Endogenous reference points and the adjusted proportional solution for bargaining problems with claims

 A modification of the proportional solution for bargaining problems with claims is proposed. This solution is constructed by considering an endogenous reference point. Characterization results of the aforementioned solution are provided. Received: 22 December 1993/Accepted: 12 August 1996     

Preference intensity representation: strategic overstating in large elections

If voters vote strategically, is it useful to offer them the possibility of expressing nuanced opinions, or would they always overstate the intensity of their preferences? For additive voting rules, say that a ballot is extremal if it is neither abstention-like nor can be expressed as a mixture of the available ballots. We give a sufficient condition for strategic equivalence: if two rules share the same set of extremal ballots (up to an homothetic transformation), they are strategically equivalent in large elections. This condition is also necessary for the strategic equivalence of positional rules. These results do not hold for small electorates.     

A Borda count for partially ordered ballots

The application of the theory of partially ordered sets to voting systems is an important development in the mathematical theory of elections. Many of the results in this area are on the comparative properties between traditional elections with linearly ordered ballots and those with partially ordered ballots. In this paper we present a scoring procedure, called the partial Borda count, that extends the classic Borda count to allow for arbitrary partially ordered preference rankings. We characterize the partial Borda count in the context of weighting procedures and in the context of social choice functions.     

Some chance for consensus: voting methods for which consensus is an equilibrium

We introduce the following basic voting method: voters submit both a “consensus” and a “fall-back” ballot. If all “consensus” ballots name the same option, it wins; otherwise, a randomly drawn “fall-back” ballot decides. If there is one potential consensus option that everyone prefers to the benchmark lottery which picks the favorite of a randomly drawn voter, then naming that option on all “consensus” ballots builds a very strong form of correlated equilibrium. Unlike common consensus procedures, ours is not biased toward the status quo and removes incentives to block consensus. Variants of the method allow for large groups, partial consensus, and choosing from several potential consensus options.     

Truncated Egalitarian solutions

A family of solutions to the bargaining problem with a variable population, generalizing the Egalitarian solution, is introduced under the name of Truncated Egalitarian solutions. A Truncated Egalitarian solution solves small problems at thier Egalitarian outcome and larger problems at some fixed and therefore non-optimal point, violations of optimality being more severe for large than for small groups. Any solution satisfying Symmetry, Independence of Irrelevant Alternatives, Continuity and Monotonicity (when the claims of more agents have to be accomodated, all agents should sacrifice) coincides with a Truncated Egalitarian solution except perhaps when only two agents are involved, in which case utility substitutions are possible in some limited range.     

Characterizing the Nash bargaining solution without Pareto-Optimality

We consider the bargaining problems with a variable number of agents. Lensberg had previously characterized the Nash solution as the only solution to satisfy the following axioms: Pareto-Optimality, Symmetry, Scale Invariance, and Multilateral Stability. We show that the disagreement solution is the only additional solution to satisfy the restricted list of axioms obtained by dropping Pareto-Optimality.Support from NSF under grant 8511136 is gratefully acknowledged. Thanks are also due to H. Moulin for his comments at an early stage of this research.     

Reference functions and possibility theorems for cardinal social choice problems

 In this paper, we provide axiomatic foundations for social choice rules on a domain of convex and comprehensive social choice problems when agents have cardinal utility functions. We translate the axioms of three well known approaches in bargaining theory (Nash 1950; Kalai and Smorodinsky 1975; Kalai 1977) to the domain of social choice problems and provide an impossibility result for each. We then introduce the concept of a reference function which, for each social choice set, selects a point from which relative gains are measured. By restricting the invariance and comparison axioms so that they only apply to sets with the same reference point, we obtain characterizations of social choice rules that are natural analogues of the bargaining theory solutions. Received: 8 August 1994/Accepted: 12 February 1996     

Do Absentee Voters Differ from Polling Place Voters?: New Evidence from California

In the 2003 California gubernatorial recall election 2,775,785absentee ballots were cast, representing about 30 percent ofall voters statewide. Given the number of absentee ballots andthe increasing propensity for voters in California and elsewhereto choose this voting method, we some basic questions: Who areabsentee voters, and are they different from polling place voters?To answer these questions, we fielded a statewide survey ofabsentee voters in the days before the October 7 recall election,asking respondents why they voted absentee, their partisan andideological preferences, demographic characteristics, and otherrelevant questions. We find that absentee voters do not differsignificantly from the overall state electorate in terms oftheir vote preferences, despite being older and better educated.For example, 56 percent of absentee voters in our survey voted"yes" on the recall, compared with 55 percent for the entirestate, according to official returns. Further, absentee votersfavored Arnold Schwarzenegger over Cruz Bustamante by a considerablemargin, similar to the overall election results. We found partyregistration among absentee voters to be nearly identical tostatewide partisan registration.     

