A characterization of consistent collective choice rules

We characterize a class of collective choice rules such that collective preference relations are consistent. Consistency is a weakening of transitivity and a strengthening of acyclicity requiring that there be no cycles with at least one strict preference, which excludes the possibility of a “money pump.” The properties of collective choice rules used in our characterization are unrestricted domain, strong Pareto, anonymity and neutrality. If there are at most as many individuals as there are alternatives, the axioms provide an alternative characterization of the Pareto rule. If there are more individuals than alternatives, however, further rules become available.     

Observable restrictions of general equilibrium models with financial markets

This paper examines whether general equilibrium models of exchange economies with incomplete financial markets impose restrictions on prices of commodities and assets given the stochastic processes of dividends and aggregate endowments. We show that the assumption of time-separable expected utility implies restriction on the cross-section of asset prices as well as on spot commodity prices. However, a relaxation of the assumption of time separability will generally destroy these restriction.     

Attention economies

A new theoretical model is developed which describes the structure of competition for attention and characterizes equilibria. The exogenous fundamentals of an attention economy are the space of receiving subjects with their attention capacity, and the potential set of competing firms (senders) with their radiation technology. The endogenous variables explained by the theory are equilibrium audiences (the clients belonging to a sender), their signal exposure and attention, and the diversity of senders surviving the contest for attention. Application of the equilibrium analysis suggests that international integration or progress in information technologies tend to decrease global diversity. Local diversity, perceived by the individual receivers, may increase nonetheless.     

The structure of strategy-proof social choice — Part I: General characterization and possibility results on median spaces

We define a general notion of single-peaked preferences based on abstract betweenness relations. Special cases are the classical example of single-peaked preferences on a line, the separable preferences on the hypercube, the “multi-dimensionally single-peaked” preferences on the product of lines, but also the unrestricted preference domain. Generalizing and unifying the existing literature, we show that a social choice function is strategy-proof on a sufficiently rich domain of generalized single-peaked preferences if and only if it takes the form of voting by issues (“voting by committees”) satisfying a simple condition called the “Intersection Property.”Based on the Intersection Property, we show that the class of preference domains associated with “median spaces” gives rise to the strongest possibility results; in particular, we show that the existence of strategy-proof social choice rules that are non-dictatorial and neutral requires an underlying median space. A space is a median space if, for every triple of elements, there is a fourth element that is between each pair of the triple; numerous examples are given (some well-known, some novel), and the structure of median spaces and the associated preference domains is analysed.     

Electing a representative committee by approval ballot: An impossibility result

We consider methods of electing a fixed number of candidates, greater than one, by approval ballot. We define a representativeness property and a Pareto property and show that these jointly imply manipulability.     

Countercyclical pricing: A consumer heterogeneity explanation

We show that a seasonal good could be priced countercyclically due to the heterogeneous seasonal shifts in consumer valuations. We provide empirical support for our explanation based on two product categories (canned soup and tuna) studied in the literature.     

On the universally beneficial manipulation conjecture

The universally beneficial manipulation conjecture of Campbell and Kelly states that for a social choice rule, if everyone gains as a result of any optimal manipulation, then the rule satisfies universally beneficial manipulation, i.e., everyone gains as a result of any manipulation, optimal or not. We prove the conjecture for three alternatives and any number of individuals. We also construct a counterexample in a general form with more than three alternatives and at least two individuals.     

On the learnability of majority rule

We establish how large a sample of past decisions is required to predict future decisions of a committee with few members. The committee uses majority rule to choose between pairs of alternatives. Each member's vote is derived from a linear ordering over all the alternatives. We prove that there are cases in which an observer cannot predict precisely any decision of a committee based on its past decisions. Nonetheless, approximate prediction is possible after observing relatively few random past decisions.     

Social orderings for the assignment of indivisible objects

In the assignment problem of indivisible objects with money, we study social ordering functions which satisfy the requirement that social orderings should be independent of changes in preferences over infeasible bundles. We combine this axiom with efficiency, consistency and equity axioms. Our result is that the only social ordering function satisfying those axioms is the leximin function in money utility.     

Factoring out the impossibility of logical aggregation

According to a theorem recently proved in the theory of logical aggregation, any nonconstant social judgment function that satisfies independence of irrelevant alternatives (IIA) is dictatorial. We show that the strong and not very plausible IIA condition can be replaced with a minimal independence assumption plus a Pareto-like condition. This new version of the impossibility theorem likens it to Arrow's and arguably enhances its paradoxical value.     

Kidney exchange: An egalitarian mechanism

Kidney exchange programs utilize both deceased-donor and live-donor kidneys. One of these programs, a two-way kidney paired donation (KPD), involves two patients exchanging their live donors? kidneys. Another possibility is a list exchange (LE): a living incompatible donor provides a kidney to a candidate on the deceased-donor waitlist and in return the intended recipient of this donor receives a priority on the waitlist. By taking into consideration the fact that transplants from live donors have a higher chance of success than those from cadavers, we characterize the set of efficient and egalitarian exchanges involving the KPD?s and LE?s.     

