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Abstract: Abstract We adopt the notion of the farsighted stable set to determine which matchings are stable when agents are farsighted in matching markets with couples. We show that a singleton matching is a farsighted stable set if and only if the matching is stable. Thus, matchings that are stable with myopic agents remain stable when agents become farsighted. Examples of farsighted stable sets containing multiple non-stable matchings are provided for markets with and without stable matchings. For couples markets where the farsighted stable set does not exist, we propose the DEM farsighted stable set to predict the matchings that are stable when agents are farsighted. PubDate: 2024-08-08
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Abstract: Abstract We define a class of pure exchange Edgeworth trading processes that under minimal assumptions converge to a stable set in the space of allocations, and characterise the Pareto set of these processes. Choosing a specific process belonging to this class, that we define fair trading, we analyse the trade dynamics between agents located on a weighted network. We determine the conditions under which there always exists a one-to-one map between the set of networks and the set of limit points of the dynamics, and derive an analog of the Second Welfare Theorem for networks. This result is used to explore what is the effect of the network topology on the trade dynamics and on the final allocation. PubDate: 2024-08-05
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Abstract: Abstract We present various results about Euclidean preferences in the plane under \(\ell _1,\) \(\ell _2\) and \(\ell _{\infty }\) norms. When there are four candidates, we show that the maximum size (in terms of the number of pairwise distinct preferences) of Euclidean preference profiles in \({\mathbb {R}}^2\) under norm \(\ell _1\) or \(\ell _{\infty }\) is 19. Whatever the number of candidates, we prove that at most four distinct candidates can be ranked in the last position of a two-dimensional Euclidean preference profile under norm \(\ell _1\) or \(\ell _\infty ,\) which generalizes the case of one-dimensional Euclidean preferences (for which it is well known that at most two candidates can be ranked last). We generalize this result to \(2^d\) (resp. 2d) for \(\ell _1\) (resp. \(\ell _\infty \) ) for d-dimensional Euclidean preferences. We also establish that the maximum size of a two-dimensional Euclidean preference profile on m candidates under norm \(\ell _1\) is in \(\varTheta (m^4),\) which is the same order of magnitude as the known maximum size under norm \(\ell _2.\) Finally, we provide a new proof that two-dimensional Euclidean preference profiles under norm \(\ell _2\) for four candidates can be characterized by three inclusion-maximal two-dimensional Euclidean profiles. This proof is a simpler alternative to that proposed by Kamiya et al. (Adv Appl Math 47(2):379–400, 2011). PubDate: 2024-08-01
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Abstract: Abstract Fishburn’s alternating scheme domains occupy a special place in the theory of Condorcet domains. Karpov (2023) generalised these domains and made an interesting observation proving that all of them are single-peaked on a circle. However, an important point that all generalised Fishburn domains are maximal Condorcet domain remained unproved. We fill this gap and suggest a new combinatorial interpretation of generalised Fishburn’s domains which provide a constructive proof of single-peakedness of these domains on a circle. We show that classical single-peaked domains and single-dipped domains as well as Fishburn’s alternating scheme domains belong to this family of domains while single-crossing domains do not. PubDate: 2024-08-01
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Abstract: Abstract We consider a setting in which the alternatives are binary vectors and the preferences of the agents are determined by the Hamming distance from their most preferred alternatives. We consider only rules that are unanimous, anonymous, and component-neutral, and focus on strategy-proofness, weak group strategy-proofness, and strong group strategy-proofness. We show that component-wise majority rules are strategy-proof, and for three agents or two components also weakly group strategy-proof, but not otherwise. These rules are even strongly group strategy-proof if there are two or three agents. Our main result is an impossibility result: if there are at least four agents and at least three components, then no rule is strongly group strategy-proof. PubDate: 2024-08-01
