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Bayesian Social Aggregation: Beyond Ex Ante and Ex Post| old_uid | 15053 |
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| title | Bayesian Social Aggregation: Beyond Ex Ante and Ex Post |
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| start_date | 2015/02/05 |
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| schedule | 17h-19h |
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| online | no |
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| summary | 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 payo for each individual, but these payos 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 suer from three shortcomings:
They assume that all agents can formulate preferences over all possible social prospects, even those which are infeasible or logically absurd.
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.
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 dened on an open, connected set of social prospects. From these weaker hypotheses, we still obtain the conclusions of Harsanyi's theorem; SEU-maximization 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 dierent beliefs about the subjective uncertainty source. |
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| responsibles | Baccelli |
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