Single-peaked preferences with several commodities

We consider the problem of allocating m commodities among n agents with single-peaked preferences. When m≥2 and n=2 any strategy-proof and efficient solution is dictatorial. We propose an extension of the Uniform Rule that (in the two-agents case) is the only one that satisfies strategy-proofness, envy-freeness, and a weak requirement related to efficiency. Alternatively, the envy-freeness property may be replaced by weak-anonymity. Received: 7 November 1997/Accepted: 1 August 2000     

MOVING OUT TO MOVE UP: DUAL‐CAREER MIGRATION AND WORK–FAMILY TRADEOFFS

Using data from a survey of new entrants to the junior PhD job market in economics, this paper shows that dual‐career location problems compromise the personal and professional lives of early‐career PhDs. Contrary to the common assumption that couples who do not live together break up, we find that living apart is a viable solution to location problems in the first year after graduate school. Surprisingly, PhDs facing moderate location problems are more likely than those facing severe location problems to make career sacrifices on behalf of their relationship; PhDs facing severe location problems are more likely to live apart. (JEL, J12, J44, A11)     

Rationalizable solutions to pure population problems

In pure population problems, a single resource is to be distributed equally among the agents in a society, and the social planner chooses population size(s) and per-capita consumption(s) for each resource constraint and set of feasible population sizes within the domain of the solution. This paper shows that a weak condition regarding the possible choice of a zero population is necessary and sufficient for the rationalizability of a solution by a welfarist social ordering. In addition, solutions that are rationalized by critical-level generalized utilitarianism are characterized by means of a homogeneity property. Received: 1 December 1997/Accepted: 26 February 1998     

Consistency in one-sided assignment problems

One-sided assignment problems combine important features of two well-known matching models. First, as in roommate problems, any two agents can be matched and second, as in two-sided assignment problems, the division of payoffs to agents is flexible as part of the solution. We take a similar approach to one-sided assignment problems as Sasaki (Int J Game Theory 24:373–397, 1995) for two-sided assignment problems, and we analyze various desirable properties of solutions including consistency and weak pairwise-monotonicity. We show that for the class of solvable one-sided assignment problems (i.e., the subset of one-sided assignment problems with a non-empty core), if a subsolution of the core satisfies [Pareto indifference and consistency] or [invariance with respect to unmatching dummy pairs, continuity, and consistency], then it coincides with the core (Theorems 1 and 2). However, we also prove that on the class of all one-sided assignment problems (solvable or not), no solution satisfies consistency and coincides with the core whenever the core is non-empty (Theorem 4). Finally, we comment on the difficulty in obtaining further positive results for the class of solvable one-sided assignment problems in line with Sasaki’s (1995) characterizations of the core for two-sided assignment problems.     

The two-party system under alternative voting procedures

Countries that elect their policy-makers by means of Plurality Voting tend to have a two-party system. This observation can be explained by the strategic behavior of voters. This article derives two broad classes of voting procedures under which strategic voting behavior induces a two-party system under standard assumptions on voter preferences. One class consists of the voting procedures with unique top-score, i.e., under which a voter can cast a top-score vote for only one candidate (e.g., Plurality Voting, Borda Count). The other class consists of the voting procedures that permit truncated ballots, i.e., under which voters do not have to cast all their votes (e.g., Approval Voting). This analysis suggests that the key for strategic voting behavior to induce a two-party system is that voters can always cast a different score for the two candidates they rank first and second on their ballots.     

Solidarity in choosing a location on a cycle

We study the implications of two solidarity conditions on the efficient location of a public good on a cycle, when agents have single-peaked, symmetric preferences. Both conditions require that when circumstances change, the agents not responsible for the change should all be affected in the same direction: either they all gain or they all loose. The first condition, population-monotonicity, applies to arrival or departure of one agent. The second, replacement-domination, applies to changes in the preferences of one agent. Unfortunately, no Pareto-efficient solution satisfies any of these properties. However, if agents’ preferred points are restricted to the vertices of a small regular polygon inscribed in the circle, solutions exist. We characterize them as a class of efficient priority rules.     

