Consistent representative democracy

We study axioms which define “representative democracy” in an environment in which agents vote over a finite set of alternatives. We focus on a property that states that whether votes are aggregated directly or indirectly makes no difference. We call this property representative consistency. Representative consistency formalizes the idea that a voting rule should be immune to gerrymandering. We characterize the class of rules satisfying unanimity, anonymity, and representative consistency. We call these rules “partial priority rules.” A partial priority rule can be interpreted as a rule in which each agent can “veto” certain alternatives. We investigate the implications of imposing other axioms to the list specified above. We also study the partial priority rules in the context of specific economic models.     

Population-monotonicity and separability for economies with single-dipped preferences and the assignment of an indivisible object

We study two allocation models. In the first model, we consider the problem of allocating an infinitely divisible commodity among agents with single-dipped preferences. In the second model, a degenerate case of the first one, we study the allocation of an indivisible object to a group of agents. We consider rules that satisfy Pareto efficiency, strategy-proofness, and in addition either the consistency property separability or the solidarity property population-monotonicity. We show that the class of rules that satisfy Pareto efficiency, strategy-proofness, and separability equals the class of rules that satisfy Pareto efficiency, strategy-proofness, and non-bossiness. We also provide characterizations of all rules satisfying Pareto efficiency, strategy-proofness, and either separability or population-monotonicity. Since any such rule consists for the largest part of serial-dictatorship components, we can interpret the characterizations as impossibility results. Received: September 29, 1999; revised version: March 22, 2000     

Allocation problems among sharing groups

We deal with allocation problems among sharing groups. There are n agents. The agents are divided into several sharing groups. A homogeneous good is allocated among sharing groups rather than among the agents. The good is a private good for sharing groups, and a public good for the members of each sharing group. That is, all of them in the same sharing group can consume it without rivalry. We introduce some allocation rules and axioms. The utilitarian allocation rule and the egalitarian allocation rule are characterized by some axioms.     

The separability principle in bargaining

Summary. We investigate the implications of the separability principle in the context of bargaining. For two bargaining problems with the same population, suppose that there is a subgroup of agents who receive the same payoffs in both bargaining problems. Moreover, if we imagine the departure of this subgroup with their payoffs, then the remaining agents face the same opportunities in both bargaining problems. The separability principle requires that under these hypotheses, the remaining agents should receive the same payoffs in both bargaining problems. We begin with investigating the logical relations between separability and two other axioms, contraction independence and consistency. Then, we establish characterizations of the Nash and egalitarian solutions on the basis of separability. Received: 12 August 2002, Revised: 22 March 2004, JEL Classification Numbers: C71, C78.Youngsub Chun: This work was supported by the Brain Korea 21 Project in 2003. I am grateful to William Thomson, a referee, and an associate editor for their valuable comments.     

Separability and aggregation of equivalence relations

We provide axiomatic characterizations of two natural families of rules for aggregating equivalence relations: the family of join aggregators and the family of meet aggregators. The central conditions in these characterizations are two separability axioms. Disjunctive separability, neutrality, and unanimity characterize the family of join aggregators. On the other hand, conjunctive separability and unanimity characterize the family of meet aggregators. We show another characterization of the family of meet aggregators using conjunctive separability and two Pareto axioms, Pareto⁺ and Pareto^?. If we drop Pareto^?, then conjunctive separability and Pareto⁺ characterize the family of meet aggregators along with a trivial aggregator.     

Prize sharing in collective contests

The characteristics of endogenously determined sharing rules and the group-size paradox are studied in a model of group contest with the following features: (i) The prize has mixed private–public good characteristics. (ii) Groups can differ in marginal cost of effort and their membership size. (iii) In each group the members decide how much effort to put without observing the sharing rules of the other groups. It is shown that endogenous determination of group sharing rules completely eliminates the group-size paradox, i.e. a larger group always attains a higher winning probability than a smaller group, unless the prize is purely private. In addition, an interesting pattern of equilibrium group sharing rules is revealed: The group attaining the lower winning probability is the one choosing the rule giving higher incentives to the members.     

The Possibility of Issue-Specific Decisions on Multiple Social Choice Issues

This paper considers an aggregation rule when each alternative consists of elements of multiple issues. I assume that each issue-specific aggregation rule can be applied to each issue and explore whether various different issue-specific aggregation rules are compatible. When the set of alternatives has some structure (which we call a set connected by loops), there exists a powerful individual whose preference always coincides with the social ordering in every issue. As a corollary, Arrow's General Possibility Theorem is obtained.     

