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  1. Representación democrática, reglas de decisión y la constitución.Ricardo Restrepo - manuscript
    Este artículo brinda algunas respuestas y alternativas a ciertos problemas y propuestas en el área de la teoría democrática. El ensayo tiene como enfoque la cuestión de distinguir sistemas que pueden parecer democráticos sin serlo de sistemas realmente democráticos. Develando algunos actores disfrazados del discurso democrático en América Latina, el artículo argumenta que es preferible la regla de la mayoría como base para la identificación del bien común por medio del interés general, que reglas de minorías, consentimiento total o bases (...)
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  2. Arrow's theorem, ultrafilters, and reverse mathematics.Benedict Eastaugh - forthcoming - Review of Symbolic Logic.
    This paper initiates the reverse mathematics of social choice theory, studying Arrow's impossibility theorem and related results including Fishburn's possibility theorem and the Kirman–Sondermann theorem within the framework of reverse mathematics. We formalise fundamental notions of social choice theory in second-order arithmetic, yielding a definition of countable society which is tractable in RCA0. We then show that the Kirman–Sondermann analysis of social welfare functions can be carried out in RCA0. This approach yields a proof of Arrow's theorem in RCA0, and (...)
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  3. Multidimensional Concepts and Disparate Scale Types.Brian Hedden & Jacob M. Nebel - forthcoming - Philosophical Review.
    Multidimensional concepts are everywhere, and they are important. Examples include moral value, welfare, scientific confirmation, democracy, and biodiversity. How, if at all, can we aggregate the underlying dimensions of a multidimensional concept F to yield verdicts about which things are Fer than which overall? Social choice theory can be used to model and investigate this aggregation problem. Here, we focus on a particularly thorny problem made salient by this social choice-theoretic framework: the underlying dimensions of a given concept might be (...)
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  4. Escaping Arrow's Theorem: The Advantage-Standard Model.Wesley Holliday & Mikayla Kelley - forthcoming - Theory and Decision.
    There is an extensive literature in social choice theory studying the consequences of weakening the assumptions of Arrow's Impossibility Theorem. Much of this literature suggests that there is no escape from Arrow-style impossibility theorems unless one drastically violates the Independence of Irrelevant Alternatives (IIA). In this paper, we present a more positive outlook. We propose a model of comparing candidates in elections, which we call the Advantage-Standard (AS) model. The requirement that a collective choice rule (CCR) be rationalizable by the (...)
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  5. Why Arrow's Theorem Matters for Political Theory Even If Preference Cycles Never Occur.Sean Ingham - forthcoming - Public Choice.
    Riker (1982) famously argued that Arrow’s impossibility theorem undermined the logical foundations of “populism”, the view that in a democracy, laws and policies ought to express “the will of the people”. In response, his critics have questioned the use of Arrow’s theorem on the grounds that not all configurations of preferences are likely to occur in practice; the critics allege, in particular, that majority preference cycles, whose possibility the theorem exploits, rarely happen. In this essay, I argue that the critics’ (...)
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  6. Strong dictatorship via ratio-scale measurable utilities: a simpler proof.Jacob M. Nebel - forthcoming - Economic Theory Bulletin.
    Tsui and Weymark (Economic Theory, 1997) have shown that the only continuous social welfare orderings on the whole Euclidean space which satisfy the weak Pareto principle and are invariant to individual-specific similarity transformations of utilities are strongly dictatorial. Their proof relies on functional equation arguments which are quite complex. This note provides a simpler proof of their theorem.
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  7. Extensive Measurement in Social Choice.Jacob M. Nebel - forthcoming - Theoretical Economics.
    Extensive measurement is the standard measurement-theoretic approach for constructing a ratio scale. It involves the comparison of objects that can be concatenated in an additively representable way. This paper studies the implications of extensively measurable welfare for social choice theory. We do this in two frameworks: an Arrovian framework with a fixed population and no interpersonal comparisons, and a generalized framework with variable populations and full interpersonal comparability. In each framework we use extensive measurement to introduce novel domain restrictions, independence (...)
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  8. Affect, desire and interpretation.Robert Williams - forthcoming - Philosophical Studies.
