Pub Date : 2026-01-10DOI: 10.1016/j.mathsocsci.2026.102506
Adam Graham-Squire , Matthew I. Jones , David McCune
In real-world elections where voters cast preference ballots, voters often provide only a partial ranking of the candidates. Despite this empirical reality, prior social choice literature frequently analyzes fairness criteria under the assumption that all voters provide a complete ranking of the candidates. We introduce new fairness criteria for multiwinner ranked-choice elections concerning truncated ballots. In particular, we define notions of the independence of losing voters blocs and independence of winning voters blocs, which state that the winning committee of an election should not change when we remove truncated ballots which rank only losing candidates, and the winning committee should change in reasonable ways when removing ballots which rank only winning candidates. Of the voting methods we analyze, the Chamberlin-Courant rule performs the best with respect to these criteria, the expanding approvals rule performs the worst, and the method of single transferable vote falls in between.
{"title":"New fairness criteria for truncated ballots in multi-winner ranked-choice elections","authors":"Adam Graham-Squire , Matthew I. Jones , David McCune","doi":"10.1016/j.mathsocsci.2026.102506","DOIUrl":"10.1016/j.mathsocsci.2026.102506","url":null,"abstract":"<div><div>In real-world elections where voters cast preference ballots, voters often provide only a partial ranking of the candidates. Despite this empirical reality, prior social choice literature frequently analyzes fairness criteria under the assumption that all voters provide a complete ranking of the candidates. We introduce new fairness criteria for multiwinner ranked-choice elections concerning truncated ballots. In particular, we define notions of the <em>independence of losing voters blocs</em> and <em>independence of winning voters blocs</em>, which state that the winning committee of an election should not change when we remove truncated ballots which rank only losing candidates, and the winning committee should change in reasonable ways when removing ballots which rank only winning candidates. Of the voting methods we analyze, the Chamberlin-Courant rule performs the best with respect to these criteria, the expanding approvals rule performs the worst, and the method of single transferable vote falls in between.</div></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"140 ","pages":"Article 102506"},"PeriodicalIF":0.7,"publicationDate":"2026-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145979659","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-10DOI: 10.1016/j.mathsocsci.2026.102504
Badr Bahloul, Ahmed Doghmi
Strategic candidacy in multi-winner elections describes situations where candidates may enter or withdraw to influence which candidates are elected. Existing studies typically assume all eligible candidates are interested in participating. In reality, some eligible candidates are uninterested in winning but may enter strategically, while interested candidates may strategically withdraw; both types of moves can change the set of elected candidates. This paper extends the standard framework by distinguishing interested and uninterested candidates and studying manipulation via coordinated entry and exit. We focus on evaluating whether multi-winner rules are immune to manipulation by coalitions of candidates with respect to the number of voters and the committee size . Specifically, we say that a rule satisfies candidate-coalition strategy-proofness (CCSP) for an election-point if the “true” strategy profile—where candidates enter the election if and only if they are interested—constitutes a strong Nash equilibrium (i.e., no coalition of players can achieve a collective benefit by deviating from the actions dictated by their true types). Focusing on five committee-scoring rules—-Borda, -Anti-plurality, BLOC, -Plurality, and -CC—we provide complete characterizations of the election-points where each rule satisfies CCSP. Specifically, -Plurality is CCSP exactly when ; -CC exactly when ; BLOC only when or ; and -Anti-plurality and -Borda never satisfy CCSP.
