Susumu Cato

This paper offers the very first formal model of Robert Nozick's model of possible worlds and his vision of a utopian society, as outlined in Part III of Anarchy, State, and Utopia. Nozick envisioned utopia as a meta‐utopia—a collection of self‐organized, voluntary sub‐communities—arguing that such an institutional framework is equivalent to the minimal state justified in earlier parts of his book. Nozick's strategy was to define utopia (the best of all possible worlds) in terms of stability achieved in his possible worlds model, where individuals can create and migrate to any world they imagine. However, Nozick left many key components of this model informal and underdeveloped. This paper fills these gaps by providing a rigorous formal model of Nozick's possible worlds. We introduce a new stability concept, Nozick stability. We demonstrate that Nozick stability imposes stricter requirements than other established solution concepts, such as core and Nash stability, making the existence of a stable framework significantly more difficult to achieve. We then identify sufficient conditions for the existence of a Nozick‐stable framework. However, these conditions are highly restrictive and unlikely to hold in reality. Furthermore, contrary to Nozick's conjecture, individuals may receive far less than their marginal contribution within Nozick‐stable frameworks, and, in this sense, Nozick‐stable frameworks may institutionalize and perpetuate systemic exploitation. These findings cast doubt on whether Nozick's minimal state can genuinely function as an inspiring utopian ideal, as he claims.

The purpose of this paper is to address some ambiguities and misunderstandings that appear in previous studies of population ethics. In particular, we examine the structure of intervals that are employed in assessing the value of adding people to an existing population. Our focus is on critical-band utilitarianism and critical-range utilitarianism, which are commonly-used population theories that employ intervals, and we show that some previously assumed equivalences are not true in general. The possible discrepancies can be attributed to the observation that critical bands need not be equal to critical sets. The critical set for a moral quasi-ordering is composed of all utility numbers such that adding someone with a utility level in this set leads to a distribution that is not comparable to the original (non-augmented) distribution. The only case in which critical bands and critical sets coincide obtains when the critical band is an open interval. In this respect, there is a stark contrast between critical-band utilitarianism and critical-range utilitarianism: the critical set that corresponds to a critical-range quasi-ordering always coincides with the interval that is used to define the requisite quasi-ordering. As a consequence, an often presumed equivalence of critical-band utilitarianism and critical-range utilitarianism is not valid unless, again, the critical band and the critical range (and, consequently, the requisite critical sets) are given by the same open interval.

This paper considers an electoral system in which voters may approve any subset of options. We introduce the class of proportional threshold methods that select the subset of options whose share of approvals in the population meets or exceeds a certain threshold. We provide an axiomatic characterization of these methods using a principle of consistency between populations and profiles of approval voting ballots. A distinctive feature of our approach is to provide a geometric proof of this characterization result.

Although sufficientarianism has been gaining interest as a theory of distributive justice in recent years, it has not been examined in the presence of risk. We propose an ex post approach to sufficientarianism that has a strong link to ex post prioritarianism. Both ex post criteria are based on an axiom that we refer to as prospect independence of the unconcerned, a natural extension of the independence axiom known from the literature that focuses on situations with no risk. We characterize a class of ex post prioritarian orderings as well as the corresponding class of ex post sufficientarian orderings. In addition, we point out some important differences between these two ex post criteria, and we examine how they fare when assessed in terms of specific ex ante Paretian axioms.

This paper offers a formal analysis of continuity, welfarism, value satiability, lifeboat cases, along with their interconnectedness with sufficientarianism, with particular attention to the recent defences of sufficientarianism by Ben Davies and Lasse Nielsen in response to Hun Chung’s Prospect Utilitarianism (PU). It demonstrates how precise formal definitions help resolve conceptual ambiguities and sharpen philosophical argumentation in distributive ethics. Without such precision, one risks misidentifying or mischaracterizing important normative concepts and theories, leading to confusion or strawman critiques. By highlighting these risks, the paper underscores the methodological importance of precise definitions and formal analysis in ensuring clarity, consistency, and rigor in ethical theorizing.

One of the biggest debates on the functioning of democracy concerns voter competence. It is sometimes claimed that voters are incompetent due to unreasonableness and ignorance, which has led some to advocate decision-making by experts—that is, epistocracy. However, in this paper, I show that under certain conditions—namely, asymmetric information signals—reasonable and non-ignorant voters can still be incompetent, even in the absence of misleading information. This rational incompetence can be a threat to democracy, but it can be a threat to epistocracy just as well, and for the same reason. Experts may be more rational than other citizens, but rationality does not necessarily imply competence.