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Abstract: Abstract Social decision schemes (SDSs) map the preferences of a group of voters over some set of m alternatives to a probability distribution over the alternatives. A seminal characterization of strategyproof SDSs by Gibbard (Econometrica 45(3):665–681, 1977) implies that there are no strategyproof Condorcet extensions and that only random dictatorships satisfy ex post efficiency and strategyproofness. The latter is known as the random dictatorship theorem. We relax Condorcet-consistency and ex post efficiency by introducing a lower bound on the probability of Condorcet winners and an upper bound on the probability of Pareto-dominated alternatives, respectively. We then show that the randomized Copeland rule is the only anonymous, neutral, and strategyproof SDS that guarantees the Condorcet winner a probability of at least 2/m. Secondly, we prove a continuous strengthening of Gibbard’s random dictatorship theorem: the less probability we put on Pareto-dominated alternatives, the closer to a random dictatorship is the resulting SDS. Finally, we show that the only anonymous, neutral, and strategyproof SDSs that maximize the probability of Condorcet winners while minimizing the probability of Pareto-dominated alternatives are mixtures of the uniform random dictatorship and the randomized Copeland rule. PubDate: 2024-08-01
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Abstract: Abstract We revise a result stating that there is a positive relationship between contributions and welfare in a public good provision game under price uncertainty (Gradstein et al. Soc Choice Welf 10(4):371–382, 1993). The authors state in Proposition 3 that welfare decreases when price uncertainty induces a reduction in private contributions. By contrast, we show that, under certain conditions, a reduction in contributions can be associated with an improvement in consumer welfare. This result is important because public policy regarding the provision of public goods is often based on indicators such as citizen participation, which, as this note shows, may constitute a misleading signal. PubDate: 2024-08-01
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Abstract: Abstract The single transferable vote (STV) voting method is used to elect multiple candidates in ranked-choice elections. One weakness of STV is that it fails multiple fairness criteria related to monotonicity and no-show paradoxes. We analyze 1079 local government STV elections in Scotland to estimate the frequency of such monotonicity anomalies in real-world elections, and compare our results with prior empirical and theoretical research about the rates at which such anomalies occur. In 62 of the 1079 elections we found some kind of monotonicity anomaly. We generally find that anomaly rates are similar to prior empirical research and much lower than what most theoretical research has found. Most STV anomalies we find are the first of their kind to be documented in real-world multiwinner elections. PubDate: 2024-08-01
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Abstract: Abstract A novel axiomatization of relative utilitarianism is provided using the single-profile setting used in Harsanyi’s Social Aggregation Theorem. Harsanyi’s axioms are supplemented with an impartiality axiom that requires social alternative lotteries p and q to be socially indifferent when (i) two individuals have conflicting preferences for them and everybody else is indifferent and (ii) the concerned individuals’ strengths of preference for p over q have the same magnitude. This axiomatization shows that equality of the social weights can be obtained in a single-profile setting and that no interprofile condition is needed to obtain profile-independent weights in a multi-profile setting. PubDate: 2024-08-01
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Abstract: Abstract I analyze the role of the distribution of skills in shaping optimal nonlinear income tax schedules. I use theoretical skill distributions as well as empirical skill distributions for 14 OECD countries. I find that a more dispersed log-normal skill distribution implies a more progressive optimal tax schedule. Optimal marginal tax rates should be lower throughout if a greater number of unskilled agents cluster at the bottom, and the scheme is more progressive if a greater number of agents locate at the top. I also highlight how the impact of the skill distribution is affected by the form of the social welfare function and the utility function. The findings using empirical skill distributions suggest that the results are sensitive to the type of statistical estimator used to estimate the skill distribution. PubDate: 2024-07-25
