Christopher P. Chambers

Incentives in Experiments: A Theoretical Analysis

Experimental economists currently lack a convention for how to pay subjects in experiments with multiple tasks. We provide a theoretical framework for analyzing this question. Assuming statewise monotonicity and nothing else, we prove that paying for one randomly chosen problem—the random problem selection mechanism—is essentially the only incentive compatible mechanism. Paying for every period is similarly justified when we assume only a “no complementarities at the top” condition. To help experimenters decide which is appropriate for their particular experiment, we discuss empirical tests of these two assumptions.

Gains from trade

In a social choice context, we ask whether there exists a rule in which nobody loses under trade liberalization. We consider a resource allocation problem in which the traded commodities vary. We propose an axiom stating that enlarging the set of tradable commodities hurts nobody. We show that if a rule satisfies this axiom, together with an allocative efficiency axiom and an institutional constraint axiom stating that only preferences over tradable commodities matter, gains from trade can be given to only one individual in the first step of liberalization.

Group order preservation and the proportional rule for the adjudication of conflicting claims

Abstract We investigate the existence of rules for the adjudication of conflicting claims satisfying ‘group order preservation’: given two groups of claimants, suppose that the sum of the claims of the members of the first group is greater than or equal to the sum of the claims of the members of the second group. Then, similar inequalities should hold for the sums of the awards to the members of the two groups, and for the sums of the losses incurred by the members of two groups. The property is easily satisfied. We then combine it with two others. First is ‘claims continuity’: the chosen awards vector should vary continuously with the claims vector. Second is ‘consistency’: the awards vector chosen for each problem should be ‘in agreement’ with the awards vector chosen for each problem derived from it by imagining some of the claimants receiving their awards and leaving. We show that only the proportional rule satisfies all three requirements. This characterization holds even if the number of potential claimants is as low as 3. We also offer a version of the characterization for a variant of the model in which the set of claimants is modelled as a continuum.

Preference aggregation under uncertainty: Savage vs. Pareto

Following Mongin [12, 13], we study social aggregation of subjective expected utility preferences in a Savage framework. We argue that each of Savages P3 and P4 and incompatible with the Strong Pareto property. A representation theorem for social preferences satisfying Pareto indifference and conforming to the state-dependent expected utility model is provided.

Supermodularity and preferences

We uncover the complete ordinal implications of supermodularity on finite lattices under the assumption of weak monotonicity. In this environment, we show that supermodularity is ordinally equivalent to the notion of quasisupermodularity introduced by Milgrom and Shannon. We conclude that supermodularity is a weak property, in the sense that many preferences have a supermodular representation.

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.

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.

Choice and individual welfare

We propose an abstract method of systematically assigning a “rational” ranking to non-rationalizable choice data. Our main idea is that any method of ascribing welfare to an individual as a function of choice is subjective, and depends on the economist undertaking the analysis. We provide a simple example of the type of exercise we propose. Namely, we define an individual welfare functional as a mapping from stochastic choice functions into weak orders. A stochastic choice function (or choice distribution) gives the empirical frequency of choices for any possible opportunity set (framing factors may also be incorporated into the model). We require that for any two alternatives x and y, if our individual welfare functional recommends x over y given two distinct choice distributions, then it also recommends x over y for any mixture of the two choice distributions. Together with some mild technical requirements, such an individual welfare functional must weight every opportunity set and assign a utility to each alternative x which is the sum across all opportunity sets of the weighted probability of x being chosen from the set. It therefore requires us to have a “prior view” about how important or representative a choice of x at a given situation is.

Ordinal aggregation and quantiles

Abstract Consider the problem of aggregating a profile of interpersonally comparable utilities into a social utility. We require that the units of measurement of utility used for agents is the same as the units of measurement for society (ordinal covariance) and a mild Pareto condition (monotonicity). We provide several representations of such social aggregation operators: a canonical representation, a Choquet expectation representation, a minimax representation, and a quantile representation (with respect to a possibly non-additive set function on the agents). We also isolate an additional condition that gives us a quantile representation with respect to a probability measure, in both the finite and infinite agents case.

A Measure of Bizarreness

We introduce a path-based measure of convexity to be used in assessing the compactness of legislative districts. Our measure is the probability that a district contains the shortest path between a randomly selected pair of its points. The measure is defined relative to exogenous political boundaries and population distributions.