Allocation rules for land division

This paper studies the classical land division problem formalized by Steinhaus (Econometrica 16 (1948) 101-104) in a multi-profile context. We propose a notion of an allocation rule for this setting.  We discuss several examples of rules and properties they may satisfy. Central among these properties is division independence: a parcel may be partitioned into smaller parcels, these smaller parcels allocated according to the rule, leaving a recommended allocation for the original parcel. In conjunction with two other normative properties, division independence is shown to imply the principle of utilitarianism.     

The wisdom of the minority

We consider a simple variant of the canonical model of social learning and show that in many situations it is optimal for an agent to abandon her own information and follow the minority rather than the majority. This possibility depends on two economically meaningful requirements: agents are differentially informed and observe only the number of agents having chosen each option, such as consumers observing only market shares. We show that minority wisdom arises when information is sufficiently heterogeneous and the well informed are not overly abundant, yet the conditions necessary are not overly restrictive. In fact, it is possible for the minority to be wise even when the minority consists of a lone dissenter and a majority of citizens are well informed.     

The exact law of large numbers via Fubini extension and characterization of insurable risks

A Fubini extension is formally introduced as a probability space that extends the usual product probability space and retains the Fubini property. Simple measure-theoretic methods are applied to this framework to obtain various versions of the exact law of large numbers and their converses for a continuum of random variables or stochastic processes. A model for a large economy with individual risks is developed; and insurable risks are characterized by essential pairwise independence. The usual continuum product based on the Kolmogorov construction together with the Lebesgue measure as well as the usual finitely additive measure-theoretic framework is shown further to be not suitable for modeling individual risks. Measurable processes with essentially pairwise independent random variables that have any given variety of distributions exist in a rich product probability space that can also be constructed by extending the usual continuum product.     

Nonlinear incentive provision in Walrasian markets: a Cournot convergence approach

The paper studies insurance with moral hazard in a system of contingent-claims markets. Insurance buyers are modelled as Cournot monopolists or oligopolists. The other agents condition their expectations on market prices, as in models of rational-expectations equilibrium with asymmetric information. Thereby they correctly anticipate accident probabilities corresponding to effort incentives induced by insurance buyers’ net trades. When there are many agents to share the insurance buyers’ risks, Cournot equilibrium outcomes are close to being second-best. In contrast, if insurance buyers are price takers, equilibria fail to exist or are bounded away from being second-best.     

Certainty Independence and the Separation of Utility and Beliefs

Economists often operate under an implicit assumption that the tastes of a decision maker are quite stable, while his beliefs change with the availability of new information. We show that for a general class of preferences, a separation of a key component of tastes, the utility function, from the other components of the representation is possible only if the decision maker's preferences satisfy a mild but not completely innocuous condition, called ‘certainty independence’. We also outline the axiomatic characterization of the preferences that obtain such separation, which are a subset of the biseparable preferences.     

Sharing the surplus: An extension of the Shapley value for environments with externalities

Economic activities, both on the macro and micro level, often entail wide-spread externalities. This in turn leads to disputes regarding the compensation levels to the various parties affected. We propose a method of deciding upon the distribution of the gains (costs) of cooperation in the presence of externalities when forming the grand coalition is efficient. We show that any sharing rule satisfying efficiency, linearity, dummy player and a strong symmetry axioms can be obtained through an average game. Adding an additional axiom, we identify one unique rule satisfying these properties.     

The competitive firm and the role of information about uncertain factor prices

This paper studies the role of information about uncertain input prices for a competitive firm. The production decision has to be taken when the price of an input factor is perceived as random. However, a signal is observable in advance, conveying some information about the future factor price. Transparency is linked to the informational content of this signal. The impact of a higher level of transparency is analyzed from an ex ante perspective, i.e. before the information signal is observed. The change of factor use, production amount and cost are determined by comparing the strength of the curvatures of total and marginal product. By contrast, ex ante profit always increases, independently of the shape of the production function.     

Manipulating uncertainty

Uncertainty about the distributional incidence of policy reforms may, if it impinges selectively on particular subsets of voters, alter the direction of the majority vote. This possibility should be a matter of special concern when subject to potential manipulation by a purposeful agent such as a Leviathan-like bureaucracy. This paper discusses a constitutional defense against such prospect. This paper was prepared for a conference on “Constitutional Status Quo and Prospects for Change” held at George Mason University in April, 1994. I am grateful to participants in that conference and to my colleagues at Nova, especially to Mário Páscoa, for their comments and criticisms. I also benefited from comments of an anonymous referee. Responsibility for errors remains with me.