    Are interpersonal comparisons of desire possible? Can we give an account of how facts about desires are grounded, that underpins such comparisons? This paper supposes the answer to the first question is yes, and provides an account of the nature of desire that explains how this is so. The account is a modification of the interpretationist metaphysics of representation that the author has recently been developing. The modification is to allow phenomenological affective valence into the “base facts” on which correct (...)
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  9. Public Finance or Public Choice? The Scholastic Political Economy As an Essentialist Synthesis.Mohammadhosein Bahmanpour-Khalesi - 2024 - International Journal of New Political Economy 5 (1):217-238.
    Nowadays, it is thought that there are only two approaches to political economy: public finance and public choice; however, this research aims to introduce a new insight by investigating scholastic sources. We study the relevant classic books from the thirteenth to the seventeenth centuries and reevaluate the scholastic literature based on public finance and public choice doctrines. The findings confirm that the government is the institution for realizing the common good according to a scholastic attitude. Therefore, scholastic thinkers saw a (...)
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  10. Ethics without numbers.Jacob Nebel - 2024 - Philosophy and Phenomenological Research 108 (2):289-319.
    This paper develops and explores a new framework for theorizing about the measurement and aggregation of well-being. It is a qualitative variation on the framework of social welfare functionals developed by Amartya Sen. In Sen’s framework, a social or overall betterness ordering is assigned to each profile of real-valued utility functions. In the qualitative framework developed here, numerical utilities are replaced by the properties they are supposed to represent. This makes it possible to characterize the measurability and interpersonal comparability of (...)
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  11. Two impossibility results for social choice under individual indifference intransitivity.Gustav Alexandrie - 2023 - Social Choice and Welfare 61:919–936.
    Due to the imperfect ability of individuals to discriminate between sufficiently similar alternatives, individual indifferences may fail to be transitive. I prove two impossibility theorems for social choice under indifference intransitivity, using axioms that are strictly weaker than Strong Pareto and that have been endorsed (sometimes jointly) in prior work on social choice under indifference intransitivity. The key axiom is Consistency, which states that if bundles are held constant for all but one individual, then society’s preferences must align with those (...)
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  12. Independent, neutral, and monotonic collective choice: the role of Suzumura consistency.Walter Bossert, Susumu Cato & Kohei Kamaga - 2023 - Social Choice and Welfare 61:835–852.
    We examine the impact of Suzumura’s (Economica 43:381–390, 1976) consistency property when applied in the context of collective choice rules that are independent of irrelevant alternatives, neutral, and monotonic. An earlier contribution by Blau and Deb (Econometrica 45:871–879, 1977) establishes the existence of a vetoer if the collective relation is required to be complete and acyclical. The purpose of this paper is to explore the possibilities that result if completeness and acyclicity are dropped and Suzumura consistency is imposed instead. A (...)
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  13. Split Cycle: a new Condorcet-consistent voting method independent of clones and immune to spoilers.Wesley Holliday & Eric Pacuit - 2023 - Public Choice 197:1-62.
    We propose a Condorcet-consistent voting method that we call Split Cycle. Split Cycle belongs to the small family of known voting methods satisfying the anti-vote-splitting criterion of independence of clones. In this family, only Split Cycle satisfies a new criterion we call immunity to spoilers, which concerns adding candidates to elections, as well as the known criteria of positive involvement and negative involvement, which concern adding voters to elections. Thus, in contrast to other clone-independent methods, Split Cycle mitigates both “spoiler (...)
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  14. Stable preference aggregation with infinite population.Susumu Cato - 2022 - Social Choice and Welfare 59:287–304.
    In this paper, we explore the stability of the aggregation procedure of individual preferences. In particular, we propose the stability under the addition of social preference, which is a normative property of democratic collective decision making. We establish impossibility and possibility theorems for non-dictatorial aggregation procedures.
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  15. Proxy Selection in Transitive Proxy Voting.Jacqueline Harding - 2022 - Social Choice and Welfare 58:69-99.
