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In this paper we examine algorithmic fairness from the perspective of law aiming to identify best practices and strategies for the specification and adoption of fairness definitions and algorithms in real-world systems and use cases. We…
Infinite chess is chess played on an infinite edgeless chessboard. The familiar chess pieces move about according to their usual chess rules, and each player strives to place the opposing king into checkmate. The mate-in-n problem of…
This paper has a twofold scope. The first one is to clarify and put in evidence the isomorphic character of two theories developed in quite different fields: on one side, threshold logic, on the other side, simple games. One of the main…
Recommender systems are an essential tool to relieve the information overload challenge and play an important role in people's daily lives. Since recommendations involve allocations of social resources (e.g., job recommendation), an…
We introduce a novel system of matching and scoring players in tournaments, called Multi-Tier Tournaments, illustrated by chess and based on the following rules: 1. Players are divided into skill-based tiers, based on their Elo ratings. 2.…
The allocation of resources among multiple agents is a fundamental problem in both economics and computer science. In these settings, fairness plays a crucial role in ensuring social acceptability and practical implementation of resource…
In limited overs cricket, the team batting first posts a target score for the team batting second to achieve in order to win the match. The team batting second is constrained by decreasing resources in terms of number of balls left and…
Knockout tournaments, also known as single-elimination or cup tournaments, are a popular form of sports competitions. In the standard probabilistic setting, for each pairing of players, one of the players wins the game with a certain (a…
The Swiss-system is an increasingly popular competition format as it provides a favourable trade-off between the number of matches and ranking accuracy. However, there is no empirical study on the potential unfairness of Swiss-system chess…
In the game "Super Six", after successfully getting rid of a stick by rolling with the die a number that is not occupied, the player has the choice to continue to roll the die or to stop and to hand over the die to their opponent. The…
In the light of the need to achieve a ranking which is understood by all tennis supporters, the ATP ranking is exposed to constant complaints from players and at the same time exposes new players to be benefited with a good tournament to be…
We investigate the probability of scoring a point when playing the basketball shooting game called "Horse". We show that under the Traditional Rules, it is optimal to choose very easy shots. We propose alternative rules called Pops Rules,…
The multiplication game is a two-person game in which each player chooses a positive integer without knowledge of the other player's number. The two numbers are then multiplied together and the first digit of the product determines the…
For a topological space $X$ and a point $x \in X$, consider the following game -- related to the property of $X$ being countably tight at $x$. In each inning $n\in\omega$, the first player chooses a set $A_n$ that clusters at $x$, and then…
We develop a Markov model of curling matches, parametrised by the probability of winning an end and the probability distribution of scoring ends. In practical applications, these end-winning probabilities can be estimated econometrically,…
Service sports include two-player contests such as volleyball, badminton, and squash. We analyze four rules, including the Standard Rule (SR), in which a player continues to serve until he or she loses. The Catch-Up Rule (CR) gives the…
We extend the fair machine learning literature by considering the problem of proportional centroid clustering in a metric context. For clustering $n$ points with $k$ centers, we define fairness as proportionality to mean that any $n/k$…
In many countries poker is one of the most popular card games. Although each variant of poker has its own rules, all involve the use of money to make the challenge meaningful. Nowadays, in the collective consciousness, some variants of…
The debate around bias in AI systems is central to discussions on algorithmic fairness. However, the term bias often lacks a clear definition, despite frequently being contrasted with fairness, implying that an unbiased model is inherently…
We analyze misere play of impartial tic-tac-toe---a game suggested by Bob Koca in which both players make X's on the board, and the first player to complete three-in-a-row loses. This game was recently discussed on mathoverflow.net in a…