Plurality Rule Works In Three-Candidate Elections

In the citizen–candidate approach each citizen chooses whether or not to run as candidate. In a single-peaked preference domain, we find that the strategic entry decision of the candidates eliminates one of the most undesirable properties of Plurality rule, namely to elect a poor candidate in three-candidate elections since as we show, the Condorcet winner among the self-declared candidates is always elected. We find that the equilibria with three candidates are basically 2-fold, either there are two right-wing candidates and a left-wing candidate who wins the elections (or its symmetric), or there is a right-wing candidate, a left-wing candidate, and a candidate located in between the two others who becomes winner. We also show that when four or more candidates enter the contest, Plurality rule can elect the Condorcet-loser among the self-declared candidates.      

On the derivation of majority rule

It is well established that majority rule is transitive on some restricted domain and that majority rule is the unique social welfare function satisfying some standard axioms on the universal domain. We prove that majority rule is the unique social welfare function satisfying these axioms on a standard restricted domain over which majority rule is transitive. That is, the only profiles which are used to derive majority rule belong to the restricted domain.This paper was prepared while the author was visiting at the Ontario Economic Council, Toronto. It is a pleasure to acknowledge the hospitality of the OEC and the financial support of the Social Sciences and Humanities Research Council, Ottawa. Neither Council bears responsibility for the views expressed herein.     

Sleepiness,choice consistency,and risk preferences

We investigate the consistency and stability of individual risk preferences by manipulating cognitive resources. Participants are randomly assigned to an experiment session at a preferred time of day relative to their diurnal preference (circadian matched) or at a non-preferred time (circadian mismatched) and choose allocations between two risky assets [using the Choi et al. (Am Econ Rev 27(5):1921–1938, 2007), design]. We find that choices of circadian matched and mismatched subject are statistically similar in terms of satisfying basic requirements for preference consistency. However, mismatched subjects tend to choose riskier asset bundles.     

Revealed desirability: a novel instrument for social welfare

The note puts forward the idea of revealed desirability, a novel instrument, which like revealed preference is observable from choice and important for individual and social welfare. We provide the axiomatic underlying individual’s choice model, preliminary experimental results that support the idea, and an appealing allocation rule that uses the revealed desirability information along with the revealed-preference information.

     

Any complete preference structure without circuit admits an interval representation

This article proves that all complete preference structures where the strict preference relation (P) has no circuit admit a representation by intervals of the real line; the rule for deciding whether an interval is indifferent or preferred to another is less straightforward than for interval orders: strict preference is indeed compatible with a certain degree of overlapping of intervals, the allowed degree being specified by means of a so-called tolerance function.     

A No-Trade Theorem under Knightian Uncertainty with General Preferences

This paper derives a no-trade theorem under Knightian uncertainty, which generalizes the theorem of Milgrom and Stokey (1982, Journal of Economic Theory 26, 17) by allowing general preference relations. It is shown that the no-trade theorem holds true as long as agents' preferences are dynamically consistent in the sense of Machina and Schmeidler (1991, Econometrica 60, 745), and satisfies the so-called piece-wise monotonicity axiom. A preference satisfying the piece-wise monotonicity axiom does not necessarily imply the additive utility representation, nor is necessarily based on beliefs. This revised version was published online in June 2006 with corrections to the Cover Date.     

A geometric approach to revealed preference via Hamiltonian cycles

It is shown that a fundamental question of revealed preference theory, namely whether the weak axiom of revealed preference (WARP) implies the strong axiom of revealed preference (SARP), can be reduced to a Hamiltonian cycle problem: A set of bundles allows a preference cycle of irreducible length if and only if the convex monotonic hull of these bundles admits a Hamiltonian cycle. This leads to a new proof to show that preference cycles can be of arbitrary length for more than two but not for two commodities. For this, it is shown that a set of bundles satisfying the given condition exists if and only if the dimension of the commodity space is at least three. Preference cycles can be constructed by embedding a cyclic $(L-1)$ -polytope into a facet of a convex monotonic hull in $L$ -space, because cyclic polytopes always admit Hamiltonian cycles. An immediate corollary is that WARP only implies SARP for two commodities. The proof is intuitively appealing as this gives a geometric interpretation of preference cycles.     

