### INTERNATIONAL GROUP OF COORDINATORS:

**Youngsub Chun (ychun@snu.ac.kr)**

**Gleb Koshevoy (koshevoyga@gmail.com)**

**Clemens Puppe (clemens.puppe@kit.edu)**

**Remzi Sanver (remzi.sanver@lamsade.**dauphine.fr )

**Arkadii Slinko (a.slinko@auckland.ac.nz)**

**Bill Zwicker (zwickerw@union.edu)**

[*To join,* c*ontact **one of the coordinators to get a meeting ID and password*]

**LIST OF TALKS**

**Date and time**:

**7 July 8AM GMT**(i.e., for example, 10am in Paris, 8pm in AKL)

**A****bstract: **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.

**Date and time**:

**30 June 8AM GMT**

**A****bstract: **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.

**Date and time**:

**23 June 8AM GMT**

**Contributor**:

**Nimrod Talmon**

**Title**: Participatory Budgeting with Cumulative Votes

**A****bstract: **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.

**Date and time**:

**16 June 8AM GMT**

**Contributor**:

**Gleb Koshevoy**

**Title**: Condorcet super-domains

**A****bstract: **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).

**Date and time**:

**9 June 8AM GMT**

**Contributors**:

**Simona Fabrizi**,

**Steffen Lippert**,

**Addison Pan**and

**Matthew Ryan**

**Title**: Unanimous Jury Voting with an Ambiguous Likelihood

**A****bstract: **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.

**Date and time**:

**2 June 11AM GMT**

**Contributors**:

**Ayumi Igarashi**and

**William S. Zwicker**

**Title**: Fair division of graphs and of tangled cakes

**Abstract: **Recent work by Bilò et al [2019] 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.”

**Date and time**:

**26 May 8AM GMT**

**Contributors**:

**M. Remzi Sanver**and

**Shin Sato**

**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.