An efficiency characterization of plurality social choice on simple preference domains

Summary. We consider a model of social choice dealing with the problem of choosing a subset from a set of objects (e.g. candidate selection, membership, and qualification problems). Agents have trichotomous preferences for which objects are partitioned into three indifference classes, goods, bads, and nulls, or dichotomous preferences for which each object is either a good or a bad. We characterize plurality-like social choice rules on the basis of the three main axioms, known as Pareto efficiency, anonymity, and independence.Received: 29 August 2003, Revised: 3 June 2004, JEL Classification Numbers: D70, D71, D72.Biung-Ghi Ju: I am grateful to William Thomson and Jianbo Zhang for their helpful comments and discussions. I also thank Brandon Dupont, the participants in seminars at Iowa State University, University of Kansas, and the Midwest Theory Meeting at University of Notre Dame. I thank an anonymous referee for detailed comments and suggestions that were very helpful in simplifying the proof of Theorem 1 and in revising the paper.     

Dynamic stability and reform of political institutions

This paper examines endogenous institutional change in a class of dynamic political games. The political aggregation rules used at date t+1 are instrumental choices under rules at date t. Effectively, rules are “players” who can strategically delegate future policy-making authority to different rules. A political rule is stable if it selects itself. A reform occurs when an alternative rule is selected. The stability of a political rule is shown to depend on whether its choices are dynamically consistent. For instance, simple majority rules can be shown to be dynamically consistent in many common environments where wealth-weighted voting rules are not. The result extends to political rules that incorporate private activities such as extra-legal protests, threats, or private investment. The approach is one way of understanding various explanations of institutional change proposed in the literature. A parametric model of public goods provision gives an illustration.     

STRATEGIC CANDIDACY AND SINGLE‐PEAKEDNESS*

In elections, the voting outcomes are affected by strategic entries of candidates. We study a class of voting rules immune to strategic candidacy. Dutta et al. (2001 ) show that such rules satisfying unanimity are dictatorial if all orderings of candidates are admissible for voters’ preferences. When voters’ preferences are single‐peaked over a political spectrum, there exist non‐dictatorial rules immune to strategic candidacy. An example is the rule selecting the m‐th peak from the left among the peaks of voters’ preferences, where m is any natural number no more than the number of voters. We show that immunity from strategic candidacy with basic axioms fully characterizes the family of the m‐th leftmost peak rules.     

Preference revelation with a limited number of indifference classes

Suppose that g is a strategy-proof social choice rule on the domain of all profiles of complete and transitive binary relations that have exactly m indifference classes. If and the range of g has three or more members, then g is dictatorial. If m = 2, then for any set X of feasible alternatives, there exist non-dictatorial and strategy-proof rules that are sensitive to the preferences of every individual and which have X as range.     

The Austrian theory of the marginal use and of ordinal marginal utility

Conclusion The Austrian theory of the marginal use raises almost as many problems as it has solved. We list here a few of these unsolved problems.Complementarity and rivalness do lead to the ALEP criterion in the examples we worked out above, but we have made no attempt to formalize this rule into a general theorem. Intuitively, the ALEP condition must appear when the complementary or rival relationships are somehow active in the inner or outer marginal uses, but it is not clear exactly what the circumstances are under which this holds.Although the theory leads to quasi-concavity of commodity preferences over goods in the particular cases we worked out, even when rival or complementary interactions are present, it has only been proven that this must be generally true when there are two goods, and then only in the case when the two goods are independent. Perhaps preferences do not really have to be quasi-concave after all.And finally, it must be resolved whether the possibility of intrinsically ordinal preferences nullifies the von Neumann-Morgenstern axiom system, or if instead the validity of those axioms rules out intrinsically ordinal preferences.After over a century, the Austrian theory is still in its youth. Perhaps the day has come for Felix Kaufmann's youngGrenznutzler to return from the netherworld of economic doctrine: There I will quietly lie in wait, Amid my neglected writings, Until I hear the trumpet call of Complementary Goods. Then through the sky will gallop Böhm-Bawerk, Polemics will thunder and flash! Then armed with a quill I'll rise up from the grave, To fight for theGrenznutzen school!²⁷ The author is Scherman Research Fellow at NBER-West and Assistant Professor at Boston College. He is grateful for helpful suggestions made by J. R. Meginniss and by various participants in seminars at Boston College, at the Universities of Hartford and Chicago, at Stanford University, and at NBER-West.     

Designing incentives for online question-and-answer forums

We provide a game-theoretic model of sequential information aggregation motivated by online question-and-answer forums. An asker posts a question and each user decides when to aggregate a unique piece of information with existing information. When the quality exceeds a certain threshold, the asker closes the question and allocates points to users. We consider the effect of different rules for allocating points on the equilibrium behavior. A best-answer rule provides a unique, efficient equilibrium in which all users respond in the first round, for substitutes valuations over information. However, the best-answer rule isolates the least efficient equilibrium for complements valuations. We demonstrate alternate scoring rules that provide an efficient equilibrium for distinct subclasses of complements valuations, and retain an efficient equilibrium for substitutes valuations. We introduce a reasonable set of axioms, and establish that no rule satisfying these axioms can achieve the efficient outcome in a unique equilibrium for all valuations.     

