2022 Past Seminars

Host: Simona Fabrizi

Abstract. A "cyclic order" may be thought of informally as a way to seat people around a table for a game of chance, but also as a way to schedule a finite number of events in a coherent, recurring fashion. Given a set of agents/events such as A, B, and C, we can formalize this by defining a cyclic order as a permutation on this finite set, under the equivalence relation where A>B>C is identified with both B>C>A and C>A>B.

Just as with other choices involving sets with some structure, we might want to aggregate preferences of a set of voters (possibly different from the agents) on the set of possible ways to make this choice. However, given the large number of possibilities as the cardinality of the set of agents increases, we may not wish to use the usual machinery of full ranked linear orders on all these options. This raises the question of what sort of ballots may be appropriate; a single cyclic order, a set of them, or some other ballot type?

Similarly, there is a natural action of the group of permutations on the set of agents. A reasonable requirement for a choice procedure would be to respect this symmetry (the equivalent of neutrality in normal voting theory), or even take advantage of it. This talk will use representation theory of the symmetric group to analyze natural types of possible ballots for voting on cyclic orders, and what that tells us about all possible points-based voting methods for them.

(Joint work with Abraham Holleran, Micah Martin, and Josephine Noonan)

Host: Simona Fabrizi

Abstract. In real-life assignment problems there are oftentimes diversity and distributional objectives. For example, public schools aim for a diverse student body in terms of socioeconomic background, and selective colleges try to admit more applicants from underrepresented groups. First, we study a single school's problem of choosing a set of applicants to be assigned to the school. We provide an axiomatic characterization of a general class of choice rules where distributional objectives are met through type-specific reserves and quotas. The choice rules in the class differ by the order in which applicants are considered for units reserved for different types. We show that a particular rule, where all applicants are first considered for units reserved for their own types and which we call the regular reserves-and-quotas rule, uniquely minimizes priority violations in this class. Next, we study a general setup with multiple schools. We show that when all schools use the regular reserves-and-quotas rule, the Deferred Acceptance mechanism minimizes priority violations in a large class of mechanisms that satisfy the distributional constraints.

Host: Danilo Coelho

Abstract. We study the susceptibility of committee governance (e.g. by boards of directors), modelled as the collective determination of a ranking of a set of alternatives, to manipulation of the order in which pairs of alternatives are voted on -- agenda-manipulation. We exhibit an agenda strategy called insertion sort that allows a self-interested committee chair with no knowledge of how votes will be cast to do as well as if she had complete knowledge. Strategies with this 'regret-freeness' property are characterised by their efficiency, and by their avoidance of two intuitive errors. What distinguishes regret-free strategies from each other is how they prioritise among alternatives; insertion sort prioritises lexicographically.

This is joint work with Ludvig Sinander.

Host: Marcus Pivato

Abstract. A committee makes repeated decisions at a qualified majority rule, under complete information on current preferences. We show that the optimal equilibrium of this repeated game coincides on path with a cutoff decision rule: at each stage, an efficient proposal is collectively accepted if and only if the pivotal individual’s utility exceeds some fixed negative cutoff. In contrast with the stage-game equilibrium, where individuals vote sincerely, the optimal equilibrium involves a form of implicit logroll, individuals sometimes voting against their preference to achieve the efficient decision. As a result, both the expected level of utility and the degree of consensus may be significantly higher than at the stage-game equilibrium. We characterize the set of optimal voting rules in the limit case where the number of individuals grows large and show that it always contains either the simple majority rule or the unanimity rule. We then introduce Abreu et al. (1993)’s renegotiation-proofness requirement, and characterize the optimal renegotiation-proof equilibrium. In the limit case, simple majority is always optimal but the set of optimal voting rules expands as the discount factor increases, eventually including all majority thresholds if individuals are patient enough. The model provides a rationale for the use of unanimity rule, while explaining the prevalence of consensus in committees using a lower majority threshold.

Joint with Rafael Treibich.

Host: Marcus Pivato

Abstract. Plurality with runoff is a widely used voting rule, consisting of two rounds, the second round being a duel between two finalists selected at the first round using plurality scores. The talk will also consist of two rounds.

Round I: plurality with runoff, no!

Using examples from French presidential elections (especially the ongoing one, which will be over at the time of the talk), I will comment on the numerous drawbacks of the rule, and its only advantage, namely the existence of a runoff and of a time gap between the two rounds.

Round II: approval with runoff

We claim that it is possible to retain the idea of a runoff and avoid the catastrophic drawbacks of its coupling with plurality, by having voters cast approval-type ballots at the first round. With approval-type ballots, there are various ways to select the finalists. We leverage known approval-based committee rules and study the obtained runoff rules from an axiomatic point of view. Then we analyse the outcome of these rules on single-peaked profiles, and on real data.

(Joint work with Théo Delemazure, Jean-François Laslier and Remzi Sanver.)

