INTERNATIONAL GROUP OF COORDINATORS:
[To join, please contact one of the coordinators to get a meeting ID and password]
LIST OF TALKS
Abstract: We take the axiomatic approach to uncover the structure of the revenue-sharing problem from broadcasting sports leagues. Our starting point is to explore the implications of three basic axioms: additivity, order preservation and weak upper bound. We show that the combination of these axioms characterizes a large family of rules, which is made of compromises between the uniform rule and concede-and-divide, such as the one represented by the equal-split rule. The members of the family are fully ranked according to the Lorenz dominance criterion, and the structure of the family guarantees the existence of a majority voting equilibrium. Strengthening some of the previous axioms, or adding new ones, we provide additional characterizations within the family. Weakening some of those axioms, we also characterize several families encompassing the original one. Joint paper with Gustavo Bergantiños (ECOSOT, Universidade de Vigo).
Abstract: The Borda rule as evaluates an alternatives by the average of the majority margins over all feasible alternatives. Generalized Borda rules (GBRs) evaluate alternatives by a weighted average of the majority margins over all feasible alternatives, where the weights may depend on the set of feasible alternatives. We call this weighting function the “relevance index” defining the GBR. A basic result of the paper characterizes GBRs in terms of an axiom of Ordinal Admissibility. Ordinal Admissibility expresses the normative desideratum that the social choice rule be justifiable as optimal on “purely ordinal” grounds. The Borda rule itself is not a satisfactory response to Arrow’s impossibility challenge, since it is highly vulnerable to the exact specification of the feasible set. In particular, it starkly violates the Independence of Clone axiom due to Tideman 1987. The original formulation due to Tideman 1987 has proved rather restrictive and is arguably too strong. In particular, essentially forces Polarization, ie. social choice of an alternative that is top ranked by a majority of the agents and bottom ranked by all others. By contrast, we how that moderate versions of Invariance to Cloning are satisfied by GBRs whenever their relevance indices satisfying appropriate invariance conditions. Such GBRs need not, and, typically, do not exhibit Polarization. A simple and naturally axiomatized index is the plurality index given by the distribution of agents preference tops. The induced GBR, the “Pluri-Borda rule”, has attractive properties and instantiates a new possibility result on Post-Arrowian social choice.
Abstract: We propose strike mechanisms as a solution to the classical problem of Hurwicz and Schmeidler  and Maskin  according to which, in two- person societies, no Pareto efficient rule is Nash-implementable. A strike mechanism specifies the number of alternatives that each player vetoes. Each player simultaneously casts these vetoes and the mechanism selects randomly one alternative among the unvetoed ones. For strict preferences over alternatives and under a very weak condition for extending preferences over lotteries, these mechanisms are deterministic-in-equilibrium. They Nash implement a class of Pareto efficient social choice rules called Pareto-and-veto rules. Moreover, under mild richness conditions on the domain of preferences over lotteries, any Pareto efficient Nash-implementable rule is a Pareto-and-veto rule and hence is implementable through a strike mechanism. Joint paper with JF Laslier and Matias Nuñez.
Abstract: This paper explores approaches to comparative justice (Sen 2009) by drawing on Social Choice Theory. We introduce a procedure to correct for the influence of unquestioned parochial values on individual justice rankings: individuals are put into the position of other members of society allowing them to question (and possibly change) their justice ordering. In a first step, it is shown under which conditions this procedure leads to a domain restriction such that majority rule yields a social justice ordering. In a second step, it is examined how the introduced procedure can be used to distinguish between “reasoned” and “unreasoned” agreement. The paper concludes with a discussion as to how the findings cast doubt on the unqualified acceptance of the (weak) Pareto condition.
Abstract: Consider the following principle regarding the performance of collective choice rules. ì If a rule selects alternative x in situation 1, and alternative y in situation 2, there must be an alternative z, and some member of society whose appreciation of z relative to x has increased when going from situation 1 to situation 2.î This principle requires a minimal justiÖcation for the fall of x in the consideration of society: someone must have decreased its appreciation relative to some other possible alternative. We study the consequences of imposing this requirement of pairwise justifiability on a large class of collective choice rules that includes social choice and social welfare functions as particular cases. When preference profiles are unrestricted, it implies dictatorship, and both Arrowís and the Gibbard-Satterthwaite theorems become corollaries of our general result. On appropriately restricted domains, pairwise justifiability, along with anonymity and neutrality, characterize Condorcet consistent rules, thus providing a foundation for the choice of the alternatives that win by majority over all others in pairwise comparisons, when they exist. This is a joint paper with Dolors Berga, Bernardo Moreno, and Antonio Nicoló.
