Bargaining Solutions as Social Compromises

A bargaining solution is a social compromise if it is metrically rationalizable, i.e., if it has an optimum (depending on the situation, smallest or largest) distance from some reference point. We explore the workability and the limits of metric rationalization in bargaining theory where compromising is a core issue. We demonstrate that many well-known bargaining solutions are social compromises with respect to reasonable metrics. In the metric approach, bargaining solutions can be grounded in axioms on how society measures differences between utility allocations. Using this approach, we provide an axiomatic characterization for the class of social compromises that are based on p-norms and for the attending bargaining solutions. We further show that bargaining solutions which satisfy Pareto Optimality and Individual Rationality can always be metrically rationalized.     

An axiomatization of cumulative prospect theory

This paper presents a method for axiomatizing a variety of models for decision making under uncertainty, including Expected Utility and Cumulative Prospect Theory. This method identifies, for each model, the situations that permit consistent inferences about the ordering of value differences. Examples of rankdependent and sign-dependent preference patterns are used to motivate the models and the “tradeoff consistency” axioms that characterize them. The major properties of the value function in Cumulative Prospect Theory—diminishing sensitivity and loss aversion—are contrasted with the principle of diminishing marginal utility that is commonly assumed in Expected Utility.     

Conditioning Capacities and Choquet Integrals: The Role of Comonotony

Choquet integrals and capacities play a crucial role in modern decision theory. Comonotony is a central concept for these theories because the main property of a Choquet integral is its additivity for comonotone functions. We consider a Choquet integral representation of preferences showing uncertainty aversion (pessimism) and propose axioms on time consistency which yield a candidate for conditional Choquet integrals. An other axiom characterizes the role of comonotony in the use of information. We obtain two conditioning rules for capacities which amount to the well-known Bayes' and Dempster–Schafer's updating rules. We are allowed to interpret both of them as a lack of confidence in information in a dynamic extension of pessimism. This revised version was published online in June 2006 with corrections to the Cover Date.     

Reasoning-based introspection

We show that if an agent reasons according to standard inference rules, the truth and introspection axioms extend from the set of non-epistemic propositions to the whole set of propositions. This implies that the usual axiomatization of partitional possibility correspondences is redundant, and provides a justification for truth and introspection that is partly based on reasoning.