Susumu Cato

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

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.

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.

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.

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.

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.

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.

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.

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.’

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.

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.

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.

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.

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 conceptually similar but logically independent version of the combined axiom that requires the collective decision mechanism to be independent, neutral, and monotonic is employed. In the case of a finite population, we obtain an alternative impossibility theorem if a collective choice rule is assumed to be non-degenerate and a modified no veto requirement is imposed instead of Blau and Deb’s (1977) condition. If the population is countably infinite, the impossibility can be avoided but it resurfaces if our new no veto property is extended to a coalitional variant.

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.

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.

This paper examines collective decision-making with an infinite-time horizon setting. First, we establish a result on the collection of decisive sets: if there are at least four alternatives and Arrow’s axioms are satisfied on the selfish domain, then the collection of decisive sets forms an ultrafilter. Second, we impose generalized versions of stationarity axiom for social preferences, which are substantially weaker than the standard version. We show that if any of our generalized versions are satisfied in addition to Arrow’s axioms, then some generation is dictatorial. Moreover, we specify a very weak stationarity axiom that guarantees a possibility result.

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.