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Abstract: Abstract Measuring the well-being of individuals is a significant challenge for social scientists, policy makers, and suppliers of social programming, since well-being consists of many dimensions that are difficult to measure, both individually and collectively. Moreover, the relative contribution of each of the various aspects to overall well-being is unknown. We try to answer this challenge using the methodology of Benjamin et al. (Am Econ Rev 104(9):2698–2735, 2014) and using a survey that measures preferences over 27 aspects of individual well-being. We provide estimates of these preferences for a representative sample of the Israeli population. We also document heterogeneity in preferences for respondents with different current levels of well-being and for different demographic groups. For some aspects of well-being, we provide evidence of decreasing marginal utility. For other aspects, we find evidence for what appears to be an increasing marginal utility but we argue that it likely reflects an endogenous determination of the level of well-being. We discuss the policy implications of our findings and how our results could be aggregated to a well-being index that could be used to evaluate and compare the effects of different policy interventions. PubDate: 2024-07-19
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Abstract: Abstract Sprumont (Games Econ Behav 2:378–394, 1990) introduces population monotonic allocation schemes (PMAS) and proves that every assignment game with at least two sellers and two buyers, where each buyer-seller pair derives a positive gain from trade, lacks a PMAS. In particular glove games lacks PMAS. We propose a new cooperative TU-game concept, population Lorenz-monotonic allocation schemes (PLMAS), which relaxes some population monotonicity conditions by requiring that the payoff vector of any coalition is Lorenz dominated by the corresponding restricted payoff vector of larger coalitions. We show that every TU-game having a PLMAS is totally balanced, but the converse is not true in general. We obtain a class of games having a PLMAS, but no PMAS in general. Furthermore, we prove the existence of PLMAS for every glove game and for every assignment game with at most five players. Additionally, we also introduce two new notions, PLMAS-extendability and PLMAS-exactness, and discuss their relationships with the convexity of the game. PubDate: 2024-07-16
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Abstract: Abstract Considering voting rules based on evaluation inputs rather than preference rankings modifies the paradigm of probabilistic studies of voting procedures. This article proposes several simulation models for generating evaluation-based voting inputs. These models can cope with dependent and non identical marginal distributions of the evaluations received by the candidates. A last part is devoted to fitting these models to real data sets. PubDate: 2024-07-09
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Abstract: Abstract In an environment with private information, we study the class of sequencing problems with welfare lower bounds. The “generalized welfare lower bound” represents some of the lower bounds that have been previously studied in the literature. Every agent is offered a protection in the form of a minimum guarantee on their utilities. We provide a necessary and sufficient condition to identify an outcome efficient and strategyproof mechanism that satisfies generalized welfare lower bound. We then characterize the entire class of mechanisms that satisfy outcome efficiency, strategyproofness and generalized welfare lower bound. These are termed as “relative pivotal mechanisms”. Our paper proposes relevant theoretical applications namely; ex-ante initial order, identical costs bound and expected cost bound. We also give insights on the issues of feasibility and/or budget balance. PubDate: 2024-07-09
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Abstract: Abstract Padding is the practice of adding nonvoters (e.g., noncitizens or disenfranchised prisoners) to an electoral district in order to ensure that the district meets the size quota prescribed by the one man, one vote doctrine without affecting the voting outcome in the district. We show how padding— and its mirror image, pruning—, can lead to arbitrarily large deviations from the socially optimal composition of elected legislatures. We solve the partisan districter’s optimal padding problem. PubDate: 2024-07-09
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Abstract: Abstract We consider the two-sided many-to-one matching problem and introduce a class of preferences reflecting natural forms of complementarities. For example, academic departments hire seniors and then supporting juniors, teams recruit different roles and specialties, starting with the critical ones, and firms hire workers at various levels, starting with the executives. The key feature is that a firm can partition workers into types and prioritize certain types before others. Despite this partitionability requirement of choice functions being weaker than substitutes—an essential condition concerning the existence of a stable assignment—we show that it still guarantees the existence of a stable assignment and is further a maximal domain for such. PubDate: 2024-07-09