Host: Marcus Pivato

Abstract. We propose a model of the joint evolution of opinions and social relationships in a setting where social influence decays over time. The dynamics are based on bounded confidence: social connections between individuals with distant opinions are severed while new connections are formed between individuals with similar opinions. Our model naturally gives rise to strong diversity, i.e., the persistence of heterogeneous opinions in connected societies, a phenomenon that most existing models fail to capture. The intensity of social interactions is the key parameter that governs the dynamics. First, it determines the asymptotic distribution of opinions. In particular, increasing the intensity of social interactions brings society closer to consensus. Second, it determines the risk of polarization, which is shown to increase with the intensity of social interactions. Our results allow us to frame the problem of the design of public debates in a formal setting. We hence characterize the optimal strategy for a social planner who controls the intensity of the public debate and thus faces a trade-off between the pursuit of social consensus and the risk of polarization. We also consider applications to political campaigning and show that both minority and majority candidates can have incentives to lead society towards polarization.

(Joint work with Michel Grabisch and Antoine Mandel)

Host: Simona Fabrizi

Abstract. In dispute resolution, arbitrator assignments are decentralized and they incorporate parties’ preferences, in total contrast to referee assignments in sports. We suggest that there can be gains (i) in dispute resolution from centralizing the allocation by bundling the newly arriving cases, and (ii) in sports from incorporating teams’ preferences. To that end, we introduce a class of Arbiter Assignment Problems where a set of matches (e.g., disputes or games), each made up of two agents, are to be assigned arbiters (e.g., arbitrators or referees). In this new set of problems, the question of how agents in a match should compromise becomes critical. To evaluate the value of an arbiter for a match, we introduce the (Rawlsian) notion of depth, defined as the arbiter’s worst position in the two agents’ rankings. Depth optimal assignments minimize depth over matches, and they are Pareto optimal. We first introduce and analyze depth optimal (and fair) mechanisms. We then propose and study strategy-proof mechanisms.

Host: Marcus Pivato

Abstract. In the problem of aggregating experts’ probabilistic predictions or opinions over an ordered set of outcomes, we introduce the axiom of level-strategyproofness (Level-SP) and argue that it is natural in several real-life applications and robust as a notion. It implies truthfulness in a rich domain of single-peaked preferences over the space of cumulative distributions. This contrasts with the existing literature, where we usually assume single-peaked preferences over the space of probability distributions. Our main results are:

1. Explicit characterizations of all Level-SP methods with and without the addition of other axioms (certainty preservation, plausibility preservation, proportionality, weighted voters);
   

2. Comparisons and axiomatic characterizations of two new and practical Level-SP methods: the proportional-cumulative and the middlemost-cumulative;

3. A use of the proportional-cumulative to construct a new voting method (MJU) that extends majority judgment (MJ) method for electing and ranking alternatives.

In MJ, a voter attributes a grade on a scale of merits such as Λ = { Great; Good; Average; Poor; Terrible} to each candidate/alternative. In MJU, voters can express their uncertainties/doubts about the merits (e.g. a voter can submit, for each candidate, a probability distribution over Λ). We show that MJU inherits most of the salient properties of MJ (e.g. it avoids Arrow and Condorcet paradoxes and it resists to some natural strategic manipulations).

(Joint work with Estelle Varloot, University of Liverpool)

Host: Marcus Pivato

Abstract. This paper considers a binary decision to be made by a committee — canonically, a jury — through a voting procedure. Each juror must vote on whether a defendant is guilty or not guilty. The voting rule aggregates the votes to determine whether the defendant is convicted or acquitted. We focus on the unanimity rule (convict if, and only if, all vote guilty), and we consider jurors who share ambiguous prior beliefs as in Ellis (2016). Our contribution is twofold. First, we identify all symmetric equilibria of these voting games. Second, we show that ambiguity may drastically undermine McLennan’s (1998) results on decision quality: unlike in the absence of ambiguity, the ex-ante optimal symmetric strategy profile need not be an equilibrium; indeed, there are games for which it is possible to reduce both Type I and Type II error starting from any (non-trivial) equilibrium. Finally, we explain the significance of these results for our on-going experimental work on voting behaviour.

Joint work with Steffen Lippert (University of Auckland), Addison Pan (Xi'an Jiaotong-Liverpool University) and Matthew Ryan (Auckland University of Technology).

Host: Marcus Pivato

Abstract. In democratic societies, different groups often favor different, conflicting alternatives. Sometimes, political compromises based on social conventions as equity or economic arguments as efficiency are available, but they fail to gather the necessary support. We study different voting methods in three experiments (total N = 5, 820), including small, medium-sized, and large electorates, and find that currently-used methods (Plurality Voting and Rank-Order systems) can lead to widespread selection of egoistic options. In contrast, alternative, more nuanced methods (Approval Voting and Borda Count) favor equity and efficiency, avoiding extreme outcomes. Those two methods differ in their support of equity vs. efficiency when the latter benefits a majority. Our evidence suggests that targeted changes in the electoral system could favor socially-desirable compromises and increase social stability.

Host: Simona Fabrizi

Abstract. We proposed two mechanisms for two parties to jointly select a group of fixed size. We show that these mechanisms have good properties if the parties' preferences over sets are leximin or leximax extensions of the parties' preferences over candidates then these mechanisms may induce compromise and Pareto efficient outcomes.

(Joint work with Salvador Barberà)