多赢家选举中的策略性候选是指候选人可以参选或退出以影响哪位候选人当选的情况。现有的研究通常假设所有符合条件的候选人都有兴趣参加。实际上，一些符合条件的候选人对获胜不感兴趣，但可能会战略性地进入，而感兴趣的候选人可能会战略性地退出；这两种举动都可以改变当选候选人的组合。本文通过区分感兴趣和不感兴趣的候选人以及研究通过协调进入和退出的操纵来扩展标准框架。我们专注于评估多赢家规则是否不受候选人联盟在选民数量n和委员会规模k方面的操纵。具体来说，我们说，如果“真正的”策略概况-候选人进入选举当且仅当他们感兴趣-构成强纳什均衡(即，任何玩家联盟都不可能通过背离他们的真实类型所决定的行动而获得集体利益。重点关注5个委员会评分规则——k- borda、k- anti -plurality、BLOC、k- plurality和l1 - cc——我们提供了每个规则满足CCSP的选举点（n,k）的完整特征。具体来说，当n<；2k+2；当n<；k+1；只有当(n,k)=(3,1)或n=2时，才有块；k-Anti-plurality和k-Borda不满足CCSP。
{"title":"Candidate coalitions and strategic manipulation in multi-winner elections: An evaluation of committee scoring rules","authors":"Badr Bahloul, Ahmed Doghmi","doi":"10.1016/j.mathsocsci.2026.102504","DOIUrl":"10.1016/j.mathsocsci.2026.102504","url":null,"abstract":"<div><div>Strategic candidacy in multi-winner elections describes situations where candidates may enter or withdraw to influence which candidates are elected. Existing studies typically assume all eligible candidates are interested in participating. In reality, some eligible candidates are uninterested in winning but may enter strategically, while interested candidates may strategically withdraw; both types of moves can change the set of elected candidates. This paper extends the standard framework by distinguishing interested and uninterested candidates and studying manipulation via coordinated entry and exit. We focus on evaluating whether multi-winner rules are immune to manipulation by <em>coalitions of candidates</em> with respect to the number of voters <span><math><mi>n</mi></math></span> and the committee size <span><math><mi>k</mi></math></span>. Specifically, we say that a rule satisfies <em>candidate-coalition strategy-proofness</em> (CCSP) for an <em>election-point</em> <span><math><mrow><mo>(</mo><mi>n</mi><mo>,</mo><mi>k</mi><mo>)</mo></mrow></math></span> if the “true” strategy profile—where candidates enter the election if and only if they are interested—constitutes a strong Nash equilibrium (i.e., no coalition of players can achieve a collective benefit by deviating from the actions dictated by their true types). Focusing on five committee-scoring rules—<span><math><mi>k</mi></math></span>-Borda, <span><math><mi>k</mi></math></span>-Anti-plurality, BLOC, <span><math><mi>k</mi></math></span>-Plurality, and <span><math><msub><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span>-CC—we provide complete characterizations of the election-points <span><math><mrow><mo>(</mo><mi>n</mi><mo>,</mo><mi>k</mi><mo>)</mo></mrow></math></span> where each rule satisfies CCSP. Specifically, <span><math><mi>k</mi></math></span>-Plurality is CCSP exactly when <span><math><mrow><mi>n</mi><mo><</mo><mn>2</mn><mi>k</mi><mo>+</mo><mn>2</mn></mrow></math></span>; <span><math><msub><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span>-CC exactly when <span><math><mrow><mi>n</mi><mo><</mo><mi>k</mi><mo>+</mo><mn>1</mn></mrow></math></span>; BLOC only when <span><math><mrow><mrow><mo>(</mo><mi>n</mi><mo>,</mo><mi>k</mi><mo>)</mo></mrow><mo>=</mo><mrow><mo>(</mo><mn>3</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></mrow></math></span> or <span><math><mrow><mi>n</mi><mo>=</mo><mn>2</mn></mrow></math></span>; and <span><math><mi>k</mi></math></span>-Anti-plurality and <span><math><mi>k</mi></math></span>-Borda never satisfy CCSP.</div></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"140 ","pages":"Article 102504"},"PeriodicalIF":0.7,"publicationDate":"2026-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145979660","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-08DOI: 10.1016/j.mathsocsci.2026.102502
Shohei Yanagita
This paper characterizes a simple model of belief updating in response to recommendations from black boxes, recommenders whose information-generating processes are complex and opaque. In particular, we focus on two types of reactions to recommendations. The first is a skeptical response, in which individuals receive recommendations that are highly inconsistent with their prior beliefs and respond skeptically by updating their beliefs conservatively. The second is a credulous response, in which individuals readily accept recommendations that are aligned with their prior beliefs. These two contrasting reactions are jointly captured under the resulting updating rule.
