SMU SOE Economics Lecture Series (Oct 27, 2022, 4.00pm-5.30pm): Collective Choices under Risk Uncertainty

Collective Choices under Risk Uncertainty

This lecture will discuss the problem of making sound collective decisions in situations involving risk or uncertainty. When the probabilities attached to the relevant uncertain events are known, the normative issue consists in aggregating individual preferences over lotteries. Harsanyi's theorem on utilitarianism falls short of providing a complete solution because it does not provide any guidelines for calibrating the utility functions representing the individuals' preferences. We will review and compare several solutions proposed in the literature, including Dhillon and Mertens's relative utilitarianism. 

When no objective probabilities are attached to the possible events, uncertain prospects should be modelled à la Savage as social acts from states of nature into collective outcomes. The issue consists in aggregating subjective expected utility preferences over such acts. This leads to a conflict between the Pareto principle and the requirement that the collective preference should satisfy the subjective expected utility axioms. We will review a compare the leading aggregation methods proposed in the literature.

Some relevant papers (click on the titles to view):

1) Belief-weighted Nash aggregation of Savage preferences

The belief-weighted Nash social welfare functions are methods for aggregating Savage preferences defined over a set of acts. Each such method works as follows. Fix a 0-normalized subjective expected utility representation of every possible preference and assign a vector of individual weights to each profile of beliefs. To compute the social preference at a given preference profile, rank the acts according to the weighted product of the individual 0-normalized subjective expected utilities they yield, where the weights are those associated with the belief profile generated by the preference profile. We show that these social welfare functions are characterized by the weak Pareto principle, a continuity axiom, and the following informational robustness property: the social ranking of two acts is unaffected by the addition of any outcome that every individual deems at least as good as the one she originally found worst. This makes the belief-weighted Nash social welfare functions appealing in contexts where the best relevant outcome for an individual is difficult to identify.

2) Strategyproof Choice of Social Acts

We model uncertain social prospects as acts mapping states of nature to social  outcomes. A social choice function or SCF assigns an act to each profile of subjective expected utility preferences over acts. An SCF is strategyproof if no agent ever has an incentive to misrepresent her beliefs about the states of nature or her valuation of the outcomes. It is unanimous if it picks the feasible act that all agents find best whenever such an act exists. We offer a characterization of the class of strategyproof and unanimous SCFs in two settings. In the setting where all acts are feasible, the chosen act must yield the favorite outcome of some possibly different) agent in every state of nature. The set of states in which an agent’s favorite outcome is selected may vary with the reported belief profile; it is the union of all states assigned to her by a collection of constant, bilaterally dictatorial, or bilaterally consensual assignment rules. In a setting where each state of nature defines a possibly different subset of available outcomes, bilaterally dictatorial or consensual rules can only be used to assign control rights over states characterized by identical sets of available outcomes.