    Transitive proxy voting (or "liquid democracy") is a novel form of collective decision making, often framed as an attractive hybrid of direct and representative democracy. Although the ideas behind liquid democracy have garnered widespread support, there have been relatively few attempts to model it formally. This paper makes three main contributions. First, it proposes a new social choice-theoretic model of liquid democracy, which is distinguished by taking a richer formal perspective on the process by which a voter chooses a proxy. (...)
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  16. Social choice problems with public reason proceduralism.Henrik D. Kugelberg - 2022 - Economics and Philosophy 38 (1):51-70.
    Most political liberals argue that only rules, policies and institutions that are part of society’s basic structure need to be justified with so-called public reasons. Laws enacted outside this set are legitimate if and when public reasons can justify the procedure that selects them. I argue that this view is susceptible to known problems from social choice theory. However, there are resources within political liberalism that could address them. If the scope of public reason is extended beyond the basic structure (...)
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  17. Superset-robust collective choice rules.Walter Bossert & Susumu Cato - 2021 - Mathematical Social Sciences 109:126–136.
    A new property of collective choice rules that we refer to as superset robustness is introduced, and we employ it in several characterization results. The axiom requires that if all individual preference orderings expand weakly (in the sense of set inclusion), then the corresponding social preference relation must also expand weakly. In other words, if a given profile is changed by adding instances of weak preference to some individual relations, then the social weak preference relation for the expanded profile must (...)
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  18. Preference aggregation and atoms in measures.Susumu Cato - 2021 - Journal of Mathematical Economics 94:102446.
    This paper examines the aggregation of preferences with a finitely additive measure space of agents. We consider three types of non-dictatorship axioms: non-dictatorship, coalitional non-dictatorship, and atomic non-dictatorship. First, we show that the existence of an atom is a necessary and sufficient condition for the existence of a social welfare function that satisfies weak Pareto, independence of irrelevant alternatives, and coalitional non-dictatorship. Second, we simultaneously impose non-dictatorship and coalitional non-dictatorship, and specify a necessary and sufficient condition for the finitely additive (...)
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  19. The Necessity of Commensuration Bias in Grant Peer Review.Remco Heesen - 2021 - Ergo: An Open Access Journal of Philosophy 8 (39):423--443.
    Peer reviewers at many funding agencies and scientific journals are asked to score submissions both on individual criteria and overall. The overall scores should be some kind of aggregate of the criteria scores. Carole Lee identifies this as a potential locus for bias to enter the peer review process, which she calls commensuration bias. Here I view the aggregation of scores through the lens of social choice theory. I argue that, when reviewing grant proposals, it is in many cases impossible (...)
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  20. Voting Theory in the Lean Theorem Prover.Wesley H. Holliday, Chase Norman & Eric Pacuit - 2021 - In Sujata Ghosh & Thomas Icard (eds.), Logic, Rationality, and Interaction: 8th International Workshop, Lori 2021, Xi’an, China, October 16–18, 2021, Proceedings. Springer Verlag. pp. 111-127.
    There is a long tradition of fruitful interaction between logic and social choice theory. In recent years, much of this interaction has focused on computer-aided methods such as SAT solving and interactive theorem proving. In this paper, we report on the development of a framework for formalizing voting theory in the Lean theorem prover, which we have applied to verify properties of a recently studied voting method. While previous applications of interactive theorem proving to social choice have focused on the (...)
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  21. Axioms for Defeat in Democratic Elections.Wesley H. Holliday & Eric Pacuit - 2021 - Journal of Theoretical Politics 33 (4):475 - 524.
    We propose six axioms concerning when one candidate should defeat another in a democratic election involving two or more candidates. Five of the axioms are widely satisfied by known voting procedures. The sixth axiom is a weakening of Kenneth Arrow's famous condition of the Independence of Irrelevant Alternatives (IIA). We call this weakening Coherent IIA. We prove that the five axioms plus Coherent IIA single out a method of determining defeats studied in our recent work: Split Cycle. In particular, Split (...)
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  22. From Utilitarianism to Prioritarianism – an Empathy-Based Internalist Foundation of Welfare Ethics.Christoph Lumer - 2021 - In Michael Schefczyk & Christoph Schmidt-Petri (eds.), Utility, Progress, and Technology: Proceedings of the 15th Conference of the International Society for Utilitarian Studies. Karlsruhe: KIT Scientific Publishing. pp. 139-151.
