Related papers: An impossibility theorem for paired comparisons
We consider N quantum systems initially prepared in pure states and address the problem of unambiguously comparing them. One may ask whether or not all $N$ systems are in the same state. Alternatively, one may ask whether or not the states…
The standard definition formula for probabilities of independent events is derived as a consequence of the Insufficient Reason Principle expressed as the Maximum Relative Divergence Principle for grading (order-comonotonic) functions on a…
We consider a decision-making problem to evaluate absolute ratings of alternatives from the results of their pairwise comparisons according to two criteria, subject to constraints on the ratings. We formulate the problem as a bi-objective…
Pairwise comparisons are a well-known method for the representation of the subjective preferences of a decision maker. Evaluating their inconsistency has been a widely studied and discussed topic and several indices have been proposed in…
Preference Inference involves inferring additional user preferences from elicited or observed preferences, based on assumptions regarding the form of the user's preference relation. In this paper we consider a situation in which…
We propose new results for the existence and uniqueness of a general nonparametric and nonseparable competitive equilibrium with substitutes. These results ensure the invertibility of a general competitive system. The existing literature…
In this work, we propose a theory for information matching. It is motivated by the observation that retrieval is about the relevance matching between two sets of properties (features), namely, the information need representation and…
The emergence of increasingly sophisticated artificial intelligence (AI) systems have sparked intense debate among researchers, policymakers, and the public due to their potential to surpass human intelligence and capabilities in all…
The hiring problem is studied for general strategies based only on the relative ranking of the candidates; this includes some well known strategies studied before such as hiring above the median. We give general limit theorems for the…
This paper is devoted to the bipartite ranking problem, a classical statistical learning task, in a high dimensional setting. We propose a scoring and ranking strategy based on the PAC-Bayesian approach. We consider nonlinear additive…
In this work we generalize standard Decision Theory by assuming that two outcomes can also be incomparable. Two motivating scenarios show how incomparability may be helpful to represent those situations where, due to lack of information,…
Recent discussion in the public sphere about algorithmic classification has involved tension between competing notions of what it means for a probabilistic classification to be fair to different groups. We formalize three fairness…
This paper considers the problem of ranking objects based on their latent merits using data from pairwise interactions. We allow for incomplete observation of these interactions and study what can be inferred about rankings in such…
With the increasing pervasive use of machine learning in social and economic settings, there has been an interest in the notion of machine bias in the AI community. Models trained on historic data reflect biases that exist in society and…
Performance analysis is crucial in optimization research, especially when addressing black-box problems through nature-inspired algorithms. Current practices often rely heavily on statistical methods, which can lead to various logical…
In social choice theory, anonymity (all agents being treated equally) and neutrality (all alternatives being treated equally) are widely regarded as ``minimal demands'' and ``uncontroversial'' axioms of equity and fairness. However, the ANR…
We propose a game-theoretic framework that incorporates both incomplete information and general ambiguity attitudes on factors external to all players. Our starting point is players' preferences on payoff-distribution vectors, essentially…
Proportionality is an attractive fairness concept that has been applied to a range of problems including the facility location problem, a classic problem in social choice. In our work, we propose a concept called Strong Proportionality,…
This paper studies the problem of finding the exact ranking from noisy comparisons. A comparison over a set of $m$ items produces a noisy outcome about the most preferred item, and reveals some information about the ranking. By repeatedly…
We construct several definitions of imbalance and playability, both of which are related to the existence of dominated strategies. Specifically, a maximally balanced game and a playable game cannot have dominated strategies for any player.…