Any normative political theory presumes an understanding of the positive processes of its proposed institutional arrangements. As such, I believe that formal theory (viz. game theory or social choice theory), by offering a better understanding of the positive processes of different kinds of political institutions, can greatly help the normative theorizing of political theorists by showing what can and what cannot be realistically achieved from the practical implementation of their proposed political theory. Formal theory can also help us clarify the precise logical relationships between fundamental normative concepts and, thereby, allow us to understand which set of normative concepts can be coherently endorsed without committing any logical inconsistencies.
When Liberty Dominates Patterns: A Welfare Comparison of Political Regimes under Incomplete Contracts (with Susumu Cato and Jacob Watkins-Strand)
The paper develops (to the best of our knowledge) the very first systematic formal analysis of five canonical political regimes proposed in political philosophy: socialist joint ownership, Nozick’s right-libertarianism, Steiner’s left-libertarianism, Otsuka’s luck-egalitarian left-libertarianism, and Rawls’s property-owning democracy. Based on an incomplete contract theory framework, our model yields closed-form equilibrium expressions that allow us to compare each political regime in terms of the overall welfare level it generates to its members, who differ in their productive abilities, under varying economic conditions. Our model is parametrized by two economically interpretable parameters: (i) the ratio of individual productive capabilities and (ii) the level of cooperative surplus generated by joint production. We show that the resulting parameter space is partitioned into three geometrically asymmetric zones: (a) a bounded (and collapsing) Egalitarian-Dominance Zone, where some form of egalitarianism Pareto dominates Nozick’s right-libertarianism, (b) an unbounded (and expanding) Nozick-Dominance Zone, where Nozick’s right-libertarianism Pareto dominates all other political regimes, and (c) a Disagreement Zone that lies between the first two zones, where the welfare outcomes are mixed, rendering regime choice irreducibly political. We characterize the precise economic conditions under which each zone obtains and examine their philosophical implications.
Utopia as Equilibrium: Stability, Existence, and Exploitation in Nozick’s Framework for Utopia (Prepared for Robert Nozick's Anarchy, State, and Utopia at 50' edited by Ralf Bader, Cambridghe University Press)
For fifty years, Part III of Anarchy, State, and Utopia has been admired as a flourish and neglected as an argument. I contend that it is neither: it is the keystone on which the whole edifice rests, and it can now be assessed with the formal tools Nozick himself requested. Drawing on two recent papers—“Stable Dystopia” (Analysis, 2024) and “A Formal Theory of Robert Nozick's Framework for Utopia” (Noûs, 2026)—this chapter reconstructs Nozick's possible worlds model informally and reports what the formal analysis reveals. Nozick's original circular definition of stability is indeterminate, can certify slavery as stable, can crown worlds that are best for nobody, and is in any case redundant. The non-circular alternative secures the link between stability and utopia, but at a price: it is strictly stronger than both core and Nash stability; Nozick-stable frameworks exist only under harmony conditions that suppress the very pluralism the framework celebrates; and even where they exist, they can stabilize exploitation in perpetuity, contrary to Nozick's marginal-contribution conjecture. I then develop three theses that go beyond the papers: the circular definition operates as an east-berlin of the imagination, building censorship into the very concept of stability; Nozick's meta-utopia tolerates diversity of ideals but not diversity of attachments; and the marginal-contribution conjecture fails not for want of competition but for want of prices.
The Priority Axiom: A New Foundation for Prioritarianism (with Kaname Miyagishima)
This paper introduces a novel axiom—Priority—which formalizes the core prioritarian idea that benefiting the worse-off matters more. We establish the precise logical relationships between Priority and the standard axioms of distributive ethics. Three results stand out. First, Priority is logically equivalent—without any auxiliary assumptions—to what we call the Gap-Diminishing Principle, a paradigmatically egalitarian transfer principle. This shows that conceptually distinct commitments to prioritizing the worse-off and to reducing inequality impose exactly the same constraints on moral rankings. Second, under Continuity, Priority implies Anonymity: treating individuals impartially need not be assumed as a separate moral commitment, but follows from giving moral priority to the worse-off. Third, the prioritarian social welfare ordering is the only continuous ordering satisfying Priority, Separability, and Strong Pareto. We then examine what these results demand of the measurement and interpersonal comparison of well-being. Prioritarianism, so characterized, is impossible if well-being is only ordinally or even cardinally measurable and fully interpersonally comparable; it becomes possible only under translation-scale or ratio-scale measurability. Prioritarianism is thus informationally more demanding than utilitarianism. We draw out the implications for the equality-versus-priority debate and for the methodology of normative theory.
Unanimity, Sufficiency, and Coherence Across Time: An Impossibility Theorem for Intertemporal Justice and Its Escape Routes (with Kaname Miyagishima)
How should we evaluate distributions of well-being that unfold over time? We consider three normative principles that any plausible account of intertemporal justice must satisfy. These are: Weak Pareto (WP), Sufficientarian Equity (SE), and Time Consistency (TC). WP requires society to generate a social ranking that respects strict unanimous improvements in wellbeing. SE requires society, whenever possible, to lift a person who would otherwise suffer indefinite deprivation onward above a minimum threshold of wellbeing through a rank-preserving wellbeing transfer. TC requires there to be intertemporal coherence between society’s rankings of the past and its rankings of the present. We prove an impossibility theorem that demonstrates that the three normative principles cannot be jointly satisfied even by a partial social quasi-order that is not necessarily complete. This is so even when all individuals share a common discount factor. The result is tight: giving up any one principle will allow us to recover a social quasi-order that respects the other two normative principles. We explore each escape route and examine their normative costs.
In developing a theory of first appropriation of external resources John Locke tells us that persons must leave “enough and as good” for others. This is known as the Lockean Proviso. Fleshing out just exactly what this restriction requires has been an intense source of scholarly debate, and broadly divides right libertarians – who interpret the Lockean Proviso as requiring very minimal restrictions – and left libertarians – who interpret the Lockean Proviso as requiring some form of egalitarian ownership of external resources. This paper examines and compares the economic consequences of right- and left-libertarianism (where left-libertarianism is understood as a doctrine that combines full self-ownership with what Johnathan Quong has recently called “reciprocity-based egalitarianism”) via a formal model. The results of the formal model show that everybody (including those with low productive abilities) will be better off living under right-libertarianism rather than left-libertarianism as long as the discrepancy in productive abilities between the high-ability person and the low-ability person is not too great. The upshot is that a more egalitarian ownership of external goods produced by social cooperation does not universally work in favor of those who have low productive abilities – the type of abilities caused by their unchosen circumstance for which they are not responsible.