In recent years, much public attention has been devoted to the existence of pay discrepancies between men and women at the upper end of the income scale. For example, there has been considerable discussion of the ‘Hollywood gender pay gap’. We can refer to such discrepancies as cases of millionaire inequality. These cases generate conflicting intuitions. On the one hand, the unequal remuneration involved looks like a troubling case of gender injustice. On the other, it’s natural to feel uneasy when confronted with the suggestion that multi-millionaires are somehow being paid inadequately. In this paper, we consider two arguments for rectifying millionaire inequality, clarifying their appeal but also identifying the obstacles that each will have to surmount in order to succeed.

Institutions can be strong or weak. But what does this mean? Equilibrium theories equate institutions with behavioural regularities. In contrast, rule theories explicate them in terms of a standard that people are supposed to meet. I propose that, when an institution is weak, a discrepancy exists between the regularity and the standard or rule. To capture this discrepancy, I present a hybrid theory, the Rules-and-Equilibria Theory. According to this theory, institutions are rule-governed behavioural regularities. The Rules-and-Equilibria Theory provides the basis for two measures of institutional strength. First, institutions that pertain to coordination games solve problems of information. Their strength is primarily a matter of the expected degree of compliance. Second, institutions that concern mixed-motive games solve problems of motivation. Their strength can be measured in terms of the weight people attribute to its rule.

While ordinary decision theory focuses on empirical uncertainty, real decision-makers also face normative uncertainty: uncertainty about value itself. From a purely formal perspective, normative uncertainty is comparable to (Harsanyian or Rawlsian) identity uncertainty in the ‘original position’, where one’s future values are unknown. A comprehensive decision theory must address twofold uncertainty – normative and empirical. We present a simple model of twofold uncertainty, and show that the most popular decision principle – maximizing expected value (‘Expectationalism’) – has different formulations, namely Ex-Ante Expectationalism, Ex-Post Expectationalism, and hybrid theories. These alternative theories recommend different decisions, reasoning modes, and attitudes to risk. But they converge under an interesting (necessary and sufficient) condition.

Lexical views in population axiology can avoid the Repugnant Conclusion without violating Transitivity or Separability. However, they imply a dilemma: either some good life is better than any number of slightly worse lives, or else the ‘at least as good as’ relation on populations is radically incomplete. In this paper, I argue that Archimedean views face an analogous dilemma. I thus conclude that the lexical dilemma gives us little reason to prefer Archimedean views. Even if we give up on lexicality, problems of the same kind remain.

Even where willingness-to-pay as a measure of welfare impact is adjusted for diminishing marginal utility, welfare economics is shown to favour policies that add to the life expectancy or that enhance the quality of life of persons who are already better-off. I propose an alternative, Equal Respect methodology, under an axiomatic claim that at the point of decision the prospective life years of all individuals are of equal intrinsic social value. This justifies equal valuation of risk mitigation across all persons; similarly, all appraised impacts should be scaled to accord equal respect to difficult but no-less-valuable lives.

We highlight a new paradox for the social evaluation of risk that bears on the evaluation of individual well-being rather than social welfare, but has serious implications for social evaluation. The paradox consists in a tension between rationality, respect for individual preferences, and a principle of informational parsimony that excludes individual risk attitudes from the assessment of riskless situations. No evaluation criterion can satisfy these three principles. This impossibility result has implications for the evaluation of social welfare under risk, especially when the preferences of some individuals are not known. It generalizes existing impossibility results, while relying on very weak principles of social rationality and respect for individual preferences. We explore the possibilities opened by weakening each of our three principles and discuss the advantages and drawbacks of these different routes.

Need-based justice is an important ingredient for a pluralistic theory of justice. But how can need-based justice be measured? I will argue that need-based justice cannot be measured by measuring need-satisfaction. This is because need-based justice does not only depend on need-satisfaction, but also on opportunities to avoid or at least mitigate undersupply. Depending on these opportunities, one and the same degree of undersupply can be unjust to different degrees. In this article, I establish a number of desiderata that a measure of need-based justice has to comply with. Resulting measures treat avoidable undersupply as the main source of injustice.