{"title":"Skeptical and credulous belief updating under black box recommendations","authors":"Shohei Yanagita","doi":"10.1016/j.mathsocsci.2026.102502","DOIUrl":"10.1016/j.mathsocsci.2026.102502","url":null,"abstract":"<div><div>This paper characterizes a simple model of belief updating in response to recommendations from black boxes, recommenders whose information-generating processes are complex and opaque. In particular, we focus on two types of reactions to recommendations. The first is a skeptical response, in which individuals receive recommendations that are highly inconsistent with their prior beliefs and respond skeptically by updating their beliefs conservatively. The second is a credulous response, in which individuals readily accept recommendations that are aligned with their prior beliefs. These two contrasting reactions are jointly captured under the resulting updating rule.</div></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"140 ","pages":"Article 102502"},"PeriodicalIF":0.7,"publicationDate":"2026-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145940473","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-01-08DOI: 10.1016/j.mathsocsci.2026.102503
Hirokazu Sakane
Although it is extremely rare for real markets to adjust excess demand through the Walrasian tâtonnement, the standard in market adjustment theory, it is also true that excess demand is eventually eliminated. This gap suggests that some other factors, besides the price mechanism, contribute to adjusting excess demand. We hypothesize that consumers and firms, and therefore excess demand, spill over into neighboring markets in response to price differences that arise between markets. This motion must contribute to ameliorating excess demand. It is rational for some consumers (firms) to shift to markets where the prices of commodities are lower (higher) if price differences arise beyond those due to the characteristics of the commodities. Furthermore, excess demand fluctuates depending on the actions of consumers and firms. Thus, we study an economy in which excess demand advects and diffuses owing to price gradients. The application of partial differential equations is appropriate for this type of analysis.
Specifically, we model market price adjustment and the way consumers and firms respond by shifting toward other markets, thus causing excess demand to spill over and disperse. We represent these flows as advection and diffusion driven by price gradients and formalize their dynamics using partial differential equations. We prove that the competitive equilibrium price is locally and exponentially stable under certain conditions.
{"title":"Market adjustment with advection and diffusion in excess demand","authors":"Hirokazu Sakane","doi":"10.1016/j.mathsocsci.2026.102503","DOIUrl":"10.1016/j.mathsocsci.2026.102503","url":null,"abstract":"<div><div>Although it is extremely rare for real markets to adjust excess demand through the Walrasian tâtonnement, the standard in market adjustment theory, it is also true that excess demand is eventually eliminated. This gap suggests that some other factors, besides the price mechanism, contribute to adjusting excess demand. We hypothesize that consumers and firms, and therefore excess demand, spill over into neighboring markets in response to price differences that arise between markets. This motion must contribute to ameliorating excess demand. It is rational for some consumers (firms) to shift to markets where the prices of commodities are lower (higher) if price differences arise beyond those due to the characteristics of the commodities. Furthermore, excess demand fluctuates depending on the actions of consumers and firms. Thus, we study an economy in which excess demand advects and diffuses owing to price gradients. The application of partial differential equations is appropriate for this type of analysis.</div><div>Specifically, we model market price adjustment and the way consumers and firms respond by shifting toward other markets, thus causing excess demand to spill over and disperse. We represent these flows as advection and diffusion driven by price gradients and formalize their dynamics using partial differential equations. We prove that the competitive equilibrium price is locally and exponentially stable under certain conditions.</div></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"140 ","pages":"Article 102503"},"PeriodicalIF":0.7,"publicationDate":"2026-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145979658","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-30DOI: 10.1016/j.mathsocsci.2025.102493
Urs Schweizer
In this paper, a game-theoretic setting with transferable utility serves to explore the scope of damages rules for internalizing multidirectional external effects. From the legal perspective, damages rules aim at compensating victims for the wrongdoing of others (compensation requirement). Yet, to be held liable, it must be an agent’s wrongdoing that has caused harm to the victim (causation requirement). The two requirements can be at conflict when causation is meant in the sense of the but-for test. The paper proposes a causation test that resolves this conflict quite generally. It combines the legal idea of the NESS test with the Shapley value of a suitable characteristic function. The resulting damages rules fully internalize externalities even if they are of multidirectional nature.