Abstract: We propose an alternative strategy of modelling contests by introducing a new class of truncated polynomial probability-of-win functions. Our approach permits finding a closed form solution and obtaining valuable comparative static results not only for the complete information case, (both for mixed and pure strategies), but also for the case of incomplete (private) information. Particularly, we are able to address an important question of information design in contests. In addition, this approach also allows to explore the case when a further increase in maximal effort exerted in a contest bestows a positive externality on other contenders with lower efforts, increasing their marginal probability of winning. We argue that this situation usually arises in R&D competition and patent races and cannot be modelled by standard Tullock-style contest models. This is a joint work with Alexander Matros, North Carolina and Lancester.
Title: Population ethics in an infinite universe [paperand slides]
Abstract: Population ethics studies the tradeoff between the total number of people who will ever live, and their welfare. But widely accepted theories in modern cosmology say that spacetime is probably infinite. In this case, its population is also probably infinite, so the quantity/quality tradeoff of population ethics is no longer meaningful. Instead, we face the problem of how to evaluate the social welfare of an infinite population dispersed through time and space. I propose spatiotemporal Cesàro average utility as a way to make this evaluation, and axiomatically characterize it.
Title: Manipulation of social choice functions under incomplete information
Abstract: The failure of strategy-proofness requires the presence of an individual who completely knows the others’ preferences. However, as observed by some authors, an individual might decide to misrepresent her preferences on the basis of a smaller amount of information. It is then possible to consider weak versions of strategy-proofness which take into account the amount of information individuals can get. We analyse one of those weak versions of strategy proofness, called PC-strategy-proofness. A social choice function is PC-strategy-proof if it cannot be manipulated by an individual whose information about the preferences of the other members of the society is limited to the knowledge, for every pair of alternatives, of the number of individuals preferring the first alternative to the second one. We show that there are Pareto optimal, PC-strategy-proof and non-dictatorial social choice functions. We also prove that, when at least three alternatives are considered, no Pareto optimal, PC-strategy-proof and anonymous social choice function exists. Generalizing the definition of PC-strategy-proofness, we further propose a special family of weak versions of strategy-proofness which allows to define a new index for measuring the degree of manipulability of social choice functions. Some simple remarks on that index are discussed.
Abstract: We present a new method of constructing Condorcet domains from pairs of Condorcet domains of smaller sizes (concatenation+shuffle scheme). The concatenation+shuffle scheme provides maximal, connected, copious, peak-pit domains whenever the original domains had these properties. It provides peak-pit maximal Condorcet domains that are larger than those obtained by the Fishburn’s alternating scheme for all n≥13 (it was previously known for n≥40). The paper provides a new lower bound 2.1685^n for the size of the largest peak-pit Condorcet domain with n alternatives, and a new lower bound 2.2021^n for the size of the largest Condorcet domain without any restrictions.
Abstract: We propose three mechanisms to reach a compromise between two opposite parties that must choose one out of a set of candidates and operate under full information. All three mechanisms weakly implement the Unanimity Compromise Set. They all rely on the use of some rule of k names, whereby one of the parties proposes a shortlist of k candidates, from which the opposite party selects the one to appoint. The decision regarding which particular rule in the class will be used involves determining who will be the first mover and the size of k. The chosen rule results endogenously from the strategic interaction between the parties, rather than being imposed a priori by any exogenous convention.
Abstract: Agents share indivisible objects (desirable or not) and use cash transfers to achieve fairness. Utilities are linear in money but otherwise arbitrary. We look for n-person division rules preserving the informational simplicity of Divide and Choose or the Texas Shoot Out between two agents, treating agents symmetrically, and offering high individual welfare Guarantees. A single round of bidding for the whole manna is one such method but it does not capture the potential efficiency gains from debundling the objects as in Divide and Choose. Our Bid and Choose rules fix a price vector p for the objects; in each of the n-1 rounds of bidding the winner must also pay for the remaining objects he picks. These rules are simpler than Kuhn’s n-person generalisation of Divide and Choose, and they typically offer better Guarantees. They help agents with subadditive utilities, to the detriment of those with superadditive utilities. The talk is based on joint research with Anna Bogomolnaia.
Abstract: We study two influential voting rules proposed in the 1890s by Phragmen and Thiele, which elect a committee or parliament of k candidates which proportionally represents the voters. Voters provide their preferences by approving an arbitrary number of candidates. Previous work has proposed proportionality axioms satisfied by Thiele but not Phragmen. By proposing two new proportionality axioms (laminar proportionality and priceability) satisfied by Phragmen but not Thiele, we show that the two rules achieve two distinct forms of proportional representation. Phragmen’s rule ensures that all voters have a similar amount of influence on the choice of the committee, and Thiele’s rule ensures a fair utility distribution. (Thiele’s rule is a welfarist voting rule that maximises a function of voters’ utilities). We show that no welfarist rule can satisfy our new axiom, and we prove that no such rule can satisfy the core. Conversely, some welfarist fairness properties cannot be guaranteed by Phragmen-type rules. This formalises the difference between the two types of proportionality. We then introduce an attractive committee rule which satisfies a property intermediate between the core and extended justified representation (EJR). It satisfies laminar proportionality, priceability, and is computable in polynomial time. The talk is based on the recent paper: Dominik Peters and Piotr Skowron. Proportionality and the Limits of Welfarism. EC-2020.
