The project is set within the field of computational social choice. A particularly active and influential subarea concerns committee elections---that is, elections in which a fixed-size subset of candidates is selected based on ballots submitted by voters. Research on committee elections has shown significant potential for real-world impact: committee-selection methods apply not only to political contexts, but also to a wide range of other practical decision-making scenarios. For example, they can be used to choose nominees for awards (with experts acting as voters), or to produce rankings of movies, books, and other items. Importantly, these applications extend far beyond settings involving human voters. Committee-election rules can be used to select validators in blockchain consensus protocols, to generate search-result rankings that reflect diverse user profiles, to determine optimal locations for public facilities, or even to enhance the performance of genetic algorithms.
A critical property of voting is that it should be fair---not only to individuals but also to groups of voters with similar opinions on the subject of the vote; in other words, the outcome of an election should proportionally reflect the voters' preferences. The goal of this project is to establish foundations for a new theory that would explain how groups of voters with commons interests can affect public decisions, and that would apply to more generic models of social choice that extend the model of approval based committee elections. Our axioms and algorithms should apply to a voting model, where a subset of candidates need to be selected, but subject to certain general feasibility constraints. The model generalises committee elections (where there is a single constraint on the number of candidates that need to be selected), various elections with diversity constraints, the model of public decisions (where decisions needs to be taken on a number of independent issues), participatory budgeting, and the model of collective scheduling. The goal is also to propose a theory that would apply to more general types of voters' preferences, specifically, when the voters can assign to the candidates numerical values.
The goal of this project is to develop generic methods of reasoning about proportionality of decision rules, and to design new protocols and algorithms that satisfy the most demanding criteria of proportionality. The new methods should be applicable to a number of specific models that concern public decisions. We will (1) prove theorems specifying whether and under which conditions our notions of proportionality are satisfiable, and (2) we will analyse various rules and algorithms with respect to our criteria of proportionality and other important desiderata that are commonly considered in social choice theory. We plan to (3) determine the computational complexity of the problem of finding proportional collective decisions, and to (4) develop exact, approximation, fixed-parameter-tractable, and heuristic algorithms for this and related computational problems.