The individual rationality of maintaining a sense of justice

Let us say that an individual possesses aprincipled preference if she prefers satisfying her preferences without violating the principles of justice governing her community to satisfying her preferences by violating these principles. Although living among possessors of principled preferences benefits individuals, maintaining such a preference is individually costly. Further, individuals can benefit from others possessing principled preferences without themselves possessing one. In this paper, I argue that occupying a choice situation which mirrors key aspects of our own situation, maximizing rationality requires individuals to develop and maintain principled preferences.To establish that maintaining a principled preference is individually rational for the occupants of such a choice situation, I define a range of individual strategies for them, model their choice of individual strategies as a game, and argue that this game involves an equilibrium in which all of its participants would choose to develop and maintain a principled preference.     

Characterization of dominance relations in finite coalitional games

McGarvey (Econometrica, 21(4), 608–610, 1953) has shown that any irreflexive and anti-symmetric relation can be obtained as a relation induced by majority rule. We address the analogous issue for dominance relations of finite cooperative games with non-transferable utility (coalitional NTU games). We find any irreflexive relation over a finite set can be obtained as the dominance relation of some finite coalitional NTU game. We also show that any such dominance relation is induced by a non-cooperative game through β-effectivity. Dominance relations obtainable through α-effectivity, however, have to comply with a more restrictive condition, which we refer to as the edge-mapping property.     

Consequentialist foundations for expected utility

Behaviour norms are considered for decision trees which allow both objective probabilities and uncertain states of the world with unknown probabilities. Terminal nodes have consequences in a given domain. Behaviour is required to be consistent in subtrees. Consequentialist behaviour, by definition, reveals a consequence choice function independent of the structure of the decision tree. It implies that behaviour reveals a revealed preference ordering satisfying both the independence axiom and a novel form of sure-thing principle. Continuous consequentialist behaviour must be expected utility maximizing. Other plausible assumptions then imply additive utilities, subjective probabilities, and Bayes' rule.     

The Pareto rule and strategic voting

This paper uses a particular choice rule over sets of alternatives under the Pareto rule. Starting from the sincere situation every strategic misrevelation of preference is shown to be an improvement for all voters. The existence of an equilibrium under successive misrepresentations by sincere voters is demonstrated.     

Individual rationality and the concept of social welfare

This paper, written in October 1974, deals with some game aspects of the social choice problem. The question asked is whether there exists a social decision rule satisfying the conditions imposed by Arrow over all the preference profiles that may logically arise under it (in the sense of being compatible with individual rationality). This question is answered in the affirmative. The meaning of this result is that if Arrow's condition of unrestricted domain is modified so as to exclude any profile which contradicts individual rationality, then an Arrovian social welfare function can be shown to exist (subject to the assumption that whenever the social outcome is in doubt, individuals use the maximin criterion in order to choose their voting strategy).This research was written up in October 1974 at Northwestern University and was partially supported by the National Science Foundation.     

The conflict between naive and sophisticated choice as a form of the ‘liberal paradox’

Pareto-inefficient perfect equilibria can be represented by the liberal paradox approach of Sen, appropriately reconfigured to model intertemporal decision-making by an individual. We show that the preference profile used by Grout (1982) to construct a case in which naive choice Pareto-dominates sophisticated choice can be so represented, if tastes change and if the individual can make decisions at time t, which restrict or determine opportunities available in period t + 1 and beyond. This ability to make a decision that binds oneself in the future is a form of rights assignment. We also show how two resolutions of the liberal paradox work out in the individual decision framework.     

