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(Paris School of Economics)
Jury Theorems: Thursday, June 17 at 10 AM EDT
Jury theorems are mathematical theorems about the ability of collectives to make correct decisions, for instance of juries to form correct verdicts, or of advisory commissions to give correct advice, or parliament to pass effective laws. Several jury theorems carry the optimistic message that, in suitable circumstances, ‘crowds are wise': many individuals together (using, for instance, majority voting) tend to make good decisions, outperforming fewer or just one individual. Some jury theorems even conclude, somewhat implausibly, that ‘huge groups are infallible’: asymptotically large groups reach correct decisions with probability one. The optimistic conclusions of jury theorems often stem from misguided premises. Revising those premises yields more realistic jury theorems, with more nuanced conclusions. Jury theorems form the technical core of epistemic arguments for democracy, and provide probabilistic tools for reasoning about the epistemic quality of collective decisions. The popularity of jury theorems spans across various disciplines such as economics, political science, philosophy, and computer science. This talk reviews and critically assesses a variety of jury theorems. It first discusses Condorcet's initial jury theorem, and then progressively introduces jury theorems with more appropriate premises and conclusions. It explains the philosophical foundations, and relates jury theorems to diversity, deliberation, shared evidence, shared perspectives, and other phenomena.
(University of Warwick)
Voting in Committees: Friday, June 18 at 9:30 AM EDT
The talk will focus on voting procedures that are appropriate for use by small electorates or committees. The main focus of the talk will be on probabilistic decision schemes that map profiles of individual preferences to probability distributions over the set of feasible outcomes. However, I will introduce in passing some results on deterministic social aggregation rules, describing in detail an example on approval voting that emphasises the poor strategic properties of non-ranked voting rules.
The talk will introduce some probabilistic decision rules and discuss their properties including a recent axiomatic characterisation of the Maximal Lottery. The last part of the talk will be on strategic analysis of decision schemes. Different definitions of strategyproofness are possible, depending on how individuals evaluate lotteries over outcomes, given their rankings over outcomes. Gibbard (1977) had introduced a particularly strong concept of strategyproofness and proved that only random dictatorships satisfy this strong concept of strategyproofness and ex post Pareto optimality. I will discuss some recent results which show that different degrees of efficiency can be reconciled with weaker concepts of strategyproofness.
(Emory University)
Information, incentives, and algorithmic fairness: Friday, June 18 at 3:30 PM EDT
This talk will cover algorithmic fairness, a newly emerging field within computer science, statistics, and data science. In addition to formalizing a family of related notions of fairness, the field has already generated a small family of impossibility theorems that illuminate the challenges inherent to simultaneously achieving multiple fairness goals. I will discuss these goals and results, with the goal of linking the questions and concepts at play with similar issues that both philosophers and social scientists have grappled with for over two centuries. Finally, I will describe some directions that are promising for future research and for which social scientists are particularly well-positioned to advance, such as incorporating strategic behavior into the broader discussion of these fairness concepts.
Pairwise justifiable changes in collective choices: Saturday, June 19 at 10 AM EDT
Consider the following principle regarding the performance of collective choice rules when individual preferences are ordinal and strict. “If a rule selects alternative x in situation 1, and alternative y in situation 2, there must be an alternative z, and some individual whose appreciation of z relative to x has increased when going from situation 1 to situation 2”. This principle requires a minimal justification for the fall of x. We study two consequences of this novel requirement, that we call pairwise justifiability, on a large class of aggregation methods, that we call collective choice rules, defined as follows.
A situation is given by a profile of individual preferences R and a set of alternatives B, from which society must choose. Collective choice rules are defined on collections of situations, consisting of preference profiles included in a set D, and of subsets of alternatives, called agendas, belonging to a collection B. A collective choice rule selects, for each profile in D, an alternative in each of the agendas in B.
Social choice theory has studied a variety of models, and these include two salient ones: social choice functions and social welfare functions. Social choice functions select a unique alternative out of all possible ones for each relevant profile of individual preferences. Social welfare functions are essentially methods that deliver one or several alternatives for all possible combinations of agendas and preference profiles, in such a way that the choices across agendas for each given profile are transitively rationalizable. In our context, social choice functions and social welfare functions are special cases of collective choice rules.
We first prove that among collective choice rules defined on the strict universal domain, only dictatorial ones can be pairwise justifiable. By contrast, we also obtain a positive consequence of our condition: we show that, in appropriately restricted subsets of preference profiles, it guarantees that pairwise justifiable rules will always select the strong Condorcet winner when one exists.
An important application of our one-axiom dictatorship result is to throw light on an important puzzle in voting theory, regarding the exact connection between the two most important negative results in social choice: Arrow’s and Gibbard-Satterthwaite’s theorems. We can prove that they are both corollaries of ours.
We discuss the relationship between our principle and other important conditions used in social choice theory, which turn out to be either stronger or not directly comparable with it when applied to restricted domains. Our result on Condorcet consistency is an example of the consequences of pairwise justifiability when applied to collective choice rules defined on restricted domains, and an invitation to pursue the study of that condition in other contexts and applications…
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