    The article develops an internalist justification of welfare ethics based on empathy. It takes up Hume’s and Schopenhauer’s internalistic (but not consistently developed) justification approach via empathy, but tries to solve three of their problems: 1. the varying strength of empathy depending on the proximity to the object of empathy, 2. the unclear metaethical foundation, 3. the absence of a quantitative model of empathy strength. 1. As a solution to the first problem, the article proposes to limit the foundation of (...)
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  23. How to Define 'Prioritarianism' and Distinguish It from (Moderate) Egalitarianism.Christoph Lumer - 2021 - In Michael Schefczyk & Christoph Schmidt-Petri (eds.), Utility, Progress, and Technology: Proceedings of the 15th Conference of the International Society for Utilitarian Studies. Karlsruhe: KIT Scientific Publishing. pp. 153-166.
    In this paper, first the term 'prioritarianism' is defined, with some mathematical precision, on the basis of intuitive conceptions of prioritarianism, especially the idea that "benefiting people matters more the worse off these people are". (The prioritarian weighting function is monotonously ascending and concave, while its first derivation is smoothly descending and convex but positive throughout.) Furthermore, (moderate welfare) egalitarianism is characterized. In particular a new symmetry condition is defended, i.e. that egalitarianism evaluates upper and lower deviations from the social (...)
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  24. Acyclicity, anonymity, and prefilters.Walter Bossert & Susumu Cato - 2020 - Journal of Mathematical Economics 87:134–141.
    We analyze the decisiveness structures associated with acyclical collective choice rules. In particular, we examine the consequences of adding anonymity to weak Pareto, thereby complementing earlier results on acyclical social choice. Both finite and countably infinite populations are considered. As established in contributions by Donald Brown and by Jeffrey Banks, acyclical social choice is closely linked to prefilters in the presence of the weak Pareto principle. We introduce the notion of a conditional prefilter and use it to generalize their results. (...)
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  25. Incompleteness, regularity, and collective preference.Susumu Cato - 2020 - Metroeconomica 71 (2):333–344.
    This paper examines the incompleteness of collective preference. We provide a series of Arrovian impossibility theorems without completeness. First, we consider the notion of regularity introduced by Eliaz and Ok (2006, Games and Economic Behavior 56, 61–86); it is an appropriate richness property for strict preference when preference is allowed to be incomplete. We examine the implication of imposing regularity on collective preference. Second, we propose responsiveness, a variation of positive responsiveness. This axiom requires that some changes in individual preferences (...)
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  26. A note on Murakami’s theorems and incomplete social choice without the Pareto principle.Wesley H. Holliday & Mikayla Kelley - 2020 - Social Choice and Welfare 55:243-253.
    In Arrovian social choice theory assuming the independence of irrelevant alternatives, Murakami (1968) proved two theorems about complete and transitive collective choice rules that satisfy strict non-imposition (citizens’ sovereignty), one being a dichotomy theorem about Paretian or anti-Paretian rules and the other a dictator-or-inverse-dictator impossibility theorem without the Pareto principle. It has been claimed in the later literature that a theorem of Malawski and Zhou (1994) is a generalization of Murakami’s dichotomy theorem and that Wilson’s (1972) impossibility theorem is stronger (...)
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  27. Arrow's Decisive Coalitions.Wesley H. Holliday & Eric Pacuit - 2020 - Social Choice and Welfare 54:463–505.
    In his classic monograph, Social Choice and Individual Values, Arrow introduced the notion of a decisive coalition of voters as part of his mathematical framework for social choice theory. The subsequent literature on Arrow’s Impossibility Theorem has shown the importance for social choice theory of reasoning about coalitions of voters with different grades of decisiveness. The goal of this paper is a fine-grained analysis of reasoning about decisive coalitions, formalizing how the concept of a decisive coalition gives rise to a (...)
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  28. Democracy without Enlightenment: A Jury Theorem for Evaluative Voting.Michael Morreau - 2020 - Journal of Political Philosophy 29 (2):188-210.
