Tournaments are well studied objects in economic theory. Copeland (1951) provides an intuitive way to select alternatives from a tournament, the Copeland set. As a tournament solution, the Copeland set possesses many desirable properties and has been widely studied. Rubinstein (1980) axiomatizes a method to rank alternatives from a tournament which is based on their Copeland scores. This paper analyzes the Copeland set from a revealed preference perspective. A choice procedure where a decision maker has a fixed underlying tournament and selects the Copeland set from every menu is behaviorally characterized.
Whether in education, performance reviews, or elections, grades serve as tools for assessment, yet the universality of their meanings remains an open question. When voting under majority judgment, voters assign verbal grades such as “excellent, very good, good, fairly good, acceptable, insufficient, to reject” to each candidate. The meaning of these grades should be clear and consistent across all voters. Balinski and Laraki ( 2011 ) describe this as a “common language” and claim that the grade labels convey absolute meaning. This paper tests the assumption of absolute meaning by examining whether the meaning of a grade depends on the grading scale (i.e., framing effect) in a political context. We conducted an online experiment (N = 1955) in which participants voted for candidates to the French presidential elections under majority judgment with grading scales with different numbers of grades. Our findings indicate that the grade distributions obtained by candidates are significantly influenced by the grading scales available to voters. Our data therefore rejects the assertion that grades convey absolute meaning, showing instead that their interpretation depends on the number of grades available.
We reappraise the Arrow problem by studying the aggregation of choice functions. We do so in the general framework of judgment aggregation, in which choice functions are naturally representable by specifying, for each menu A and each alternative x in A, whether x is choosable from A, or not. Our framework suggests a natural strengthening of Arrow’s independence condition positing that the collective choosability of an alternative from a menu depends on the individual views on that issue, and that issue alone. Our analysis reveals that Arrovian impossibility results crucially hinge on what internal consistency requirements we impose on choice functions. While the aggregation of ‘binary’ choice functions, i.e. those satisfying both contraction ( α ) and expansion ( γ ) consistency, is necessarily dictatorial, possibilities in the form of oligarchic rules emerge for path-independent choice functions, that is, when the expansion property γ is replaced by the so-called Aizerman condition. Remarkably, the Arrovian aggregation of choice functions is shown to be almost dictatorial already under property γ alone. When giving up expansion consistency, specific quota rules become possible.
Social decision schemes (SDSs) map the voters’ preferences over multiple alternatives to a probability distribution over these alternatives. In a seminal result, Gibbard (Econometrica 45(3):665–681, 1977) has characterized the set of SDSs that are strategyproof with respect to all utility functions and his result implies that all such SDSs are either unfair to the voters or alternatives, or they require a significant amount of randomization. To circumvent this negative result, we propose the notion of U-strategyproofness which postulates that only voters with a utility function in a predefined set U cannot manipulate. We then analyze the tradeoff between U-strategyproofness and various decisiveness notions that restrict the amount of randomization of SDSs. In particular, we show that if the utility functions in the set U value the best alternative much more than other alternatives, there are U-strategyproof SDSs that choose an alternative with probability 1 whenever all but k voters rank it first. On the negative side, we demonstrate that U-strategyproofness is incompatible with Condorcet-consistency if the set U satisfies minimal symmetry conditions. Finally, we show that no ex post efficient and U-strategyproof SDS can be significantly more decisive than the uniform random dictatorship if the voters are close to indifferent between their two favorite alternatives.
In this paper we focus on the analysis of ranking methods based on a lexicographic comparison of individual evaluations. Notable examples of ranking methods in this family are the majority judgement, the lexicographic excellence and its dual version. Making a bridge with the theory of lexicographic preferences on elements with multiple factors, we provide an axiomatic characterization of the family of lexicographic methods using three well-studied properties in social choice: Anonymity, Neutrality and Independence of Irrelevant Alternatives. These assumptions allow restricting the study to the set of individual evaluations rearranged in a non increasing way. Two further assumptions of Ordinal Invariance and Dominance (restricted to this domain) allow for the requested characterization. Some operational indications on how to establish the order used by the lexicographic procedure is also discussed.