Ballot Design and Unrecorded Votes on Paper-Based Ballots

The 2000 presidential election focused attention on the problemof unrecorded votes, in which a person casts a ballot but failsto record a valid vote for a particular contest. Although muchrecent research has evaluated voting technologies and theireffects on unrecorded votes, there has been little researchon the effects of ballot design. We argue that the same theoriesused to design and evaluate self-administered surveys can beused to analyze ballot features. We collect and code paper-basedballots used in the 2002 general election from 250 countiesin 5 states. We code the ballots in terms of several graphicdesign elements, including the content and location of ballotinstructions and the layout of candidate names and office titles.Our analysis suggests that several ballot features are associatedwith unrecorded votes (both overvotes and undervotes) in thegubernatorial contests. We also find that ballot design featuresexacerbate the racial disparity in unrecorded votes. Ballotdesign can be an important factor in determining whether votersare able to cast a ballot accurately, which can influence thelegitimacy of elections.     

Generalized condorcet-winners for single peaked and single-plateau preferences

When preferences are single peaked the choice functions that are independent of irrelevant alternatives both in Nash's and in Arrow's sense are characterized. They take the Condorcet winner of the n individual peaks plus at most n-1 fixed ballots (phantom voters). These choice functions are also coalitionally strategy-proof.Next the domain of individual preferences is enlarged to allow for singleplateau preferences: again, Nash's IIA and Arrow's IIA uniquely characterize a class of generalized Condorcet winners choice functions. These are, again, coalitionally strategy-proof.     

On the (sequential) majority choice of public good size and location

This article studies majority voting over the size and location of a public good when voters differ both in income and in their preferences for the public good location. Public good provision is financed either by a lump sum tax or by a proportional income tax. We analyze both the simultaneous and the sequential determinations of the public good’s size and location. We show that, while the choice of the type of public good follows the traditional median logic, the majoritarian determination of the taxation rate need not coincide with the preferences of a median income citizen. With lump sum financing, income heterogeneity plays no role and the sequential equilibrium consists of the median location together with the public good level most-preferred by the individual located at the median distance from the median. This policy bundle also constitutes an equilibrium with simultaneous voting in the special case of a uniform bivariate distribution of individuals’ income and location. With proportional taxation, there is no policy equilibrium with simultaneous voting. We offer a complete characterization of the equations describing the sequential equilibrium in the general case and we show why and how our results depart from those most-preferred by the median income individual located at the median distance from the median. We also compare these majority voting allocations with the socially optimal one.     

Maximal domains of preferences preserving strategy-proofness for generalized median voter schemes

We characterize the maximal sets of preferences under which generalized median voter schemes are strategy-proof. Those domains are defined by a qualified version of single-peakedness, which depends on the distribution of power among agents implied by each generalized median voter scheme. Received: 28 April 1997/Accepted: 30 January 1998     

Double implementation of Lindahl allocations by a pure mechanism

This paper considers the issue of designing mechanisms whose Nash allocations and strong Nash allocations coincide with Lindahl allocations for public goods economies when coalition patterns, preferences, and endowments are unknown to the designer. It will be noted that the mechanism presented here is feasible and continuous, and the implementation result is obtained without defining an artificial preference profile on prices announced by individuals. In addition, unlike most existing Nash-implementing mechanisms which need to distinguish the case of two agents from that of three or more agents, this paper provides a unified mechanism which is irrespective of the number of agents. Received: 19 August 1997/Accepted: 16 November 1998     

The ordinal egalitarian bargaining solution for finite choice sets

Rubinstein et al. (Econometrica 60:1171–1186, 1992) introduced the Ordinal Nash Bargaining Solution. They prove that Pareto optimality, ordinal invariance, ordinal symmetry, and IIA characterize this solution. A feature of their work is that attention is restricted to a domain of social choice problems with an infinite set of basic allocations. We introduce an alternative approach to solving finite social choice problems using a new notion called the Ordinal Egalitarian (OE) bargaining solution. This suggests the middle ranked allocation (or a lottery over the two middle ranked allocations) of the Pareto set as an outcome. We show that the OE solution is characterized by weak credible optimality, ordinal symmetry and independence of redundant alternatives. We conclude by arguing that what allows us to make progress on this problem is that with finite choice sets, the counting metric is a natural and fully ordinal way to measure gains and losses to agents seeking to solve bargaining problems.