    Panels, boards, and committees throughout society evaluate all manner of things by grading them, first individually and then collectively. Thus risks are prioritized, research proposals are funded, and candidates are shortlisted for jobs. It is not usual to pick winners in political elections by grading the candidates, but there are examples in history. This article takes up a question about the quality of judgments and decisions made by grading: under which conditions are they likely to be right? An answer comes (...)
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  29. Intelligence via ultrafilters: structural properties of some intelligence comparators of deterministic Legg-Hutter agents.Samuel Alexander - 2019 - Journal of Artificial General Intelligence 10 (1):24-45.
    Legg and Hutter, as well as subsequent authors, considered intelligent agents through the lens of interaction with reward-giving environments, attempting to assign numeric intelligence measures to such agents, with the guiding principle that a more intelligent agent should gain higher rewards from environments in some aggregate sense. In this paper, we consider a related question: rather than measure numeric intelligence of one Legg- Hutter agent, how can we compare the relative intelligence of two Legg-Hutter agents? We propose an elegant answer (...)
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  30. The possibility of Paretian anonymous decision-making with an infinite population.Susumu Cato - 2019 - Social Choice and Welfare 53 (4):587–601.
    This paper considers the trade-off between unanimity and anonymity in collective decision-making with an infinite population. This efficiency-equity trade-off is a fundamental difficulty in making a normative judgment in a conflict between generations. In particular, it is known that this trade-off is quite sensitive in the formulation of unanimity axioms. In this study, we consider the trade-off in a preference-aggregation framework instead of the standard utility-aggregation framework. We show that there exists a social welfare function that satisfies I-strong Pareto, independence (...)
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  31. Strategic Voting Under Uncertainty About the Voting Method.Wesley H. Holliday & Eric Pacuit - 2019 - Electronic Proceedings in Theoretical Computer Science 297:252–272.
    Much of the theoretical work on strategic voting makes strong assumptions about what voters know about the voting situation. A strategizing voter is typically assumed to know how other voters will vote and to know the rules of the voting method. A growing body of literature explores strategic voting when there is uncertainty about how others will vote. In this paper, we study strategic voting when there is uncertainty about the voting method. We introduce three notions of manipulability for a (...)
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  32. Incomplete decision-making and Arrow’s impossibility theorem.Susumu Cato - 2018 - Mathematical Social Sciences 94:58–64.
    This paper is concerned with social choice without completeness of social preference. Completeness requires that pairs of alternatives are perfectly comparable. We introduce the concept of minimal comparability, which requires that for any profile, there is some comparable pair of distinct alternatives. Complete silence should be avoided according to this condition. We show that there exists no normatively desirable aggregation rule satisfying minimal comparability.
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  33. Collective rationality and decisiveness coherence.Susumu Cato - 2018 - Social Choice and Welfare 50:305–328.
    Arrow’s impossibility theorem states that if an aggregation rule satisfies unrestricted domain, weak Pareto, independence of irrelevant alternatives, and collective rationality, then there exists a dictator. Among others, Arrow’s postulate of collective rationality is controversial. We propose a new axiom for an aggregation rule, decisiveness coherence, which is weaker than collective rationality. It is shown that given the Arrovian axioms other than collective rationality, a dictatorship arises if and only if decisiveness coherence is satisfied. Moreover, we introduce weak versions of (...)
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  34. Decisive coalitions and positive responsiveness.Susumu Cato - 2018 - Metroeconomica 69 (1):308–323.
    This paper addresses the Arrovian social choice problem. Our focus is the role of positive responsiveness, which requires social judgments to be strongly monotonic with respect to individual judgments. We clarify the structure of decisive coalitions associated with collective choice rules that satisfy positive responsiveness and Arrow's axioms. Transitivity of social preferences is relaxed to quasi‐transitivity or acyclicity.
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  35. From Degrees of Belief to Binary Beliefs: Lessons from Judgment-Aggregation Theory.Franz Dietrich & Christian List - 2018 - Journal of Philosophy 115 (5):225-270.
