-/- This unique book develops an operational approach to preference and rationality as the author employs operators over binary relations to capture the concept of rationality. -/- A preference is a basis of individual behavior and social judgment and is mathematically regarded as a binary relation on the set of alternatives. Traditionally, an individual/social preference is assumed to satisfy completeness and transitivity. However, each of the two conditions is often considered to be too demanding; and then, weaker rationality conditions are (...) introduced by researchers. This book argues that the preference rationality conditions can be captured mathematically by “operators,” which are mappings from the set of operators to itself. This operational approach nests traditional concepts in individual/social decision theory and clarifies the underlying formal structure of preference rationality. -/- The author also applies his approach to welfare economics. The core problem of ‘new welfare economics,’ developed by Kaldor, Hicks, and Samuelson, is the rationality of social preference. In this book the author translates the social criteria proposed by those three economists into operational forms, which provide new insights into welfare economics extending beyond ‘new welfare economics.’ . (shrink)

We examine the range of anonymity that is compatible with a Paretian social welfare relation (SWR) on infinite utility streams. Three alternative coherence properties of an SWR are considered, namely, acyclicity, quasi-transitivity, and Suzumura consistency. For each case, we show that a necessary and sufficient condition for a set of permutations to be the set of permissible permutations of some Paretian SWR is given by the cyclicity of permutations and a weakening of group structure. Further, for each case of coherence (...) property, we show that the extended Pareto rule is the least element of the class of anonymous Paretian SWRs. (shrink)

Bioethics, Volume 36, Issue 4, Page 445-452, May 2022.

This paper provides an axiomatic analysis of sufficientarian social evaluation. Sufficientarianism has emerged as an increasingly important notion of distributive justice. We propose a class of principles that we label generalized critical-level sufficientarian orderings. The distinguishing feature of our new class is that its members exhibit constant critical levels of well-being that are allowed to differ from the threshold of sufficiency. Our basic axiom assigns priority to those below the threshold, a property that is shared by numerous other sufficientarian approaches. (...) When combined with the well-known strong Pareto principle and the assumption that there be a constant critical level, the axiom implies that the critical level cannot be below the threshold. The main results of the paper are characterizations of our new class and an important subclass. As a final observation, we identify the generalized critical-level sufficientarian orderings that permit us to avoid the repugnant conclusion and the sadistic conclusion, which are known as two fundamental challenges in population ethics. (shrink)

We examine a general class of variable-value population principles. Our particular focus is on the extent to which such principles can avoid the repugnant and sadistic conclusions. We show that if a mild limit property is imposed, avoidance of the repugnant conclusion implies the sadistic conclusion. This result generalizes earlier observations by showing that they apply to a substantially larger class of principles. Our second theorem states that, under the limit property, the axiom of mere addition also conflicts with avoidance (...) of the repugnant conclusion. This result is a consequence of a similar observation that appears in the earlier literature. (shrink)

The aim of the present paper is to provide an axiomatic analysis of incomplete social judgments. In particular, we clarify the underlying power structure of Arrovian collective choice rules when social preferences are allowed to be incomplete. We propose the concept of quasi-decisiveness and investigate the properties of the collection of quasi-decisive sets associated with an Arrovian collective choice rule. In the course of this, we offer a series of applications.

The intersection approach is a common method of overcoming a conflict among multiple values. Under this approach, a state is more desirable than another if it is so for all criteria in question. A fundamental difficulty is that judgment under the intersection approach lacks completeness in too many cases. We propose alternative methods that extend the intersection approach: the union and union-intersection approaches. Our methods generate a (quasi-)coherence judgment which is more completed and can be applied to most problems of (...) ethical indices. (shrink)

Journal of Political Philosophy, EarlyView.

The purpose of this paper is to investigate the relationship between collective rationality and permissible collective choice rules using a unified approach inspired by Bossert and Suzumura (J Econ Theory 138:311–320, 2008). We consider collective choice rules satisfying four axioms: unrestricted domain, strong Pareto, anonymity, and neutrality. A number of new classes of collective choice rules as well as the Pareto and Pareto extension rules are characterized under various concepts of collective rationality: acyclicity, transitivity, quasi-transitivity, semi-transitivity, and the interval order (...) property. Further, new concepts of collective rationality, K-term acyclicity and K-term consistency, are proposed and the corresponding characterizations are provided. (shrink)

Journal of Political Philosophy, EarlyView.