{"title":"The conceivable scope of negligence rules for internalizing multidirectional externalities","authors":"Urs Schweizer","doi":"10.1016/j.mathsocsci.2025.102493","DOIUrl":"10.1016/j.mathsocsci.2025.102493","url":null,"abstract":"<div><div>In this paper, a game-theoretic setting with transferable utility serves to explore the scope of damages rules for internalizing multidirectional external effects. From the legal perspective, damages rules aim at compensating victims for the wrongdoing of others (compensation requirement). Yet, to be held liable, it must be an agent’s wrongdoing that has caused harm to the victim (causation requirement). The two requirements can be at conflict when causation is meant in the sense of the but-for test. The paper proposes a causation test that resolves this conflict quite generally. It combines the legal idea of the NESS test with the Shapley value of a suitable characteristic function. The resulting damages rules fully internalize externalities even if they are of multidirectional nature.</div></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"140 ","pages":"Article 102493"},"PeriodicalIF":0.7,"publicationDate":"2025-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145886247","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-18DOI: 10.1016/j.mathsocsci.2025.102492
Ludovic A. Julien, Gagnie P. Yebarth
This paper investigates the taxation mechanism implemented in strategic bilateral exchange by Gabszewicz and Grazzini (1999). These authors show that endowment taxation with transfers can implement a Pareto-optimal allocation when the preferences of traders are represented by some specific homothetic utility functions. We show that this taxation mechanism can also implement a Pareto-optimal allocation when the preferences of traders are represented by non homothetic utility functions. To this end, we consider a class of quasi-linear utility functions. Furthermore, we illustrate that, with quasi-linear utility functions, by introducing heterogeneity between traders, there are other environments in which this taxation mechanism implements a Pareto-optimal outcome.
{"title":"A note on Pareto-optimal taxation mechanism in noncooperative strategic bilateral exchange","authors":"Ludovic A. Julien, Gagnie P. Yebarth","doi":"10.1016/j.mathsocsci.2025.102492","DOIUrl":"10.1016/j.mathsocsci.2025.102492","url":null,"abstract":"<div><div>This paper investigates the taxation mechanism implemented in strategic bilateral exchange by Gabszewicz and Grazzini (1999). These authors show that endowment taxation with transfers can implement a Pareto-optimal allocation when the preferences of traders are represented by some specific homothetic utility functions. We show that this taxation mechanism can also implement a Pareto-optimal allocation when the preferences of traders are represented by non homothetic utility functions. To this end, we consider a class of quasi-linear utility functions. Furthermore, we illustrate that, with quasi-linear utility functions, by introducing heterogeneity between traders, there are other environments in which this taxation mechanism implements a Pareto-optimal outcome.</div></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"139 ","pages":"Article 102492"},"PeriodicalIF":0.7,"publicationDate":"2025-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145797485","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-06DOI: 10.1016/j.mathsocsci.2025.102491
Doron Klunover
We consider a lottery contest between n risk-neutral symmetric players, who compete for a prize with a common value. Prior to exerting effort, each player chooses between an old technology, in which return on effort is certain, and a new technology, in which return on effort is uncertain but on average is equal to the return on effort in the old technology. We characterize symmetric and asymmetric equilibria and show that in equilibrium the new technology is adopted by a proper subset of the players. The results offer an explanation for endogenous emergence of asymmetric technologies in contests.
