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Many social welfare measures will sometimes rank a large population of very well-faring people below a very large population of barely well-faring people. Thus, they entail the repugnant conclusion. If such rankings are indeed repugnant, there must be some mistake behind measures that imply them. This paper discusses what that mistake might be. After rejecting other proposals, I suggest that the mistaken assumption is that welfare values that are insignificant for individuals, due to being small, could have significant impact on social welfare. To avoid this mistake, two new measures are introduced that aggregate significant and insignificant welfare values differently.

A large number of diversity measures have been proposed in the literature, almost all of which are designed for sets with elements that differ in multiple aspects. However, these types of measures are not appropriate for sets with elements that differ in a single aspect only, such as duration, value or probability. In this essay I present a new measure of diversity, designed specifically for single aspect diversity. The measure captures the intuitive idea that single aspect diversity is affected by the maximal dissimilarity between the elements, the number of different elements, and the even spacing of the elements’ aspect values, when represented as points in one dimension. I show that the measure satisfies six plausible conditions for a single aspect diversity measure, which concern scale independence, minimal diversity, maximal dissimilarity, restricted function growth, strict monotonicity, and even spacing. The measure is also characterised.

Peterson presents a new hybrid ethical theory in his paper “Dutilitarianism.” As the name suggests, the theory is a mixture of Utilitarianism and Duty ethics. Its main motivation is that it will improve on both. In my commentary, I raise some doubts about this idea. One problem is that Dutilitarianism will not have morally acceptable implications: it will classify some wrong acts as right. Another problem is that it cannot provide any plausible explanation for its verdicts: a believable combination of utilitarian and Kantian explanations for why right acts are right does not seem to fit dutilitarian verdicts. A third problem is that the formula that Peterson suggests for calculating dutilitarian degrees of rightness is unhelpful: it cannot be used to compare acts that are partly right in different ways. A fourth problem is that Dutilitarianism is needlessly complex: it uses degrees of rightness, rather than the standard binary rightness, but this invention neither reflects the potential complexities of rightness grounds nor helps us decide what to do.

This essay introduces a new type of measure of social welfare, where populations are evaluated by their resemblance to an optimum population, which is an (in principle) possible population with the highest degree of social welfare, relative to some circumstances. Here, it is argued to be the largest possible population where everyone fares maximally well. The new measure is responsive to quality of welfare, equality of welfare and the number of people. It satisfies dominance and negative monotonicity, and it avoids both the repugnant conclusion and a reverse repugnant conclusion for comparisons relative to our future on earth.

In this essay I argue that even though egalitarianism and prioritarianism are different theories of social welfare, they can use the same social welfare measures. I present six different arguments for this thesis. The first argument is that conceptual connections between egalitarianism and prioritarianism ensure that any measure that works for either theory works for both. The second argument is that conditions necessary and sufficient to identify egalitarian and prioritarian measures, respectively, are equivalent. The third argument is that both egalitarianism and prioritarianism can use two standard measures, typically proposed for only one theory. The fourth to sixth arguments contend that four properties that have been proposed as distinctive of either egalitarian or prioritarian measures cannot distinguish between them. I conclude that any egalitarian measure is also a prioritarian measure, and vice versa.

In this essay I propose a new measure of social welfare. It captures the intuitive idea that quantity, quality, and equality of individual welfare all matter for social welfare. More precisely, it satisfies six conditions: Equivalence, Dominance, Quality, Strict Monotonicity, Equality and Asymmetry. These state that (i) populations equivalent in individual welfare are equal in social welfare; (ii) a population that dominates another in individual welfare is better; (iii) a population that has a higher average welfare than another population is better, other things being equal; (iv) the addition of a well-faring individual makes a population better, whereas the addition of an ill-faring individual makes a population worse; (v) a population that has a higher degree of equality than another population is better, other things being equal; and (vi) individual illfare matters more for social welfare than individual welfare. By satisfying the six conditions, the measure improves on previously proposed measures, such as the utilitarian Total and Average measures, as well as different kinds of Prioritarian measures.

This article analyses the relationship between the concept of single aspect similarity and proposed measures of similarity. More precisely, it compares eleven measures of similarity interms of how well they satisfy a list of desiderata, chosen to capture common intuitions concerning the properties of similarity and the relations between similarity and dissimilarity. Three types of measures are discussed: similarity as commonality, similarity as a function of dissimilarity, and similarity as a joint function of commonality and difference. Relative to the desiderata, it is found that a measure of the second type fares the best. However, rather than recommend this measure alone as a measure of similarity, it is suggested that there are at least three separate concepts of single aspect similarity, corresponding to the three types of measures. In light of this proposal, three of the eleven measures (and variants of these) are deemed acceptable.

This thesis studies the problem of measuring freedom of choice. It analyzes the concept of freedom of choice, discusses conditions that a measure should satisfy, and introduces a new class of measures that uniquely satisfy ten proposed conditions. The study uses a decision-theoretical model to represent situations of choice and a metric space model to represent differences between options.

The first part of the thesis analyzes the concept of freedom of choice. Different conceptions of freedom of choice are categorized into evaluative and non-evaluative, as well as preference-dependent and preference-independent kinds. The main focus is on the three conceptions of freedom of choice as cardinality of choice sets, representativeness of the universal set, and diversity of options, as well as the three conceptions of freedom of rational choice, freedom of eligible choice, and freedom of evaluated choice.

The second part discusses the conceptions, together with conditions for a measure and a variety of measures proposed in the literature. The discussion mostly focuses on preference-independent conceptions of freedom of choice, in particular the diversity conception. Different conceptions of diversity are discussed, as well as properties that could affect diversity, such as the cardinality of options, the differences between the options, and the distribution of differences between the options. As a result, the diversity conception is accepted as the proper explication of the concept of freedom of choice. In addition, eight conditions for a measure are accepted. The conditions concern domain-insensitivity, strict monotonicity, no-choice situations, dominance of differences, evenness, symmetry, spread of options, and limited function growth. None of the previously proposed measures satisfy all of these conditions.

The third part concerns the construction of a ratio-scale measure that satisfies the accepted conditions. Two conditions are added regarding scale-independence and function growth proportional to cardinality. Lastly, it is shown that only one class of measures satisfy all ten conditions, given an additional assumption that the measures should be analytic functions with non-zero partial derivatives with respect to some function of the differences. These measures are introduced as the Ratio root measures.