This article investigates the relationship among the weak Pareto principle, the strong Pareto principle, and positive responsiveness in the context of voting. First, it is shown that under a mild domain condition, if an anonymous and neutral collective choice rule (CCR) is complete and transitive, then the weak Pareto principle and the strong Pareto principle are equivalent. Next, it is shown that under another mild domain condition, if a neutral CCR is transitive, then the strong Pareto principle and positive responsiveness (...) are equivalent. By applying these results, we obtain a new characterization of the method of majority decision. (shrink)

Suzumura consistency is a necessary and sufficient condition for the existence of a weak-order extension. This paper provides some remarks on collective choice rules that generate Suzumura consistent social preferences. We examine the properties of such collective choice rules by introducing a procedural condition on collective choice rules. As applications of the procedural condition, we first investigate the decisive structure of a Paretian collective choice rule, and then consider the assignment of individual rights. In our analysis, the concept of semi-decisiveness (...) works effectively. (shrink)

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.

This paper aims to reexamine the axiom of the independence of irrelevant alternatives in the theory of social choice. A generalized notion of independence is introduced to clarify an informational requirement of binary independence which is usually imposed in the Arrovian framework. We characterize the implication of binary independence.

This paper examines the concept of ‘tsunami-tendenko,’ a guideline suggesting that individuals prioritise their own safety over aiding others during large-scale disasters. Kodama defends tsunami-tendenko against accusations of egoism by arguing that the principle can be justified ethically on consequentialist (or more precisely, utilitarian) grounds. Kodama asserts that attempting to assist others during such disasters heightens the risk of ‘tomo-daore,’ where both the rescuer and the victim may perish. He claims that having people focus solely on saving themselves can maximise (...) the overall number of lives saved. However, we challenge Kodama’s assertion that utilitarianism inherently favours tsunami-tendenko over mutual assistance during disasters. Instead, this paper proposes an alternative ethical foundation for tsunami-tendenko grounded in the ‘antiextinction principle,’ which prioritises minimising the potential for catastrophic outcomes. When considering the ethics of responding to disaster, it is important to distinguish between maximising the number of lives saved (utilitarianism) and minimising the risk of tomo-daore (antiextinction principle). This distinction may be overlooked if the distribution of probabilities is not considered. We conclude that the antiextinction principle aligns more naturally with tsunami-tendenko, emphasising the avoidance of catastrophic outcomes—a concern not always addressed by utilitarianism. Therefore, tsunami-tendenko should be regarded as a societal guideline aimed at preserving community sustainability by averting total destruction. (shrink)

This paper establishes a new impossibility result for welfaristic evaluations when the population varies. We consider a weak version of the repugnant conclusion instead of the commonly used version. It is shown that if a population principle satisfying two reasonable properties avoids the sadistic conclusion, then the weak repugnant conclusion must hold. We use a general variable-population setting where the identities of individuals can matter.

Population axiology includes two major arguments. The first is the repugnant conclusion, which was originally formulated by Derek Parfit to criticize total utilitarianism. The second is the sadistic conclusion. In this study, I demonstrate that no additively separable principle can avoid both repugnant and sadistic conclusions if individual moral values have no upper bound. This impossibility holds not only for utilitarian principles but also for any population principles that guarantee the separability of people’s well-being. I emphasize the importance of examining (...) non-separable principles in population ethics. (shrink)

This article provides a systematic analysis of social choice theory without the Pareto principle, by revisiting the method of Murakami Yasusuke. This article consists of two parts. The first part investigates the relationship between rationality of social preference and the axioms that make a collective choice rule either Paretian or anti-Paretian. In the second part, the results in the first part are applied to obtain impossibility results under various rationality requirements of social preference, such as S-consistency, quasi-transitivity, semi-transitivity, the interval-order (...) property, and acyclicity. (shrink)

This paper shows that weak Pareto and strong Pareto are equivalent under continuity and strong quasi-concavity. We use a framework that incorporates welfare as well as non-welfare information.

