Frontières de l’Économie et de la Philosophie

In this talk, I will develop the view that risk is objective conditional probability of harm by giving an interpretation of the concepts its invokes. The focus will be on objective (conditional) probability: why risk must be probabilistic, what kind of objectivity is required and what this means for the theory of rational choice under risk. My main claim will be that these questions are best addressed by taking the risks at a time t to be the evidential probabilities at t conditional on all that is settled true at t, where evidential probabilities are ideal credences warranted by the evidence.

Ever since the Harsanyi-Sen debate, it is controversial whether someone’s welfare should be measured by her von-Neumann-Morgenstern (VNM) utility, for instance when analysing welfare intensity, social welfare, interpersonal welfare comparisons, or welfare inequality. We prove that natural working hypotheses lead to a different welfare measure. It addresses familiar concerns about VNM utility, by faithfully capturing non-ordinal welfare features such as welfare intensity, despite resting on purely ordinal evidence such as revealed preferences or self-reported welfare comparisons. Using this welfare measure instead of VNM utility alters social welfare analysis — for instance, Harsanyi’s “utilitarian theorem” now effectively supports prioritarianism. VNM utility is shown to be a hybrid object, determined by an interplay of two factors: welfare and attitude to intrinsic risk, i.e., to risk in welfare rather than outcomes.

The expectation of a sum of utilities is a core criterion for evaluating policies and social welfare, but it remains contentious. We show that a set of weak assumptions yields general versions of Expected Total Utilitarianism, under social risk and variable population. Two dimensions of weak dominance (over risk and individuals) characterize a complete social welfare function with two dimensions of additive separability. We introduce a weak axiom of individual stochastic dominance with attractive properties: It only applies to lives certain to exist (so it does not compare life against non-existence), and it avoids prominent egalitarian objections to fixed-population utilitarianism.

The goal of this paper is to build an analytical bridge between Stoicism and the economic study of the value of life. We use writings of Seneca, Epictetus and Marcus Aurelius to show that the Stoic discipline of judgements (i.e., one should distinguish between things under control and things out of control, such as the duration of life) and the Stoic discipline of desires (i.e., one should wish for nothing that is out of control) imply that one should wish for nothing about one’s duration of life (i.e., longevity is neutral). Then, we formalize the Stoic thesis of the neutrality of longevity by modelling the Stoic discipline of desires as an extension of the symmetric factor of the preference relation beyond its boundaries under standard preferences. It is shown that, depending on the extension of the indifference relation, longevity is neutral either in the sense of having no intrinsic value but (at most) an instrumental value (weak neutrality), or in the sense of having no value at all (strong neutrality).

When a group confronts a decision involving uncertainty, different individuals may have different (probabilistic) beliefs about the world.  In order for the group to make rational decisions (i.e. to maximize subjective expected utility), we must construct probabilistic beliefs for the group as a whole. Probabilistic belief aggregation rules (also called opinion pooling rules) are functions that “aggregate” the individuals’ disparate beliefs into a single collective belief.  An important class of such rules are the geometric (or logarithmic) aggregation rules, in which the collective belief is a (renormalized) geometric average of the individuals’ beliefs.  These rules have many nice properties, but they have three major shortcomings:

1.   Existing definitions of geometric aggregation for uncountably infinite spaces involve a major domain restriction: they assume that all probabilities are absolutely continuous with respect to a common “reference measure”. 

2. Geometric aggregation is only well-defined for profiles that are coherent, meaning that the beliefs of the agents have overlapping support.

3.  In many decision problems, agents do not have a clear idea of the space of possible “states of nature”; they only have in mind some set of statements (each of which could be either true or false).  Formally, their beliefs take the form of a probability measure defined on an abstract Boolean algebra.  But geometric aggregation is not well-defined for these kinds of beliefs.

In this presentation, I will discuss an extended version of geometric aggregation that solves all three problems.

