Related papers: Approximately Strategyproof Tournament Rules in th…
Evolutionary game theory is a powerful mathematical framework to study how intelligent individuals adjust their strategies in collective interactions. It has been widely believed that it is impossible to unilaterally control players'…
We prove that every Condorcet-consistent voting rule can be manipulated by a voter who completely reverses their preference ranking, assuming that there are at least 4 alternatives. This corrects an error and improves a result of [Sanver,…
Stochastic games are often used to model reactive processes. We consider the problem of synthesizing an optimal almost-sure winning strategy in a two-player (namely a system and its environment) turn-based stochastic game with both a…
Tournament solutions are frequently used to select winners from a set of alternatives based on pairwise comparisons between alternatives. Prior work has shown that several common tournament solutions tend to select large winner sets and…
We settle a version of the conjecture about intransitive dice posed by Conrey, Gabbard, Grant, Liu and Morrison in 2016 and Polymath in 2017. We consider generalized dice with $n$ faces and we say that a die $A$ beats $B$ if a random face…
We study a random game in which two players in turn play a fixed number of moves. For each move, there are two possible choices. To each possible outcome of the game we assign a winner in an i.i.d. fashion with a fixed parameter p. In the…
The Gibbard-Satterthwaite theorem established that no non-trivial voting rule is strategy-proof, but that does not mean that all voting rules are equally susceptible to strategic manipulation. Over the past fifty years numerous approaches…
Rank aggregation with pairwise comparisons is widely encountered in sociology, politics, economics, psychology, sports, etc . Given the enormous social impact and the consequent incentives, the potential adversary has a strong motivation to…
In a prediction tournament, contestants "forecast" by asserting a numerical probability for each of (say) 100 future real-world events. The scoring system is designed so that (regardless of the unknown true probabilities) more accurate…
Individual sports competitions provide a natural setting for examining the relative importance of talent and luck/chance in achieving success. The belief that success is primarily due to individual abilities and hard work rather than…
In a generalized tournament, players may have an arbitrary number of matches against each other and the outcome of the games is measured on a cardinal scale with a lower and upper bound. An axiomatic approach is applied to the problem of…
We only consider finite structures. With every totally ordered set $V$ and a subset $P$ of $\binom{V}{2}$, we associate the underlying tournament ${\rm Inv}(\underline{V}, P)$ obtained from the transitive tournament $\underline{V}:=(V,…
In collective decision making, where a voting rule is used to take a collective decision among a group of agents, manipulation by one or more agents is usually considered negative behavior to be avoided, or at least to be made…
There seems to be an upper limit to predicting the outcome of matches in (semi-)professional sports. Recent work has proposed that this is due to chance and attempts have been made to simulate the distribution of win percentages to identify…
In the contest design problem, there are $n$ strategic contestants, each of whom decides an effort level. A contest designer with a fixed budget must then design a mechanism that allocates a prize $p_i$ to the $i$-th rank based on the…
The paper discusses the strategy-proofness of sports tournaments with multiple group stages, where the results of matches already played in the previous round against teams in the same group are carried over. These tournaments, widely used…
Proponents of Condorcet voting face the question of what to do in the rare case when no Condorcet winner exists. Recent work provides compelling arguments for the rule that should be applied in three-candidate elections, but already with…
Challenge the champ tournaments are one of the simplest forms of competition, where a (initially selected) champ is repeatedly challenged by other players. If a player beats the champ, then that player is considered the new (current) champ.…
We introduce a single-winner perspective on voting on matchings, in which voters have preferences over possible matchings in a graph, and the goal is to select a single collectively desirable matching. Unlike in classical matching problems,…
A Condorcet winning set addresses the Condorcet paradox by selecting a few candidates--rather than a single winner--such that no unselected alternative is preferred to all of them by a majority of voters. This idea extends to…