This paper proposes a sufficientarian theory with an interval of sufficiency levels. I assume that there are upper and lower bounds of sufficiency and that all well-being levels in between can be considered sufficiency levels. This interval reflects the vagueness of the concept of sufficiency. According to the proposed principle, a distribution is morally better than another if and only if, for each threshold within the interval, the headcount of those below the threshold under the former distribution is smaller than (...) that under the latter distribution. This necessarily leads to incommensurability in moral relations. I argue that such incommensurability makes sufficientarian principles invulnerable to some fundamental objections. (shrink)

Since Kenneth Arrow showed the general possibility theorem, a number of social choice theorists have provided alternative proofs of it. In a recent article, Geanakoplos (Econ Theory 26:211–215, 2005) has constructed a new proof of the theorem. The present article provides alternative proofs of various Arrovian impossibility results from the 1960s to the 1970s by utilizing Geanakoplos’s method. We prove semi-order impossibility theorems, the quasi-transitive veto theorem, the quasi-transitive dictatorship theorem, the triple acyclic veto theorem, and the impossibility theorem without (...) the Pareto principle. (shrink)

On March 16, 2020, the Director-General of the World Health Organization said: “We have a simple message to all countries—test, test, test.” This seems like sound advice, but what if limiting the number of tests has a positive effect on infection control? Although this may rarely be the case, the possibility raises an important ethical question that is closely related to a central tension between deontological and consequentialist approaches to ethics. In this paper, we first argue that early during the (...) COVID-19 pandemic, Japan offers an interesting case because it experienced few deaths due to COVID while the number of tests was limited, suggesting that there may be cases in which low testing contributes to infection control indeed. After that, we examine deontological constraints on such a “low-testing” policy, focusing on issues related to a supposed “right to know,” which is a central issue in medical ethics in general. (shrink)

This study investigates Suzumura consistency as a condition for the rationality of social preferences. A preference is said to be Suzumura-consistent when all preference cycles include only indifference relations. This condition is equivalent to transitivity in the presence of completeness, but, in general, it is substantially weaker than transitivity when preference is incomplete. Notably, Suzumura consistency is especially significant for a preference because it is necessary and sufficient for the existence of an ordering (transitive and complete preference) that is compatible (...) with the original preference. This coherency property can be regarded as a requirement for potential rationality. In this study, we examine the implications of shifting from actual rationality to potential rationality in collective decision-making. We introduce the concept of an alternative-dependent coherent collection in order to obtain a representation of a class of Suzumura-consistent collective choice rules that satisfy the axioms imposed in Arrow’s impossibility theorem. This demonstrates that the power structure to determine social choice can be alternative-dependent. (shrink)

This paper is concerned with a problem of an equitable allocation. We consider the concept of ψ‐equity, which is a general concept of equity. We provide a series of examples of equity concepts that are captured by ψ‐equity. We show the existence of an efficient and ψ‐equitable allocation by employing Kakutani's fixed‐point theorem.

This paper offers a new insight on the Condorcet Jury Theorem (CJT) in the theory of epistemic democracy. This theorem states that democratic decision-making leads us to correct outcomes under certain assumptions. One key assumption is the ‘independence condition’, which requires that voters form their beliefs independently when they vote. This paper examines the role of an opinion leader as an informational source, which potentially violates independence. We demonstrate that voters’ beliefs may be correlated in the presence of the leader, (...) and that the CJT can fail if the leader’s opinions are reliable. This leads us to the following paradoxical observation: for epistemic democracy, good leaders may be bad, while bad leaders may be good. (shrink)

This article considers social choice theory without the Pareto principle. We revisit the trade-off theorem developed by Campbell and Kelly (Econometrica 61:1355–1365, 1993) and generalize their result. By introducing an alternative measure of decisive structure, a dominance relation, we show that if a social welfare function dominates another social welfare function, then the number of pairs of alternatives which social ranking is independently of individual preferences under the former is not more than that under the latter. Moreover, we offer two (...) applications of our main result. (shrink)

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 (...) decisive coherence and examine these implications. (shrink)

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.

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.

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 (...) make an alternative weakly better than another. Third, we consider coherency conditions for collective preferences; this conditionally requires the existence of comparable pairs in a certain manner. We prove an impossibility result for each condition using Arrovian axioms. (shrink)

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 (...) equal to six. (shrink)

This paper is concerned with the problem of extending an antisymmetric binary relation on a set to a linear order on the power set. A necessary and sufficient condition is offered.

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.

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.

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 (...) certain way. Then, we characterize the structure of decisive coalitions under hybrid invariance. (shrink)

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).