Democratic theorists and social epistemologists often celebrate the epistemic benefits of diversity. One of the cornerstones is the ‘diversity trumps ability’ theorem and simulation results by Hong and Page (2004). Ironically, the interplay between diversity and ability is rarely studied in radically different frameworks. In fact, Hong and Page’s landscape models apply predominantly to search problems where the groups must find the optimal decision among thousands of options. Their landscape models are ineffective in binary or sparse classification problems, i.e., where agents must select the objectively or intersubjectively correct option among a few options. To fill this gap, I will introduce a new evidential sources framework for binary classification problems, where agents rely on imperfect sources to identify the best solution. I use this new evidential sources framework to assess whether, when, and (if so) why diversity trumps expertise in binary classification problems.

A key tradeoff involved in taxation is that between equality and efficiency. Some taxes are more salient than others, and exploiting less salient taxes may ease the tradeoff between equality and efficiency. However, exploiting salience might be regarded as dishonest.  So really there is a three way tradeoff between equality, efficiency and honesty. We explore this tradeoff formally using a multi-criterion objective. We study this problem in a simple setting with a linear income tax. We show that caring for honesty always comes at a cost to utilitarian welfare. Utilitarian welfare can be decomposed into equality and efficiency, so honesty must always come at a cost to one of these. We show that, indeed, honesty and the desire to reduce inequality can conflict.  The approach taken in this paper could also be applied to other situations where both utilitarian and deontological considerations are at play.  

Sometimes the choice options we face are incommensurable because they rank differently with respect to incommensurable values. This is typically taken to imply that our action-guiding preferences are incomplete: one option is overall neither better than nor equal to the other. It is also widely argued that such incompleteness renders agents vulnerable to exploitation via money-pumps. This paper argues that the rational response to money-pumps arising from incommensurable values is to let the incommensurable values bargain over the available outcomes. More specifically, I argue that incommensurable values generate distinct demands of instrumental rationality, and that the agent must satisfy each. This plural requirement is best modeled using a bargaining framework. I show how the axioms of Nash bargaining can be fruitfully adapted to this intrapersonal context, and argue that they are in fact even more plausible in the intrapersonal context than the interpersonal context. And I show how the resulting model avoids several forms of money-pump exploitation. In addition, my model goes some way to explaining how truly incommensurable values can be traded against one another without thereby effectively introducing a common underlying measure.

We argue that the chaining argument against the Trichotomy Thesis is on the horns of a dilemma. Either it is vacuous or it is unsound. Contrary to what it has been commonly assumed, it cannot be used as a reliable basis to adjudicate whether parity does or does not obtain. Stating the premises in a formal syntax that makes them consistent with each other deprives them of their intended meaning and makes the argument vacuous. The reason is that the argument, so stated, establishes a conclusion that is compatible with a variety of natural-language understandings of it that are unrelated to the initial intention of the argument or to the nature of value relations. If, instead, the premises of the argument are expressed in the weakest formal syntax to capture their meaning, the argument is unsound since its premises are inconsistent with each other. Besides demonstrating that the chaining argument does not provide insights into axiology, our result helps orient those interested in proving the existence of parity as a value relation towards alternative arguments.

The traditional notion of welfarism requires the respect of the Independence of Irrelevant Alternatives (IIA) condition. Intuitively, however, welfarism is not bound by the binariness encoded by IIA. Welfarism fundamentally means welfare consequentialism, and IIA is added baggage. The technical notion of welfarism is, in this respect, artificially constrained. Motivated by this simple observation, this note introduces a particularly inclusive generalization of IIA. Based on the algebraic notion of idempotence, that generalization targets the large class of cases where IIA is violated inasmuch as the evaluation method builds on specially selected welfare functions. The proposed new condition is used to obtain an improved characterization of welfarism—which includes traditional welfarism as a special case—and, as a proof of concept, an improved characterization of utilitarianism—which includes Classical Utilitarianism, Relative Utilitarianism, and the Borda Count, among others, as special cases. These results are further interpreted in light of various recent discussions of non-welfarism. In particular, the need to investigate welfarism in a multi-profile setting is emphasized anew.