No-envy in queueing problems

We explore the implications of no-envy(Foley 1967) in the context of queueing problems. We identify an easy way of checking whether a rule satisfies efficiencyand no-envy. The existence of such a rule can easily be established. Next, we ask whether there is a rule satisfying efficiency and no-envytogether with an additional solidarity requirement how agents should be affected as a consequence of changes in the waiting costs. However, there is no rule satisfying efficiency, noenvy, and either one of two cost monotonicity axioms. To remedy the situation, we propose modifications of no-envy, adjusted no-envyand backward/forward no-envy. Finally, we discuss whether three fairness requirements, no-envy, the identical preferences lower bound, and egalitarian equivalence, are compatible in this context.     

An Axiomatic Foundation of the Multiplicative Human Development Index

The aggregation formula in the Human Development Index (HDI) was changed to a geometric mean in 2010. In this paper, we search for a theoretical justification for employing this new HDI formula. First, we find a maximal class of index functions, what we call quasi‐geometric means, that satisfy symmetry for the characteristics, normalization, and separability. Second, we show that power means are the only quasi‐geometric means satisfying homogeneity. Finally, the new HDI is the only power mean satisfying minimal lower boundedness, which is a local complementability axiom proposed by Herrero et al. (2010).     

Group identification with (incomplete) preferences

We consider the problem of identifying members of a group based on individual opinions. Since agents do not have preferences in the model, properties of rules that concern preferences (e.g., strategy‐proofness and efficiency) have not been studied in the literature. We fill this gap by working with a class of incomplete preferences derived directly from opinions. Our main result characterizes a new family of group identification rules, called voting‐by‐equitable‐committees rules, using two well‐known properties: strategy‐proofness and equal treatment of equals. Our family contains as a special case the consent rules (Samet & Schmeidler. J. Econ. Theory, 110 (2003), pp. 213–233), which are symmetric and embody various degrees of liberalism and democracy; and it also includes dictatorial and oligarchic rules that value agents’ opinions differently. In the presence of strategy‐proofness, efficiency turns out to be equivalent to non‐degeneracy (i.e., any agent may potentially be included or excluded from the group). This implies that a rule satisfies strategy‐proofness, efficiency, and equal treatment of equals if, and only if, it is a non‐degenerate voting‐by‐equitable‐committees rule.     

Coalitional manipulation and the Pareto rule

This paper examines aggregation procedures that map profiles of individual preferences into choice sets. An aggregation procedure is said to be “manipulable by a coalition” if there is a group of individuals, and a preference profile, such that every member of the group prefers the choice set obtained when they are misrepresenting their preferences, to the one obtained when they are honest. We show that the Pareto rule, which is an aggregation procedure that maps profiles of individual preferences into corresponding sets of Pareto optima, is not manipulable by any coalition of individuals under various behavioural assumptions which relate preferences over choice sets to preferences over alternatives. The non-manipulability of the Pareto rule by a single individual follows as a special case under these behavioural assumptions.     

RULE RATIONALITY

We study the strategic advantages of following rules of thumb that bundle different games together (called rule rationality) when this may be observed by one's opponent. We present a model in which the strategic environment determines which kind of rule rationality is adopted by the players. We apply the model to characterize the induced rules and outcomes in various interesting environments. Finally, we show the close relations between act rationality and “Stackelberg stability” (no player can earn from playing first).     

Dynamic stability and reform of political institutions

This paper examines endogenous institutional change in a class of dynamic political games. The political aggregation rules used at date t+1 are instrumental choices under rules at date t. Effectively, rules are “players” who can strategically delegate future policy-making authority to different rules. A political rule is stable if it selects itself. A reform occurs when an alternative rule is selected. The stability of a political rule is shown to depend on whether its choices are dynamically consistent. For instance, simple majority rules can be shown to be dynamically consistent in many common environments where wealth-weighted voting rules are not. The result extends to political rules that incorporate private activities such as extra-legal protests, threats, or private investment. The approach is one way of understanding various explanations of institutional change proposed in the literature. A parametric model of public goods provision gives an illustration.     

Majority rule when voters like to win

I analyze symmetric majority rule voting equilibria when voters wish to elect the better candidate and to vote for the winner. When voters care only about the winning candidate (the standard formulation) a unique responsive equilibrium exists. The addition of a desire to win creates multiple equilibria, some with unusual properties. In most of these equilibria information is not aggregated effectively, and I uncover the novel possibility of negative information aggregation in which information aggregated in equilibrium is used to select the worse rather than the better candidate.I then characterize the efficiency of optimal equilibria as the population becomes large and show that a discontinuity arises in the information aggregation capabilities of the majority rule voting mechanism: in elections without a dominant front-running candidate the better candidate is almost surely elected, whereas in races with a front-runner information cannot be effectively aggregated in equilibrium.