    What is the relationship between degrees of belief and binary beliefs? Can the latter be expressed as a function of the former—a so-called “belief-binarization rule”—without running into difficulties such as the lottery paradox? We show that this problem can be usefully analyzed from the perspective of judgment-aggregation theory. Although some formal similarities between belief binarization and judgment aggregation have been noted before, the connection between the two problems has not yet been studied in full generality. In this paper, we seek (...)
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  36. Rule by Multiple Majorities: A New Theory of Popular Control.Sean Ingham - 2018 - Cambridge University Press.
    In a democracy, citizens should have some control over how they are governed. If they do not participate directly in making policy, they ought to maintain control over the public officials who design policy on their behalf. Rule by Multiple Majorities develops a novel theory of popular control: an account of what it is, why democracy's promise of popular control is compatible with what we know about actual democracies, and why it matters. While social choice theory suggests there is no (...)
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  37. Democratic Deliberation and Social Choice: A Review.Christian List - 2018 - In André Bächtiger, Jane Mansbridge, John Dryzek & Mark Warren (eds.), Oxford Handbook of Deliberative Democracy. Oxford University Press.
    In normative political theory, it is widely accepted that democracy cannot be reduced to voting alone, but that it requires deliberation. In formal social choice theory, by contrast, the study of democracy has focused primarily on the aggregation of individual opinions into collective decisions, typically through voting. While the literature on deliberation has an optimistic flavour, the literature on social choice is more mixed. It is centred around several paradoxes and impossibility results identifying conflicts between different intuitively plausible desiderata. In (...)
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  38. The wisdom of collective grading and the effects of epistemic and semantic diversity.Aidan Lyon & Michael Morreau - 2018 - Theory and Decision 85 (1):99-116.
    A computer simulation is used to study collective judgements that an expert panel reaches on the basis of qualitative probability judgements contributed by individual members. The simulated panel displays a strong and robust crowd wisdom effect. The panel's performance is better when members contribute precise probability estimates instead of qualitative judgements, but not by much. Surprisingly, it doesn't always hurt for panel members to interpret the probability expressions differently. Indeed, coordinating their understandings can be much worse.
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  39. Unanimity, anonymity, and infinite population.Susumu Cato - 2017 - Journal of Mathematical Economics 71:28–35.
    This paper is concerned with the implications of unanimity and anonymity for the Arrovian social choice theory when population is infinite. Contrary to the finite population case, various unanimity and anonymity axioms can be formulated. We show a tension between unanimity and anonymity by providing possibility and impossibility results. We also examine the case in which social preferences are allowed to be quasi-transitive.
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  40. Hybrid invariance and oligarchic structures.Susumu Cato - 2017 - BE Journal of Theoretical Economics 18 (1):20160145.
    This study addresses the problem of Arrovian preference aggregation. Social rationality plays a crucial role in the standard Arrovian framework. However, no assumptions on social rationality are imposed here. Social preferences are allowed to be any binary relation (possibly incomplete and intransitive). We introduce the axiom of hybrid invariance, which requires that if social preferences under two preference profiles make the same judgment, then a social preference under a “hybrid” of the two profiles must extend the original judgment in a (...)
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  41. On Quine on Arrow.Maurice Salles - 2017 - Social Choice and Welfare 48 (4):877-886.
    This paper describes an unknown episode in the development of the theory of social choice. In the Summer 1949, while at RAND, Quine worked on Arrow’s (im)possibility theorem. This work was eventually published as a paper on (applied) set theory totally disconnected from social choice. The working paper directly linked to Arrow’s work was never published. I alluded to this (then unwritten) paper in a number of presentations I made on ‘Logic and Social Choice’ in Turku, Bucharest, Boston, Strasbourg and (...)
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  42. Weak independence and the Pareto principle.Susumu Cato - 2016 - Social Choice and Welfare 47:295–314.
    In this paper, the independence of irrelevant alternatives and the Pareto principle are simultaneously weakened in the Arrovian framework of social choice. Moreover, we also relax transitivity of social preferences. We show that impossibility remains under weaker versions of Arrow’s original conditions. Our results complement the recent work by Coban and Sanver (Soc Choice Welf 43(4):953–961, 2014).
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  43. Grading in Groups.Michael Morreau - 2016 - Economics and Philosophy 32 (2):323-352.