We investigate whether the definition of economic rationality as choice consistency is correlated with decision-making ability. Guided by a theoretical framework, we demonstrate that documented positive correlations may be driven by confounding properties unrelated to consistency. To address this, in a novel experiment, we isolate consistency, measured by the Weak Axiom of Revealed Preference. We show that less sophisticated decision-makers often rely on simple rules and behave consistently, while more sophisticated ones consciously randomize, appearing inconsistent. These patterns determine ambiguous correlations, raising doubts about the choice of language that equates consistency with rationality in economics.
Joint information blocking is the strategic behavior of a group of buyers that blocks competitors’ information. In the framework of diffusion auctions, joint information blocking employed by buyers’ tacit collusion can avoid competitive bidding, which leads to inefficiency of the auction mechanism. In this paper, blocking-proofness is introduced and investigated. Blocking-proofness means that buyers cannot benefit from joint information blocking, that is, from deleting diffusion relations to other buyers in the network. It is shown that blocking-proofness and incentive compatibility are independent, and both are necessary conditions for collusion-proofness. Finally, the blocking-proof diffusion auctions with monotonic allocation policies are fully characterized, and the independence of the conditions is discussed.
We introduce public-good auctions, a versatile framework addressing auction scenarios where players benefit not only from winning themselves but also when their competitors win. Distinct from private-good auctions, public-good auctions feature prizes as public goods enjoyed by all players and allow them to choose from multiple prizes. Demonstrating broad applicability, public-good auctions can be applied to various economic models, including auctions with externalities, and combinatorial auctions. The framework effectively explains unconventional situations marked by conflicting incentives between cooperation and competition and diverse behaviors, such as free-riding, cooperation, strategic voting, and multiple targeting, which are unobserved in traditional auction settings. Using a two-player model, we present four main results regarding the existence, characterization, and uniqueness of equilibrium payoffs.
Models of electoral accountability typically assume a politician provides a public good. Yet in many contexts, elected officials distribute private goods among voters with conflicting interests. We present a formal model to analyze this situation. An elected official allocates a rivalrous good to a number of voters, who each observe their own allocation but neither others’ allocations nor the official’s action. Each voter’s challenge is to determine whether the incumbent stole from other voters when deciding to sack or retain the incumbent. This problem can be resolved if voters retain the incumbent probabilistically, so that the vote of any voter from whom the incumbent steals is effectively up-weighted. However, this benefit of probabilistic voting also comes with a cost, since the fact that the incumbent may be sacked by mistake diminishes the allocation they are willing to provide to voters.
We consider the classical problem of allocating m objects to n agents where m ≥ n. In the m=n case, we analyze preference domains (called UPN-priority domains) where every strategy-proof, non-bossy and unanimous profile neutral (UPN) allocation rule is a priority rule. We show that a simple condition called the closure property characterizes priority domains. The only domain satisfying the closure property and a mild richness condition is the universal domain. We extend this result to the m >n case. We also consider the case where allocation rules satisfy a stronger neutrality property.
We study a one-to-one matching market where the population is fixed. If some exogenous reason disrupts a worker-firm pair in a stable matching, can equilibrium in the market be restored? We present an algorithm that models this situation as a re-stabilization process involving a vacancy chain. Each step of the algorithm is a link of such a chain. We show that the length of this vacancy chain is intimately connected with the lattice structure of the set of stable matchings of the market. Namely, this length can be computed by considering the cardinalities of cycles in preferences derived from the initial and final stable matchings involved.
This paper studies effort incentivisation and provision in a complete-information Tullock two-group contest. Generalised incentivisation schemes are considered that, besides distributing the prize, reward some group members by expropriating others’ private resources. Three are the main results. First, Pareto efficient zero-effort equilibria exist at some schemes that expropriate contributors to reward free-riders. Second, pure-strategy equilibria fail to exist at some other schemes with similar structure. Third, sequentiality in the determination of endogenous schemes matters only if expropriation is allowed. In that case, when schemes are sequentially set à la Stackelberg a ‘leader’s curse’ arises: the first-mover always increases its expected welfare with respect to simultaneous competition, but systematically gets less than the second-mover. Moreover, in passing from simultaneous to Stackelberg competition the probability of victory increases for the larger group and decreases for the smaller one, regardless of which of the two is the first-mover. Finally, Stackelberg equilibria imply the same odds of winning of zero-effort counterparts, but entail a welfare loss because of positive effort provision.
