Struggles over the single-seat preferential election method IRV (Instant Runoff Voting) go on in public arenas and scientific journals, with focus on two “anomalies”. “Monotonicity failures” are preference distributions that allow a startling strategic voting called Pushover or its...

The nonasymptotic Condorcet jury theorem states that, under certain conditions, group decision-making by simple majority voting can decide more efficiently than single-person decision-making, in terms of having a higher probability of choosing the better alternative. Wit (1998) showed that the...

In this paper, we classify all maximal peak-pit Condorcet domains of maximal width for n ≤ 5 alternatives. To achieve this, we bring together ideas from several branches of combinatorics. The main tool used in the classification is the ideal of a domain. In contrast to the size of maximal...

Herein, we prove a Condorcet jury theorem (CJT) for large elections with multiple alternatives. Voters have common interests that depend on an unknown state of nature. Each voter receives an imprecise private signal about the state of nature and then submits one vote (simple plurality rule). We...

We define and examine the concept of social acceptability of committees, in multi-winner elections context. We say that a committee is socially acceptable if each member in this committee is socially acceptable, i.e., the number of voters who rank her in their top half of the candidates is at...

Correct aggregation of individual preferences into collective one is central problem of nowadays Social Choice theory. After the Arrow's and Gibbard–Satterthwaite impossibility theorems it became clear that our desire to justify an electoral procedure is doomed to failure. At the same time a...