Proportional Algorithms for Democratic Decisions

The project is set in the field of computational social choice. We will focus on formal models describing scenarios, where a group of individuals, called voters, disagrees on certain matters, yet needs to make a collective decision. The decision must truly represents a compromise. We focus on group fairness understood as proportionality. There are numerous real-life scenarios that involve collective (public) decisions, and where our solutions could be applied. Examples include: elections of representative bodies (such as parliaments, faculty boards, etc.), participatory budgeting elections (where citizens decide how to allocate a part of a municipal budget), or scenarios where certain local communities (say, housing cooperatives) make series of decisions. In addition, proportional algorithms for making collective decisions can be used for selecting nominees for an award, for constructing rankings of movies or books, for selecting validators in consensus protocols, such as the blockchain, for constructing rankings of web-pages in response to user queries, for locating public facilities, or for improving genetic algorithms.The goal of this project is to develop generic methods of reasoning about equity of treatment of voters, and to design new 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 public decisions, and to (4) develop exact, approximation, fixed-parameter-tractable, and heuristic algorithms for this and related computational problems.