We develop a novel social choice experiment capable of estimating preference parameters on population ethics. Our experiment poses three within-subject treatments in which participants allocate scarce resources to determine the health-related quality-of-life, and existence, of two population groups. Within a flexible social welfare function, we estimate participant-level preferences for inequality aversion, average vs total welfare maximisation, and minimum ‘critical level’ thresholds. By combining random behavioural and random utility models we also explicitly model ‘noise’ in decision making. Using a sample of British adults (n = 115, obs. = 5060), we find that 98.7
We provide the first asymptotic analysis of the Boston Mechanism under equilibrium play in random markets. We provide two results. First, while 63% of students receive their first preference under truthful reporting-outperforming any other known mechanism in the literature-this rate converges to zero in any Nash equilibrium of the corresponding preference revelation game as the market size grows. Second, we show there exists a Nash equilibrium where the average student receives a dramatically inferior assignment: in markets with 1,000 students, the average placement shifts from the 7th choice (under truthfulness) to the 145th choice, representing a change from logarithmic to nearly linear average rank.
We examine a team contest in which players exert effort to compete against other teams for a prize, which is then divided among the members of the winning team according to a specified sharing rule. Assuming that players vary in their observable abilities to contribute to team performance, we study the structure of stable teams under different sharing rules. A head-hunting attempt is successful if the targeted player benefits from switching teams and the offering team’s probability of winning increases as a result. A team structure is defined as stable when no such successful head-hunting opportunities exist. We show that when all teams adopt an egalitarian prize-sharing rule, complete ability sorting arises, resulting in the greatest inter-team inequality. In contrast, when teams use substantially unequal sharing rules, the stable team structure features lower inter-team inequality but greater intra-team inequality. These results reveal a trade-off between intra-team and inter-team inequality in the formation of stable teams.
A vocabulary is a list of words designating subsets from a grand set X. We model a vocabulary as a partition of X and study the aggregation of individual vocabularies into a collective one. We characterize aggregation rules when X is linearly ordered and each word of the vocabulary spans an order interval. We allow for individual vocabularies to differ both in the number and in the span of their words. Under a suitable restriction on agents' preferences, we show that our aggregation rules are strategy-proof.
We use laboratory experiments to analyze decentralized decision-making in one-sided matching markets. We find that subjects tend to make decisions in line with most theoretical models, as their offering and accepting decisions are mainly guided by the objective of improving upon the status quo. In consequence, markets move towards satisfying blocking pairs making the number of remaining blocking pairs diminish and the aggregate payoffs increase over time. Overall, the theoretical solutions of absorbing sets and stable matchings to the roommate problem are supported by the experimental results. However, not all matchings in an absorbing set have the same power of attraction in the experimental laboratory. The theoretical property of P-stability refines absorbing sets as predictors of final outcomes.
We study the structure of random ordinal Bayesian incentive compatible (OBIC) rules. We restrict attention to some special class of priors that we call “uniform-like” priors. We consider a class of priors, called top uniform priors: for any two alternatives a and b, a prior is top uniform if the aggregate probability (under the prior distribution) of preferences with respectively a and b at the top are the same. Over the unrestricted domain the uniform prior is a member of this class. We consider a class of random voting rules—random vote share rules, a generalization of plurality rule. For top uniform priors and arbitrary domains, Theorem 4.1 shows that every top monotonic and symmetric random vote share rule is OBIC. Over a domain satisfying some natural “richness” condition, we demonstrate that if a symmetric and strongly top responsive random vote share rule is OBIC with respect to some prior, then that prior must necessarily be a top uniform prior. We also provide some analogous results for veto share rules that are probabilistic generalizations of anti-plurality rule.
The competence of individuals in cooperative activities can be measured through various channels. A football player is sometimes evaluated by their solo-performances, and at other times evaluated by their cooperative performances with other players with related roles. A familiar way to compare two individuals is to consider their performances ceteris paribus—that is, to see what happens if two players are substituted with one another under fixed conditions (the same teammates). However, such substitution does not make sense if the individuals have fundamentally different roles (e.g., an offensive forward and a goalkeeper). Thus, appropriate patterns of comparison can differ from context to context. The present paper formulates such comparison schemes as the set of all pairs of coalitions that are taken into consideration. Two theoretical results are demonstrated. The first is the characterization of majority rule with respect to a particular comparison scheme. The second is the determination of admissible comparison schemes under which the majority rule becomes transitive. These findings provide new insight on the method of comparison itself, showing the necessary information on coalitions to determine the achievement ranking of individuals.
