Thou Shalt not Pick all Items if Thou are First: of Strategyproof and Fair Picking Sequences

When allocating indivisible items to agents, it is known that the only strategyproof mechanisms that satisfy a set of rather mild conditions are constrained serial dictatorships: given a fixed order over agents, at each step the designated agent chooses a given number of items (depending on her position in the sequence). With these rules, also known as non-interleaving picking sequences, agents who come earlier in the sequence have a larger choice of items. However, this advantage can be compensated by a higher number of items received by those who come later. How to balance priority in the sequence and number of items received is a nontrivial question. We use a previous model, parameterized by a mapping from ranks to scores, a social welfare functional, and a distribution over preference profiles. For several meaningful choices of parameters, we show that the optimal sequence can be computed in polynomial time. Last, we give a simple procedure for eliciting scoring vectors and we study the impact of the assignment from agents to positions on the ex-post social welfare.

Online Approval Committee Elections

Assume $k$ candidates need to be selected. The candidates appear over time. Each time one appears, it must be immediately selected or rejected -- a decision that is made by a group of individuals through voting. Assume the voters use approval ballots, i.e., for each candidate they only specify whether they consider it acceptable or not. This setting can be seen as a voting variant of choosing $k$ secretaries. Our contribution is twofold. (1) We assess to what extent the committees that are computed online can proportionally represent the voters. (2) If a prior probability over candidate approvals is available, we show how to compute committees with maximal expected score.

Multi-winner Approval Voting Goes Epistemic

Epistemic voting interprets votes as noisy signals about a ground truth. We consider contexts where the truth consists of a set of objective winners, knowing a lower and upper bound on its cardinality. A prototypical problem for this setting is the aggre-gation of multi-label annotations with prior knowledge on the size of the ground truth. We posit noisemodels, for which we define rules that output an optimal set of winners. We report on experiments on multi-label annotations (which we collected).

Truth-tracking via Approval Voting: Size Matters

Epistemic social choice aims at unveiling a hidden ground truth given votes, which are interpreted as noisy signals about it. We consider here a simple setting where votes consist of approval ballots: each voter approves a set of alternatives which they believe can possibly be the ground truth. Based on the intuitive idea that more reliable votes contain fewer alternatives, we define several noise models that are approval voting variants of the Mallows model. The likelihood-maximizing alternative is then characterized as the winner of a weighted approval rule, where the weight of a ballot decreases with its cardinality. We have conducted an experiment on three image annotation datasets; they conclude that rules based on our noise model outperform standard approval voting; the best performance is obtained by a variant of the Condorcet noise model.

Online Selection of Diverse Committees

Citizens' assemblies need to represent subpopulations according to their proportions in the general population. These large committees are often constructed in an online fashion by contacting people, asking for the demographic features of the volunteers, and deciding to include them or not. This raises a trade-off between the number of people contacted (and the incurring cost) and the representativeness of the committee. We study three methods, theoretically and experimentally: a greedy algorithm that includes volunteers as long as proportionality is not violated; a non-adaptive method that includes a volunteer with a probability depending only on their features, assuming that the joint feature distribution in the volunteer pool is known; and a reinforcement learning based approach when this distribution is not known a priori but learnt online.

Morphologic for knowledge dynamics: revision, fusion, abduction

Several tasks in artificial intelligence require to be able to find models about knowledge dynamics. They include belief revision, fusion and belief merging, and abduction. In this paper we exploit the algebraic framework of mathematical morphology in the context of propositional logic, and define operations such as dilation or erosion of a set of formulas. We derive concrete operators, based on a semantic approach, that have an intuitive interpretation and that are formally well behaved, to perform revision, fusion and abduction. Computation and tractability are addressed, and simple examples illustrate the typical results that can be obtained.

Proceedings Sixteenth Conference on Theoretical Aspects of Rationality and Knowledge

This volume consists of papers presented at the Sixteenth Conference on Theoretical Aspects of Rationality and Knowledge (TARK) held at the University of Liverpool, UK, from July 24 to 26, 2017. TARK conferences bring together researchers from a wide variety of fields, including Computer Science (especially, Artificial Intelligence, Cryptography, Distributed Computing), Economics (especially, Decision Theory, Game Theory, Social Choice Theory), Linguistics, Philosophy (especially, Philosophical Logic), and Cognitive Psychology, in order to further understand the issues involving reasoning about rationality and knowledge.

Agenda Separability in Judgment Aggregation

One of the better studied properties for operators in judgment aggregation is independence, which essentially dictates that the collective judgment on one issue should not depend on the individual judgments given on some other issue(s) in the same agenda. Independence, although considered a desirable property, is too strong, because together with mild additional conditions it implies dictatorship. We propose here a weakening of independence, named agenda separability: a judgment aggregation rule satisfies it if, whenever the agenda is composed of several independent sub-agendas, the resulting collective judgment sets can be computed separately for each sub-agenda and then put together. We show that this property is discriminant, in the sense that among judgment aggregation rules so far studied in the literature, some satisfy it and some do not. We briefly discuss the implications of agenda separability on the computation of judgment aggregation rules.

New Results on Equilibria in Strategic Candidacy

We consider a voting setting where candidates have preferences about the outcome of the election and are free to join or leave the election. The corresponding candidacy game, where candidates choose strategically to participate or not, has been studied %initially by Dutta et al., who showed that no non-dictatorial voting procedure satisfying unanimity is candidacy-strategyproof, that is, is such that the joint action where all candidates enter the election is always a pure strategy Nash equilibrium. Dutta et al. also showed that for some voting tree procedures, there are candidacy games with no pure Nash equilibria, and that for the rule that outputs the sophisticated winner of voting by successive elimination, all games have a pure Nash equilibrium. No results were known about other voting rules. Here we prove several such results. For four candidates, the message is, roughly, that most scoring rules (with the exception of Borda) do not guarantee the existence of a pure Nash equilibrium but that Condorcet-consistent rules, for an odd number of voters, do. For five candidates, most rules we study no longer have this guarantee. Finally, we identify one prominent rule that guarantees the existence of a pure Nash equilibrium for any number of candidates (and for an odd number of voters): the Copeland rule. We also show that under mild assumptions on the voting rule, the existence of strong equilibria cannot be guaranteed.

Boolean Hedonic Games

We study hedonic games with dichotomous preferences. Hedonic games are cooperative games in which players desire to form coalitions, but only care about the makeup of the coalitions of which they are members; they are indifferent about the makeup of other coalitions. The assumption of dichotomous preferences means that, additionally, each player's preference relation partitions the set of coalitions of which that player is a member into just two equivalence classes: satisfactory and unsatisfactory. A player is indifferent between satisfactory coalitions, and is indifferent between unsatisfactory coalitions, but strictly prefers any satisfactory coalition over any unsatisfactory coalition. We develop a succinct representation for such games, in which each player's preference relation is represented by a propositional formula. We show how solution concepts for hedonic games with dichotomous preferences are characterised by propositional formulas.