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Abstract: Abstract Previous literature has shown that voters’ biased beliefs regarding policy outcomes incentivize the selection of seemingly better, but socially worse, policies. It has also shown that voters’ tendency to gauge an incumbent’s competence by the present state of the economy (retrospective voting) could counteract biased beliefs. In this article, we argue that, when the advantageous consequences of a measure of policy only accrue with considerable lag (the down-up problem), retrospective voting instead amplifies the effects of biased beliefs. Still, we find that it may nevertheless be optimal for an incumbent to select good long-term policies if the incumbent is strongly motivated by the success of the chosen policies. Finally, we investigate the robustness of these conclusions by considering an incumbent bias, limited accountability, and the introduction of incentive and threshold contracts. PubDate: 2024-06-24
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Abstract: Abstract The role of patent pools—one-stop systems that gather patents from multiple patent holders and offer them to users as a package—is gaining research attention. To bolster the scarce stream of the literature that has addressed how a patent pool agent distributes royalty revenues among patent holders, we conduct an axiomatic analysis of sharing rules for royalty revenue derived from patents managed by a patent pool agent. In our framework, the patent pool agent organizes the patents into some packages, which we call a package structure. By using the hypergraph formulation developed by van den Nouweland et al. (Int J Game Theory 20:255–268, 1992), we analyze sharing rules that consider the package structure. In our study, we propose a sharing rule and show that it is the unique rule that satisfies efficiency, fairness, and independence requirements. In addition, we analyze sharing rules that enable a patent pool agent to organize a revenue-maximizing and objection-free profile. PubDate: 2024-06-20
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Abstract: Abstract In the context of claims problems, we formulate an axiom of invariance of a rule with respect to its “partial implementation”: having applied the rule to a problem in its domain of definition, we imagine some claimants picking up their awards and we consider the problem of distributing what remains of the endowment among the other claimants: in this problem, the claims of the first group of claimants are set equal to zero and the endowment is adjusted down by the sum of their awards; we require of a rule that it assign to each remaining claimant the same amount as it did initially. We formulate several variants of this requirement of “partial-implementation invariance” and a “converse” of it. We investigate how the two requirements relate to known axioms and ask whether they are preserved by certain operators that have been defined on the space of rules. Our main result is a characterization in our fixed-population framework of a family of rules introduced and characterized by Young (Math Oper Res 12(3):398–414, 1987) in a variable-population framework. These rules are known under the name of “parametric rules”. PubDate: 2024-06-07 DOI: 10.1007/s00355-024-01528-z
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Abstract: Abstract Universal self-selectivity of a social choice function (SCF) F defined in Koray (Econometrica 68:981–995, 2000) implies that F is either dictatorial or anti-dictatorial. In an attempt to escape this impossibility, here we weaken self-selectivity of an SCF by introducing the notion of selection-closedness pertaining to families of SCFs. As in the self-selectivity setting, a society, which is to make a choice from a set A of alternatives, is also to choose the choice rule that will be employed in making that choice. Self-selectivity of an SCF F requires that F outrivals all available SCFs by selecting itself from among them if it is also used in choosing the choice rule, where the societal preferences on the available SCFs are induced from those on the set A of alternatives in a consequentialist way. Given a collection \({\mathscr {F}}\) of SCFs and a nonempty finite set \({\mathcal {A}}\) of available SCFs containing also members of \({\mathscr {F}},\) an SCF in \({\mathscr {F}} \cap {\mathcal {A}}\) is now not required any more to select itself from \({\mathcal {A}},\) but it suffices that it selects some member of \({\mathscr {F}}\) for \({\mathscr {F}}\) to be selection-closed. It is shown that a proper subset of the collection of all neutral SCFs is selection-closed if and only if all its members are either dictatorships or anti-dictatorships. We further weaken the notion of selection-closedness to an extent that not only enables us to escape the impossibility result, but also equips us with a yardstick to compare correspondences as to whether or not their singleton valued refinements form a weakly selection-closed family. A rich family of scoring correspondences with strict scoring vectors are shown to pass the test of weak selection-closedness, while the Pareto and Condorcet correspondences fail. PubDate: 2024-06-03 DOI: 10.1007/s00355-024-01529-y
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