We characterize the preference domains on which the Borda count satises Arrow's "independence of irrelevant alternatives" condition. Under a weak richness condition, these domains are obtained by xing one preference ordering and including all its cyclic permutations ("Condorcet cycles"). We then...

In a framework with two parties, deterministic voter preferences and a type of geographical constraints, we propose a set of simple axioms and show that they jointly characterize the districting rule that maximizes the number of districts one party can win, given the distribution of individual...

We show that optimal partisan redistricting with geographical constraints is a computationally intractable (NP-complete) problem. In particular, even when voter's preferences are deterministic, a solution is generally not obtained by concentrating opponent's supporters in \unwinnable" districts...

In the context of discrete districting problems with geographical constraints, we demonstrate that determining an (ex post) unbiased districting, which requires that the number of representatives of a party should be proportional to its share of votes, turns out to be a computationally...

In a framework with two parties, deterministic voter preferences and a type of geographical constraints, we propose a set of simple axioms and show that they jointly characterize the districting rule that maximizes the number of districts one party can win, given the distribution of individual...

Can neural networks learn to select an alternative based on a systematic aggregation of convicting individual preferences (i.e. a 'voting rule')? And if so, which voting rule best describes their behavior? We show that a prominent neural network can be trained to respect two fundamental...

We show that optimal partisan districting and majority securing districting in the plane with geographical constraints are NP-complete problems. We provide a polynomial time algorithm for determining an optimal partisan districting for a simplified version of the problem. In addition, we give...

The mixed-strategy equilibrium of the symmetric production-in-advance type capacity-constrained Bertrand-Edgeworth duopoly game has not been derived analytically over the entire range of intermediate capacities in the literature. Tasnádi (2020) constructed a symmetric mixed-strategy equilibrium...

Social choice rules (SCRs) aggregate individual preferences to social preferences. By Arrow's (1951) impossibility theorem there does not exist a non-dictatorial SCR satisfying three desirable properties. Considering this negative axiomatic result, in this paper we determine distances of SCRs...

In finitely additive exchange economies the usual definition of competitive equilibrium can result in an empty equilibrium set, and therefore one has to consider notions of ε-competitive equilibria. In this paper we investigate the relationship between two notions of ε-competitive equilibria.