Conditional egalitarianism is a form of egalitarianism that responds to the levelling-down objection by asserting that equality is intrinsically valuable only when it benefits some individuals. Andrew Mason’s original formulation of conditional egalitarianism faces criticism from Nils Holtug, who proposes a refined formulation that introduces a clause regarding the effects of additional benefits on equality. However, Holtug’s own formulation encounters internal inconsistencies. This paper proposes a positional refinement of Holtug’s conditional egalitarianism, emphasizing the importance of impartiality in evaluating distributions. This refinement incorporates an anonymity condition, ensuring that distributional evaluations remain invariant under permutations of individuals. By emphasizing how the non-instrumental value of equality is conditional on benefiting positions impartially, the proposed positional conditional egalitarianism reconciles egalitarian aims with concerns about inequality-enhancing benefits. This nuanced formulation provides a potential rebuttal to arguments against conditional egalitarianism and suggests a novel approach to distributive justice.

This paper explores the notion of species-relative critical levels, which is a crucial ethical issue in multi-species population ethics. First, the formal conditions are provided under which there are species-relative critical levels (e.g., the critical level for human beings is different from that for non-human beings). In particular, we find it a salient question of animal ethics whether the existence of a human being is morally better than that of a non-human animal when their utility levels are the same. Subsequently, we illustrate two general classes of multi-species critical-level utilitarian orderings. One class employs species-relative critical levels, which entails either the animal repugnant conclusion or the animal sadistic conclusion. The other employs species-relative critical levels plus species-lexical ordering. Although it can avoid both the animal repugnant conclusion and the animal sadistic conclusions, it has the problem of speciesism.

It has been shown that the Mere Addition Paradox occurs in a choice-functional approach with Path Independence (Stewart R.T., 2021, Path independence and a persistent paradox of population ethics, Journal of Philosophy, forthcoming). The present study is a three-part response to this finding. First, I show that Path Independence is not an essential property leading to this paradox and that logically weaker properties can get the same result. Second, I present a rationalizable choice function that does not yield the paradox. And third, I argue that menu-dependent relations are nicely examined if Path Independence is relaxed to Property $\alpha $ (or equivalently, Contraction Consistency).

In Part III of Anarchy, State, and Utopia (1974), Robert Nozick presents what he calls ‘the model of possible worlds’ (307) to examine the formal properties of utopia, defined as ‘the best of all possible worlds’ (298). The basic idea is that each person is given the power to create any possible world and its inhabitants by imagining them. Two definitions of stability have been proposed: (a) the non-circular definition according to which a world is stable if and only if nobody can imagine a better world and (b) the circular definition according to which a world is stable if and only if nobody can imagine a better world that is also stable. In this paper, we prove four theorems (namely, the indeterminacy theorem, the stable dystopia theorem, the nobody’s utopia theorem and the redundancy theorem) that provide us with decisive reasons to reject the circular definition and opt for the non-circular definition of stability to analyse Nozick’s theory of utopia.

The implications of the repugnant conclusion for consequentialist theories, such as total utilitarianism, have been extensively discussed since the work of Derek Parfit. These discussions make the paradoxes of population ethics depend on welfarist conditions, like the dominance condition (or the Pareto Principle). Thus, one might think that the repugnant conclusion is not a practical problem for deontologists, who deny that we always ought to do what produces the most aggregate welfare. In this study, we offer two impossibility results using what we call the limit aggregation property. This states that when welfaristic and non-welfaristic considerations conflict, there is a threshold number of persons such that the former can override the latter as long as more people than the threshold number can enjoy increases in well-being levels. We argue that this property should be accepted even by deontologists, insofar as they do not commit themselves to the implausible absolutist position that fails to assign any moral weight to aggregate welfare. Our results therefore state that any normative population theory that is not absolutist entails (a variant of) the repugnant conclusion or some other implausible conclusion. Therefore, the repugnant conclusion must be taken seriously even by non-absolutist deontologists, not just consequentialists.

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.

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.

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.

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.

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 provides a characterization of a new class of ordinal poverty measures that are defined by means of the aggregate generalized poverty gap. To be precise, we propose to use the sum of the differences between the transformed fixed poverty line and the transformed level of income of each person below the line as our measure. If the transformation is strictly concave, the resulting measure is strictly inequality averse with respect to the incomes of the poor. In analogy to some existing results on inequality measurement, we show that the only relative (scale-invariant) members of our class are based on strictly concave power functions or the natural logarithm. Moreover, we show that our measures allow for a useful decomposition that is akin to those examined in some earlier contributions. In an empirical analysis, we compare the logarithmic variant of our index to two well-established alternative orderings. Unlike numerous indices that appear in the earlier literature, ours do not explicitly depend on the number of poor or on the total population size, thereby ruling out any direct influence of the head-count ratio on poverty comparisons.

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.

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.

This paper extends the classical extension theorem established by Edward Szpilrajn (Fundamenta Mathematicae, 16, pp. 386–389, 1930). Szpilrajn's theorem states that every quasi‐ordering has an ordering extension. Because of its usefulness in various themes of economics, it has been applied by many researchers. Important generalizations have been presented by two authors, Kenneth Arrow and Kotaro Suzumura, among others. First, we provide concise proofs of four extension theorems by Szpilrajn, Arrow and Suzumura. We then show an extension of their extension theorems.

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.

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.