An experimental investigation of violations of transitivity in choice under uncertainty

Several models of decision-making imply systematic violations of transitivity of preference. Our experiments explored whether people show patterns of intransitivity predicted by regret theory and majority rule. To distinguish “true” violations from those produced by “error,” a model was fit in which each choice can have a different error rate and each person can have a different pattern of true preferences that need not be transitive. Error rate for a choice is estimated from preference reversals between repeated presentations of that same choice. Our results showed that very few people repeated intransitive patterns. We can retain the hypothesis that transitivity best describes the data of the vast majority of participants.

Rule utilitarianism,rights, obligations and the theory of rational behavior

The paper first summarizes the author's decision-theoretical model of moral behavior, in order to compare the moral implications of the act-utilitarian and of the rule-utilitarian versions of utilitarian theory. This model is then applied to three voting examples. It is argued that the moral behavior of act-utilitarian individuals will have the nature of a noncooperative game, played in the extensive mode, and involving action-by-action maximization of social utility by each player. In contrast, the moral behavior of rule-utilitarian individuals will have the nature of a cooperative game, played in the normal mode, and involving a firm commitment by each player to a specific moral strategy (viz. to the strategy selected by the rule-utilitarian choice criterion) — even if some individual actions prescribed by this strategy, when considered in isolation, should fail to maximize social utility.The most important advantage that rule utilitarianism as an ethical theory has over act utilitarianism lies in its ability to give full recognition to the moral and social importance of individual rights and personal obligations. It is easy to verify that action-by-action maximization of social utility, as required by act utilitarianism, would destroy these rights and obligations. In contrast, rule utilitarianism can fully recognize the moral validity of these rights and obligations precisely because of its commitment to an overall moral strategy, independent of action-by-action social-utility maximization.The paper ends with a discussion of the voter's paradox problem. The conventional theory of rational behavior cannot avoid the paradoxical conclusion that, in any large electorate, voting is always an irrational activity because one's own individual vote is extremely unlikely to make any difference to the outcome of any election. But it can be shown that, by using the principles of rule-utilitarian theory, this paradox can easily be resolved and that, in actual fact, voting, even in large electorates, may be perfectly rational action. More generally, the example of rule utilitarianism shows what an important role the concept of a rational commitment can play in the analysis of rational behavior.     

Lottery Decisions and Probability Weighting Function

This article analyzes the implications of basic lottery tests for the probability weighting function w(p). We first show that the w(p) function with one argument cannot accommodate three basic tests of lottery choice. We also discuss in detail the links between the w(p) function with one argument and the preference reversal paradox. In the last section we propose an evaluation function that accommodates the restrictions imposed by the tests and we provide an example of such function.     

Some measures of closeness to unanimity and their implications

This note demonstrates how certain collective decision methods ensure the selection of alternatives which are the closest to win unanimously. By using four different functions for measuring the distance between preference profiles, we obtain the equivalence between the closeness to unanimity procedure (CUP) and the Borda method, the plurality rule, the probabilistic Borda rule and the L-procedure respectively.     

A revealed preference analysis of solutions to simple allocation problems

We interpret solution rules on a class of simple allocation problems as data on the choices of a policy maker. We analyze conditions under which the policy maker’s choices are (i) rational (ii) transitive-rational, and (iii) representable; that is, they coincide with maximization of a (i) binary relation, (ii) transitive binary relation, and (iii) numerical function on the allocation space. Our main results are as follows: (i) a well-known property, contraction independence (a.k.a. IIA) is equivalent to rationality; (ii) every contraction independent and other-c monotonic rule is transitive-rational; and (iii) every contraction independent and other-c monotonic rule, if additionally continuous, can be represented by a numerical function.     

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.     

The Budget-Voting Paradox

The budget-voting paradox states that, when social alternatives are proper subsets of a finite set of decisions, choosing decision-wise according to the majority rule may select an alternative that is covered in the majority tournament among alternatives. Individual preferences are defined on single decisions, and are extended to preferences over the alternative set by means of a preference extension rule. We prove the existence of the paradox for any rank-based, monotone, and independent extension rule.