Can neural networks be applied in voting theory, while satisfying the need for transparency in collective decisions? We propose axiomatic deep voting: a framework to build and evaluate neural networks that aggregate preferences, using the well-established axiomatic method of voting theory. Our findings are: (1) Neural networks, despite being highly accurate, often fail to align with the core axioms of voting rules, revealing a disconnect between mimicking outcomes and reasoning. (2) Training with axiom-specific data does not enhance alignment with those axioms. (3) By solely optimizing axiom satisfaction, neural networks can synthesize new voting rules that often surpass and substantially differ from existing ones. This offers insights for both fields: For AI, important concepts like bias and value-alignment are studied in a mathematically rigorous way; for voting theory, new areas of the space of voting rules are explored.

International audience

Abstract Egalitarian considerations play a central role in many areas of social choice theory. Applications of egalitarian principles range from ensuring everyone gets an equal share of a cake when deciding how to divide it, to guaranteeing balance with respect to gender or ethnicity in committee elections. Yet, the egalitarian approach has received little attention in judgment aggregation—a powerful framework for aggregating logically interconnected issues. We make the first steps towards filling that gap. We introduce axioms capturing two classical interpretations of egalitarianism in judgment aggregation and situate these within the context of existing axioms in the pertinent framework of belief merging. We then explore the relationship between these axioms and several notions of strategyproofness from social choice theory at large. Finally, a novel egalitarian judgment aggregation rule stems from our analysis; we present complexity results concerning both outcome determination and strategic manipulation for that rule.

We study settings in which agents with incomplete preferences need to make a collective decision. We focus on a process of majority dynamics where issues are addressed one at a time and undecided agents follow the opinion of the majority. We assess the effects of this process on various consensus notions—such as the Condorcet winner—and show that in the worst case, myopic adherence to the majority damages existing consensus; yet, simulation experiments indicate that the damage is often mild. We also examine scenarios where the chair of the decision process can control the existence (or the identity) of consensus, by determining the order in which the issues are discussed.

In the context of aggregating intervals reflecting the views of several agents into a single interval, we investigate the impact of the form of representation chosen for the intervals involved. Specifically, we ask whether there are natural rules we can define both as rules that aggregate separately the left and right endpoints of intervals and as rules that aggregate separately the left endpoints and the interval widths. We show that on discrete scales it is essentially impossible to do so, while on continuous scales we can characterise the rules meeting these requirements as those that compute a weighted average of the endpoints of the individual intervals.

Restricted domains over voter preferences have been extensively studied within the area of computational social choice, initially for preferences that are total orders over the set of alternatives and subsequently for preferences that are dichotomous—i.e., that correspond to approved and disapproved alternatives. This paper contributes to the latter stream of work in a twofold manner. First, we obtain forbidden subprofile characterisations for various important dichotomous domains. Then, we are concerned with incomplete profiles that may arise in many real-world scenarios, where we have partial information about the voters’ preferences. We tackle the problem of determining whether an incomplete profile admits a completion within a certain restricted domain and design constructive, polynomial algorithms to that effect.

We develop a model for the aggregation of preferences that do not need to be either complete or transitive. Our focus is on the normative characterisation of aggregation rules under which each agent has a weight that depends only on the size of her ballot, i.e., on the number of pairs of alternatives for which she chooses to report a relative ranking. We show that for rules that satisfy a restricted form of majoritarianism these weights in fact must be constant, while for rules that are invariant under agents with compatible preferences forming pre-election pacts it must be the case that an agent's weight is inversely proportional to the size of her ballot.

We introduce a formal model of iterative judgment aggregation, enabling the analysis of scenarios in which agents repeatedly update their individual positions on a set of issues, before a final decision is made by applying an aggregation rule to these individual positions. Focusing on two popular aggregation rules, the premise-based rule and the plurality rule, we study under what circumstances convergence to an equilibrium can be guaranteed. We also analyse the quality, in social terms, of the final decisions obtained. Our results not only shed light on the parameters that determine whether iteration converges and is socially beneficial, but they also clarify important differences between iterative judgment aggregation and the related framework of iterative voting.