The Nash axiom is a basic property of consistency in choice. This paper proposes weaker versions of the axiom and examines their logical implications. In particular, we demonstrate that weak Nash axioms are useful to understand the relationship between the Nash axiom and the path independence axiom. We provide an application of weak Nash axioms to the no-envy approach. We present a possibility result and an impossibility result.

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.

This paper examines the logical relationship among Maskin monotonicity, independent person-by-person monotonicity, independent weak monotonicity, strategy-proofness, and coalitional strategy-proofness in a society with infinite individuals.

The following is a short introduction to this special issue, which builds on and significantly extends and updates the research published recently in the Iwanami Series on Japanese economic history. First, we offer a modern interpretation of four institutional elements that are particularly important for understanding the growth path of the Japanese economy. These are (a) ownership; (b) regulation of factor markets; (c) labor mobility and (d) the judiciary. These four elements properly clarify the incentive structure behind economic institutions. We (...) then briefly explain how the four articles in this special issue—two at the macro level providing updated estimates of long-run rates of growth in gross domestic product (GDP) and total factor productivity (TFP), and two at the micro level examining institutional changes in specific markets—build on this unified framework, and deepen our understanding of Japanese economic history. (shrink)

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 (...) measure that guarantees the compatibility among the axioms. Third, we impose all non-dictatorship axioms and show that the corresponding measure is extremely restricted. (shrink)

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.

This paper provides an alternative proof of the Gibbard–Satterthwaite theorem.

This paper aims to consider the meaning of the dismal theorem, as presented by Martin Weitzman [(2009) On modeling and interpreting the economics of catastrophic climate change. Review of Economics and Statistics 91, 1–19]. The theorem states that a standard cost–benefit analysis breaks down if there is a possibility of catastrophes occurring. This result has a significant influence on debates regarding the economics of climate change. In this study, we present an intuitive similarity between the dismal theorem and the St. (...) Petersburg paradox using a simple discrete probability distribution. (shrink)

Schwartz [A Procedural Condition Necessary and Sufficient for Cyclic Social Preference, J. Econ. Theory 137 (2007), 688–695] provides a generalization of the voting paradox by using the impotence‐partition condition. This paper aims to clarify his result by providing several remarks. We show that a main result of Schwartz can be strengthened by replacing strong Pareto by weak Pareto. We also discuss how the impotence partition is related to the standard concept of decisiveness, which is widely employed in the literature on (...) social choice. (shrink)

This paper provides two brief proofs of Arrow’s general possibility theorem. The second one is simple and short. Our proofs are inspired by the pioneering work by Inada (Ann. Inst. Stat. Math. 6:115–122, 1954).

The purpose of this study is to investigate a relationship between egalitarian equivalence and envy-freeness in a continuum-agent economy, where tastes vary continuously across individuals. Under efficiency, the two criteria of equity are not compatible, except in the knife-edge case. In particular, when individual utility functions are restricted to the class of Cobb–Douglas-type functions, there exists an efficient, egalitarian-equivalent, and envy-free allocation if and only if all individuals have the same taste over commodities.

Since Condorcet discovered the voting paradox in the simple majority rule, many scholars have tried to investigate conditions that yield “social-preference cycles”. The paradox can be extended to two main approaches. On the one hand, Kenneth Arrow developed a general framework of social choice theory; on the other hand, direct generalizations of the paradox were offered. The motivation and surface meaning of the two approaches are different, as are the assumed background conditions. In this paper, we investigate the relationship between (...) the two approaches by taking a close look at two works, Ferejohn and Fishburn and Schwartz. (shrink)

This paper considers the problem of fair allocation among individuals with unequal production skills. We introduce the concept of productivity‐adjusted average no‐envy. It is shown that equal‐income Walrasian allocations are the only surviving allocations that are productivity‐adjusted average envy‐free and efficient when the original economy is infinitely replicated. We also examine local versions of productivity‐adjusted average no‐envy and other equity concepts.

In this study, we propose a new direction of research on the axiomatic analysis of approval voting, which is a common democratic decision method. Its novelty is to examine an infinite population setting, which includes an application to intergenerational problems. In particular, we assume that the set of the population is countably infinite. We provide several extensions of the method of approval voting for this setting. As our main result, axiomatic characterizations of the extensions are offered by revealing a direct (...) link between approval voting and the Borda rule. The characterized methods are natural extensions of the standard approval voting method for the finite-population case and are regarded as minimum requirements for other possible infinite-population extensions, which are reasonably democratic. (shrink)