Séminaire interne du Labex MME-DII
« Social choice and welfare under uncertainty »
10h – 11h : Antoine Billot (Lemma, Université Paris 2)
TITLE: Utilitarianism with Prior Heterogeneity (joint work with Vassili Vergopoulos)
ABSTRACT: Harsanyi's axiomatic justification of utilitarianism is extended to a framework
with subjective and heterogenous priors. Contrary to the existing literature on aggregation
of preferences under uncertainty, society is here allowed to formulate probability
judgements, not on the actual state of nature as individuals do, but rather on the opinion
they each have on the actual state. An extended Pareto condition is then proposed that
characterizes the social utility function as a convex combination of individual ones and the
social prior as the independent product of individual ones.
11h – 12h : Stéphane Zuber (CNRS and Université de Paris 1)
TITLE: Fairness under risk and uncertainty (joint work with M. Fleurbaey)
ABSTRACT: I will discuss several issues with fairness in the context of risk and uncertainty. A
distinction is made between an ex ante approach (where individual welfare is assessed and
compared before the realization of a risk), and an ex post approach (where individual
welfare is assessed and compared after the realization of the risk). I will present well-known
dilemma between equity, efficiency and social rationality in that context. I will then propose
a general method for extending fair social preferences defined for riskless economic
environments to the context of risk and uncertainty. Following the fair social choice
approach, wellbeing measures are expressed in terms of the resources (income,
environmental goods, health) available to individuals, rather than `utility'. Ex ante and ex
post methodologies will be discussed in that framework. The social criteria that are obtained
do not in general take the form of an expected utility criterion, and they can also
accommodate non-expected utility individual preferences. I will indicate how these ideas can
be extended to the case of successive generations whose preferences and mere existence
are uncertain.
12 h – 13 h : Marcus Pivato, Thema, Université de Cergy-Pontoise
TITLE: Bayesian social aggregation: beyond ex ante and ex post (joint work with Philippe
Mongin)
ABSTRACT: Suppose a society must make policy choices while facing uncertainty about the
outcome of these choices. Each policy determines a social prospect, which will yield a payoff
for each individual, but these payoffs depends upon the (unknown) state of nature. The
problem is how to choose the best social prospect, given uncertainty about the true state of
nature. The first major result in this area was Harsanyi's Social Aggregation Theorem. This
theorem (and its generalizations) begins with two premises: (1) all individuals (and society as
a whole) are rational agents, and (2) the decisions of society should conform to the ex ante
Pareto axiom, which says that, if everyone prefers prospect X over prospect Y, then society
should also prefer prospect X over prospect Y . From these two premises, Harsanyi deduces
that society should seek to maximize the expected value of a utilitarian social welfare
function. However, existing versions of Harsanyi's theorem suffer from three shortcomings:
1. They assume that all agents can formulate preferences over all possible social prospects,
even those which are infeasible or logically absurd.
2. They assume that all agents are subjective expected utility (SEU) maximizers —i.e. each
agent seeks to maximize the expected value of her utility function with respect to her
probabilistic beliefs.
3. They imply that all agents must have the same probabilistic beliefs. Given the doxastic
heterogeneity we observe in the real world, this is generally regarded as a reductio ad
absurdum of the whole approach.
We relax the SEU assumption by only requiring the individuals and the society to satisfy the
Statewise Dominance axiom, which is arguably the bare minimum requirement for
rationality. Furthermore, we relax the “universal domain” assumption, by only requiring
agents' preferences to be defined on an open, connected set of social prospects. From these
weaker hypotheses, we still obtain the conclusions of Harsanyi's theorem; SEUmaximization appears as a conclusion of our theorem, not a hypothesis.
Unfortunately, this still yields the aforementioned agreement in probabilistic beliefs. To
resolve this, we introduce two independent sources of uncertainty: one objective, and one
subjective. In this framework, we obtain a version of the Social Aggregation Theorem that is
compatible with diversity in beliefs. In our result, ex ante social preferences still maximize
expected value of a utilitarian social welfare function, and all agents must have the same
beliefs about the objective uncertainty source. But they can have different beliefs about the
subjective uncertainty source.