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Recently, it has been emphasized that the possibility theory framework allows us to distinguish between i) what is possible because it is not ruled out by the available knowledge, and ii) what is possible for sure. This distinction may be…
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…
Among the various aspects of algorithmic fairness studied in recent years, the tension between satisfying both \textit{sufficiency} and \textit{separation} -- e.g. the ratios of positive or negative predictive values, and false positive or…
A celebrated impossibility result by Myerson and Satterthwaite (1983) shows that any truthful mechanism for two-sided markets that maximizes social welfare must run a deficit, resulting in a necessity to relax welfare efficiency and the use…
For a first-order theory $T$, the Constraint Satisfaction Problem of $T$ is the computational problem of deciding whether a given conjunction of atomic formulas is satisfiable in some model of $T$. In this article we develop sufficient…
The impossibility theorem in Roth (1982) states that no stable mechanism satisfies strategy-proofness. This paper explores the Machiavellian frontier of stable mechanisms by weakening strategy-proofness. For a fixed mechanism $\varphi$ and…
The paper deals with two issues: the existence of universal models of a theory T and related properties when cardinal arithmetic does not give this existence offhand. In the first section we prove that simple theories (e.g., theories…
The theory of optimal choice sets is a solution theory that has a long and well-established tradition in social choice and game theories. Some of important general solution concepts of choice problems when the set of best alternatives does…
This paper studies the strategic manipulation of set-valued social choice functions according to Kelly's preference extension, which prescribes that one set of alternatives is preferred to another if and only if all elements of the former…
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.…
We demonstrate that individual behaviors directed at the attainment of distinctiveness can in fact produce complete social conformity. We thus offer an unexpected generative mechanism for this central social phenomenon. Specifically, we…
The field of algorithmic fairness has rapidly emerged over the past 15 years as algorithms have become ubiquitous in everyday lives. Algorithmic fairness traditionally considers statistical notions of fairness algorithms might satisfy in…
We note a parallel between some ideas of stable model theory and certain topics in finite combinatorics related to the sum-product phenomenon. For a simple linear group G, we show that a finite subset X with |X X \^{-1} X |/ |X| bounded is…
The Algebraic Dichotomy Conjecture states that the Constraint Satisfaction Problem over a fixed template is solvable in polynomial time if the algebra of polymorphisms associated to the template lies in a Taylor variety, and is NP-complete…
The key contribution of the paper is a comprehensive study of the egalitarian mechanism with respect to manipulation by a coalition of agents. Our main result is that the egalitarian mechanism is, in fact, peak group strategyproof : no…
The ability to reason under uncertainty and with incomplete information is a fundamental requirement of decision support technology. In this paper we argue that the concentration on theoretical techniques for the evaluation and selection of…
In the standard arrovian framework and under the assumption that individual preferences and social outcomes are linear orders on the set of alternatives, we study the rules which satisfy suitable symmetries and obey the majority principle.…
Statistical parity metrics have been widely studied and endorsed in the AI community as a means of achieving fairness, but they suffer from at least two weaknesses. They disregard the actual welfare consequences of decisions and may…
Using a long-standing conjecture from combinatorial group theory, we explore, from multiple perspectives, the challenges of finding rare instances carrying disproportionately high rewards. Based on lessons learned in the context defined by…
Two important requirements when aggregating the preferences of multiple agents are that the outcome should be economically efficient and the aggregation mechanism should not be manipulable. In this paper, we provide a computer-aided proof…