    Juries, committees and experts panels commonly appraise things of one kind or another on the basis of grades awarded by several people. When everybody's grading thresholds are known to be the same, the results sometimes can be counted on to reflect the graders’ opinion. Otherwise, they often cannot. Under certain conditions, Arrow's ‘impossibility’ theorem entails that judgements reached by aggregating grades do not reliably track any collective sense of better and worse at all. These claims are made by adapting the (...)
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  44. Single-peakedness and semantic dimensions of preferences.Daniele Porello - 2016 - Logic Journal of the IGPL 24 (4).
    Among the possible solutions to the paradoxes of collective preferences, single-peakedness is significant because it has been associated to a suggestive conceptual interpretation: a single-peaked preference profile entails that, although individuals may disagree on which option is the best, they conceptualize the choice along a shared unique dimension, i.e. they agree on the rationale of the collective decision. In this article, we discuss the relationship between the structural property of singlepeakedness and its suggested interpretation as uni-dimensionality of a social choice. (...)
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  45. Weak independent decisiveness and the existence of a unique vetoer.Susumu Cato - 2015 - Economics Letters 131:59–61.
    This paper is concerned with an aggregation of individual preferences. We introduce the concept of weak independent decisiveness, which is a weakening of Sen’s independent decisiveness. We show that a Paretian social welfare function satisfies weak independent decisiveness if and only if the family of weakly decisive sets forms an ultrafilter.
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  46. Weak independence and social semi-orders.Susumu Cato - 2015 - Japanese Economic Review 66:311–321.
    This paper provides variants of Arrow’s impossibility theorem, which states that there exists no non-dictatorial aggregation rule satisfying weak Pareto, independence of irrelevant alternatives and collective rationality. In this paper, independence of irrelevant alternatives and collective rationality are simultaneously relaxed. Weak independence is imposed instead of independence of irrelevant alternatives. Social preferences are assumed to satisfy the semi-order properties of semi-transitivity and the interval-order property. We prove that there exists a vetoer when the number of alternatives is greater than or (...)
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  47. Aggregation Theory and the Relevance of Some Issues to Others.Franz Dietrich - 2015 - Journal of Economic Theory 160:463-493.
    I propose a relevance-based independence axiom on how to aggregate individual yes/no judgments on given propositions into collective judgments: the collective judgment on a proposition depends only on people’s judgments on propositions which are relevant to that proposition. This axiom contrasts with the classical independence axiom: the collective judgment on a proposition depends only on people’s judgments on the same proposition. I generalize the premise-based rule and the sequential-priority rule to an arbitrary priority order of the propositions, instead of a (...)
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  48. Menu dependence and group decision making.Susumu Cato - 2014 - Group Decision and Negotiation 23:561–577.
    This paper is concerned with the problem of group decision making. We introduce the notion of a collective system rule. A collective system rule maps each preference profile to a group-preference system, which is a collection of social preferences on the subsets of the alternatives. By formulating the Arrovian conditions, we show the Arrow-type impossibility theorems. We also discuss how our approach is related to the standard group decision-making process.
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  49. Common preference, non-consequential features, and collective decision making.Susumu Cato - 2014 - Review of Economic Design 18:265–287.
    This paper examines an extended framework of Arrovian social choice theory. We consider two classes of values: consequential values and non-consequential values. Each individual has a comprehensive preference based on the two. Non-consequential values are assumed to be homogeneous among individuals. It is shown that a social ordering function satisfying Arrovian conditions must be non-consequential: a social comprehensive preference gives unequivocal priority to non-consequential values. We clarify the role of common preferences over non-consequential features.
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  50. Social choice and the arrow conditions.Allan F. Gibbard - 2014 - Economics and Philosophy 30 (3):269-284.
    Arrow’s impossibility result stems chiefly from a combination of two requirements: independence and fixity. Independence says that the social choice is independent of individual preferences involving unavailable alternatives. Fixity says that the social choice is fixed by a social preference relation that is independent of what is available. Arrow found that requiring, further, that this relation be transitive yields impossibility. Here it is shown that allowing intransitive social indifference still permits only a vastly unsatisfactory system, a liberum veto oligarchy. Arrow’s (...)
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