Abstract: In participatory budgeting we are given a set of projects—each project having a cost, an integer specifying the available budget, and a set of voters who express their preferences over the projects. The goal is to select—based on voter preferences—a subset of projects whose total cost does not exceed the budget. We propose several aggregation methods based on cumulative votes, i.e., for the setting where each voter is given one coin and specifies how this coin should be split among the projects. We compare our aggregation methods based on (1) axiomatic properties and (2) computer simulations. We identify one method, Minimal Transfers over Costs, that demonstrates particularly desirable behaviour — in particular, it significantly improves on existing methods and satisfy a strong notion of proportionality — and thus is promising to be used in practice. This is a joint paper with Piotr Skowron and Arkadii Slinko.
Abstract: We consider Condorcet domains (CD) formed by a rhombus tiling on a zonogone Z(n; 2) as voting designs and consider a problem of aggregation of voting designs using the majority rule. A Condorcet super-domain is a collection of CDs obtained from rhombus tilings with the property that if voting designs (serving as ballots) belong to this collection, then the simple majority rule does not yield cycles. I will discuss methods of constructing Condorcet super-domains and related problems. The talk is based on joint paper with Vladimir Danilov and Aleksandre Karzanov (arxiv 2004.08183 math.CO).
Abstract: We study collective decision-making in a voting game under the unanimity rule, with an ambiguous likelihood and ambiguity-averse voters who are MaxMin Expected Utility maximizers. We characterize the symmetric voting equilibria of this game, demonstrating that ambiguity helps reduce Type I errors: under ambiguity, voters are less likely to vote strategically against their information. Information aggregation improves as a result, and may even be restored to a fully informative equilibrium. We report evidence from a laboratory experiment supporting these predictions. This is joint work with Steffen Lippert, Addison Pan, and Matthew Ryan.
Title: Fair division of graphs and of tangled cakes
Abstract: Recent work by Bilò et al  concerns allocating graph vertices (treated as indivisible objects) so that each share forms a connected subgraph, and so that no agent x envies another’s share “up to one outer good.” They obtain positive results that apply to arbitrarily many agents, but these are limited to Hamiltonian (aka traceable) graphs. What of the non-Hamiltonian case? We show that among topological classes of graphs, any non-Hamiltonian class has an upper bound on the number of agents for which fair shares are guaranteed. On the other hand, for the case of exactly 3 agents, positive results exist for some infinite, non-Hamiltonian graph classes. Our results – positive and negative – are obtained via transfer from related theorems in continuous fair division, but we must go beyond the standard model, which employs the unit interval [0,1] as the continuously divisible “cake.” Instead, we use several copies of [0,1] glued at their endpoints, to form the letter Y, or the figure 8, or the outline of a kiss . . . a “tangle.”
Title: Evaluationwise strategy-proof social choice correspondences
Abstract: We consider manipulation of social choice correspondences in a preference-approval environment where voters not only rank the alternatives but also evaluate them as acceptable or unacceptable. A social choice correspondence is evaluationwise strategy-proof iff no voter can misrepresent his preference and obtain an outcome which he finds more acceptable than the one that would occur if he had told the truth. As outcomes are irresolute sets of alternatives, our analysis needs to extend the notion of acceptability of alternatives over sets. Under a plausible extension, we show the existence of efficient and evaluationwise strategy-proof social choice correspondences that satisfy one of anonymity and neutrality. However, if anonymity and neutrality are jointly imposed, then an impossibility occurs when the number of voters is a multiple of 4. On the other hand, when there are three alternatives and the number of voters is not a multiple of 4, we show the existence of social choice correspondences which are efficient, evaluationwise strategy-proof, anonymous and neutral.
Date and time: 19 May, 8AM GMT
Contributor: Arkadii Slinko
Title: Generalisation and Properties of the Danilov-Karzanov-Koshevoy Construction for Peak-Pit Condorcet Domains
Abstract: Danilov, Karzanov and Koshevoy (2012) geometrically introduced an interesting operation of composition on Condorcet domains and using it they disproved a long-standing problem of Fishburn about the maximal size of connected Condorcet domains. We give an algebraic definition of this operation and investigate its properties. We give a precise formula for the cardinality of composition of two Condorcet domains and improve the Danilov, Karzanov and Koshevoy result showing that Fishburn’s alternating scheme does not always produce a largest connected Condorcet domain. I will outline some new exciting developments in the search of largest Condorcet domains.