Related papers: An impossibility theorem for paired comparisons
In a recent paper, Bruhn, Diestel, Kriesell and Wollan (arXiv:1003.3919) present four systems of axioms for infinite matroids, in terms of independent sets, bases, closure and circuits. No system of rank axioms is given. We give an easy…
In many areas of engineering and sciences, decision rules and control strategies are usually designed based on nominal values of relevant system parameters. To ensure that a control strategy or decision rule will work properly when the…
We study the problem of learning to rank from pairwise preferences, and solve a long-standing open problem that has led to development of many heuristics but no provable results for our particular problem. Given a set $V$ of $n$ elements,…
While PageRank has been extensively used to rank sport tournament participants (teams or individuals), its superiority over simpler ranking methods has been never clearly demonstrated. We use sports results from 18 major leagues to…
We study a random dynamical system such that one transformation is randomly selected from a family of transformations and then applied on each iteration. For such random dynamical systems, we consider estimates of absolutely continuous…
We analyse a mathematical model of seeding for sports contests with round-robin qualifying tournaments. The standard seeding system based on coefficients measuring the historical performance of the teams is shown to be unfair as it might…
Probabilistic properties of tennis scoring systems are examined and compared with best-of-K systems. A model, where each player has his/her own probability of winning his/her service point and which remains invariant for the duration of the…
A novel approach for solving a multiple judge, multiple criteria decision making (MCDM) problem is proposed. The ranking of alternatives that are evaluated based on multiple criteria is difficult, since the presence of multiple criteria…
In many real-world settings, institutions can and do adjust the consequences attached to algorithmic classification decisions, such as the size of fines, sentence lengths, or benefit levels. We refer to these consequences as the stakes…
Pairwise comparisons are a well-known method for modelling of the subjective preferences of a decision maker. A popular implementation of the method is based on solving an eigenvalue problem for M - the matrix of pairwise comparisons. This…
Deciding which large language model (LLM) to use is a complex challenge. Pairwise ranking has emerged as a new method for evaluating human preferences for LLMs. This approach entails humans evaluating pairs of model outputs based on a…
A \emph{fair competition}, based on the concept of envy-freeness, is a non-eliminating competition where each contestant (team or individual player) may not play against all other contestants, but the total difficulty for each contestant is…
No feature ranking can be simultaneously faithful, stable, and complete when features are collinear. For collinear pairs, ranking reduces to a coin flip. We prove this impossibility, quantify it for four model classes, resolve it via…
A group of individuals wishes to classify $m$ objects into $n$ categories in such a way that no class is left empty, a condition known as surjectivity. The opinions of the individuals are aggregated separately for each object using an…
Fairness has emerged as an important consideration in algorithmic decision-making. Unfairness occurs when an agent with higher merit obtains a worse outcome than an agent with lower merit. Our central point is that a primary cause of…
In party-approval multiwinner elections the goal is to allocate the seats of a fixed-size committee to parties based on the approval ballots of the voters over the parties. In particular, each voter can approve multiple parties and each…
This paper examines games with strategic complements or substitutes and incomplete information, where players are uncertain about the opponents' parameters. We assume that the players' beliefs about the opponent's parameters are selected…
Impartial selection problems are concerned with the selection of one or more agents from a set based on mutual nominations from within the set. To avoid strategic nominations of the agents, the axiom of impartiality requires that the…
Preference rankings virtually appear in all field of science (political sciences, behavioral sciences, machine learning, decision making and so on). The well-know social choice problem consists in trying to find a reasonable procedure to…
The paper aims at analyzing the least squares ranking method for generalized tournaments with possible missing and multiple paired comparisons. The bilateral relationships may reflect the outcomes of a sport competition, product…