{"title":"Endogenous technology choice in contests","authors":"Doron Klunover","doi":"10.1016/j.mathsocsci.2025.102491","DOIUrl":"10.1016/j.mathsocsci.2025.102491","url":null,"abstract":"<div><div>We consider a lottery contest between <em>n</em> risk-neutral symmetric players, who compete for a prize with a common value. Prior to exerting effort, each player chooses between an old technology, in which return on effort is certain, and a new technology, in which return on effort is uncertain but on average is equal to the return on effort in the old technology. We characterize symmetric and asymmetric equilibria and show that in equilibrium the new technology is adopted by a proper subset of the players. The results offer an explanation for endogenous emergence of asymmetric technologies in contests.</div></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"139 ","pages":"Article 102491"},"PeriodicalIF":0.7,"publicationDate":"2025-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145748443","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-03DOI: 10.1016/j.mathsocsci.2025.102489
Yassine Badra , Bertrand Chopard , Huizhong Liu
This paper examines the strategic implications of research joint ventures (RJVs) in an oligopolistic setting with R&D spillovers, focusing on their impact on social welfare. Using the well-known R&D model of d’Aspremont–Jacquemin (AJ), we analyze different R&D cooperation structures: the non-cooperative regime, the R&D cartel regime, the cartelized RJV, and the non-cooperative RJV. Our findings challenge conventional views on the efficiency of RJVs. While the model of Kamien–Muller–Zang (KMZ) consistently predicts that RJVs lead to lower social welfare, we show that in the AJ framework, an RJV can outperform both the standard non-cooperative and cartel regimes when spillovers remain below a certain threshold. This result underscores the importance of model-specific assumptions in assessing R&D cooperation policies and offers valuable insights for industrial policy and antitrust regulation in innovation-driven markets.
{"title":"R&D cooperation and spillovers: When do research joint ventures improve welfare?","authors":"Yassine Badra , Bertrand Chopard , Huizhong Liu","doi":"10.1016/j.mathsocsci.2025.102489","DOIUrl":"10.1016/j.mathsocsci.2025.102489","url":null,"abstract":"<div><div>This paper examines the strategic implications of research joint ventures (RJVs) in an oligopolistic setting with R&D spillovers, focusing on their impact on social welfare. Using the well-known R&D model of d’Aspremont–Jacquemin (AJ), we analyze different R&D cooperation structures: the non-cooperative regime, the R&D cartel regime, the cartelized RJV, and the non-cooperative RJV. Our findings challenge conventional views on the efficiency of RJVs. While the model of Kamien–Muller–Zang (KMZ) consistently predicts that RJVs lead to lower social welfare, we show that in the AJ framework, an RJV can outperform both the standard non-cooperative and cartel regimes when spillovers remain below a certain threshold. This result underscores the importance of model-specific assumptions in assessing R&D cooperation policies and offers valuable insights for industrial policy and antitrust regulation in innovation-driven markets.</div></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"139 ","pages":"Article 102489"},"PeriodicalIF":0.7,"publicationDate":"2025-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145748444","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-03DOI: 10.1016/j.mathsocsci.2025.102488
Frederik Van De Putte, Stefan Wintein
Claim-strength problems are a distinctive class of allocation problems in which the currency of claims is different from that of the estate that is to be divided. We study mixtures (i.e. convex combinations) of three basic allocation rules for claim-strength problems: the proportional rule, the uniform allocation rule, and the plurality allocation rule. We observe that any such mixture satisfies a generalized transfer axiom in addition to a number of invariance properties. We establish a fundamental representation theorem: taken jointly, these axioms fully characterize the class of all mixtures of the three base rules. This result is tight. From it, we derive characterizations of more specific classes and the three basic rules themselves. We moreover show that within the class of mixtures, the only three rules that satisfy a familiar consistency axiom are the base rules.
