Related papers: An impossibility theorem for paired comparisons

We study the conditions under which the iterated elimination of strictly dominated strategies is order independent and we identify a class of discontinuous games for which order does not matter. In this way, we answer the open problem…

Recently there has been much interest and progress in extending the definition of contextuality to systems with disturbance. We prove that such an endeavor cannot simultaneously satisfy the following principles: (1) any deterministic system…

We study the problem of aggregating individual preferences over alternatives into a collective ranking. A distinctive feature of our setting is that agents are matched to alternatives. Applications include rankings of colleges or academic…

Ranking systems produce ordered lists from scalar scores, yet the ranking itself depends only on pairwise comparisons. We develop a mathematical theory that takes this observation seriously, centering the analysis on pairwise margins rather…

We study the effects of randomness on competitions based on an elementary random process in which there is a finite probability that a weaker team upsets a stronger team. We apply this model to sports leagues and sports tournaments, and…

We propose a test of fairness in score-based ranking systems called matched pair calibration. Our approach constructs a set of matched item pairs with minimal confounding differences between subgroups before computing an appropriate measure…

Preference aggregation is a fundamental problem in voting theory, in which public input rankings of a set of alternatives (called preferences) must be aggregated into a single preference that satisfies certain soundness properties. The…

Possibility theory offers a framework where both Lehmann's "preferential inference" and the more productive (but less cautious) "rational closure inference" can be represented. However, there are situations where the second inference does…

In this paper, we consider the consistency of the desirability relation with the ranking of the players in a simple game provided by some well-known solutions, in particular the Public Good Index [14] and the criticality-based ranking [1].…

This study proposes a new efficiency requirement, a minimal almost weak Pareto principle, which says that x is socially better than y whenever the only one individual never prefers y to x, and all the others prefers x to y. Then, I show…

In this paper, we consider large-scale ranking problems where one is given a set of (possibly non-redundant) pairwise comparisons and the underlying ranking explained by those comparisons is desired. We show that stochastic gradient descent…

In the unidimensional unfolding model, given m objects in general position there arise 1+m(m-1)/2 rankings. The set of rankings is called the ranking pattern of the m given objects. By changing these m objects, we can generate various…

Real-world applications of machine learning tools in high-stakes domains are often regulated to be fair, in the sense that the predicted target should satisfy some quantitative notion of parity with respect to a protected attribute.…

Pairwise comparisons are an important tool of modern (multiple criteria) decision making. Since human judgments are often inconsistent, many studies focused on the ways how to express and measure this inconsistency, and several…

In many multiagent environments, a designer has some, but limited control over the game being played. In this paper, we formalize this by considering incompletely specified games, in which some entries of the payoff matrices can be chosen…

Estimating the dependences between random variables, and ranking them accordingly, is a prevalent problem in machine learning. Pursuing frequentist and information-theoretic approaches, we first show that the p-value and the mutual…

Uncertainty may be taken to characterize inferences, their conclusions, their premises or all three. Under some treatments of uncertainty, the inferences itself is never characterized by uncertainty. We explore both the significance of…

Rankings derived from pairwise comparisons are central to many economic and computational systems. In the context of large language models (LLMs), rankings are typically constructed from human preference data and presented as leaderboards…

A tournament is an oriented complete graph. The problem of ranking tournaments was firstly investigated by P. Erd\H{o}s and J. W. Moon. By probabilistic methods, the existence of "unrankable" tournaments was proved. On the other hand, they…

In this paper I present an argument and a general schema which can be used to construct a problem case for any decision theory, in a way that could be taken to show that one cannot formulate a decision theory that is never outperformed by…