{"title":"Claim-strength problems and mixtures: An axiomatic study","authors":"Frederik Van De Putte, Stefan Wintein","doi":"10.1016/j.mathsocsci.2025.102488","DOIUrl":"10.1016/j.mathsocsci.2025.102488","url":null,"abstract":"<div><div>Claim-strength problems are a distinctive class of allocation problems in which the currency of claims is different from that of the estate that is to be divided. We study mixtures (i.e. convex combinations) of three basic allocation rules for claim-strength problems: the proportional rule, the uniform allocation rule, and the plurality allocation rule. We observe that any such mixture satisfies a generalized <em>transfer</em> axiom in addition to a number of <em>invariance</em> properties. We establish a fundamental representation theorem: taken jointly, these axioms fully characterize the class of all mixtures of the three base rules. This result is tight. From it, we derive characterizations of more specific classes and the three basic rules themselves. We moreover show that within the class of mixtures, the only three rules that satisfy a familiar <em>consistency</em> axiom are the base rules.</div></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"139 ","pages":"Article 102488"},"PeriodicalIF":0.7,"publicationDate":"2025-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145694045","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-03DOI: 10.1016/j.mathsocsci.2025.102490
Pascal Toquebeuf
This paper analyzes a dynamic adverse selection market where buyers hold ambiguous beliefs about seller quality, modeled using neo-additive Choquet capacities and updated via optimistic, pessimistic, and Generalized Bayesian rules. First, we show that the choice of updating heuristic has a direct and systematic effect on the severity of adverse selection. While the optimistic and pessimistic rules invariably mitigate or amplify the problem, respectively, the Generalized Bayesian rule’s impact is conditional, its trajectory toward collapse, efficiency, or a stable partial market depending on a persistent ‘tug-of-war’ between the buyer’s static ambiguity attitude and the evolving probabilistic evidence. Our second main finding is that these immediate effects compound over time, leading to fundamentally different market trajectories. The pessimistic rule can drive the market to complete collapse, the optimistic rule can foster full participation, and the Generalized Bayesian path depends on the interplay between the buyer’s attitude and the evolving evidence. We further analyze how baseline ambiguity and ambiguity aversion modulate these dynamics, uncovering a complex role for ambiguity in shaping the rate of market evolution.
{"title":"Dynamic adverse selection with the best and the worst in mind","authors":"Pascal Toquebeuf","doi":"10.1016/j.mathsocsci.2025.102490","DOIUrl":"10.1016/j.mathsocsci.2025.102490","url":null,"abstract":"<div><div>This paper analyzes a dynamic adverse selection market where buyers hold ambiguous beliefs about seller quality, modeled using neo-additive Choquet capacities and updated via optimistic, pessimistic, and Generalized Bayesian rules. First, we show that the choice of updating heuristic has a direct and systematic effect on the severity of adverse selection. While the optimistic and pessimistic rules invariably mitigate or amplify the problem, respectively, the Generalized Bayesian rule’s impact is conditional, its trajectory toward collapse, efficiency, or a stable partial market depending on a persistent ‘tug-of-war’ between the buyer’s static ambiguity attitude and the evolving probabilistic evidence. Our second main finding is that these immediate effects compound over time, leading to fundamentally different market trajectories. The pessimistic rule can drive the market to complete collapse, the optimistic rule can foster full participation, and the Generalized Bayesian path depends on the interplay between the buyer’s attitude and the evolving evidence. We further analyze how baseline ambiguity and ambiguity aversion modulate these dynamics, uncovering a complex role for ambiguity in shaping the rate of market evolution.</div></div>","PeriodicalId":51118,"journal":{"name":"Mathematical Social Sciences","volume":"139 ","pages":"Article 102490"},"PeriodicalIF":0.7,"publicationDate":"2025-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145694046","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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