Related papers: Arrow's Impossibility Theorem as a Generalisation …
Arrow's `impossibility' theorem asserts that there are no satisfactory methods of aggregating individual preferences into collective preferences in many complex situations. This result has ramifications in economics, politics, i.e., the…
Arrow's Theorem concerns a fundamental problem in social choice theory: given the individual preferences of members of a group, how can they be aggregated to form rational group preferences? Arrow showed that in an election between three or…
Preference cycles are prevalent in problems of decision-making, and are contradictory when preferences are assumed to be transitive. This contradiction underlies Condorcet's Paradox, a pioneering result of Social Choice Theory, wherein…
Incomputability results in Formal Logic and the Theory of Computation (i.e., incompleteness and undecidability) have deep implications for the foundations of mathematics and computer science. Likewise, Social Choice Theory, a branch of…
A central theme in social choice theory is that of impossibility theorems, such as Arrow's theorem and the Gibbard-Satterthwaite theorem, which state that under certain natural constraints, social choice mechanisms are impossible to…
Arrow's Impossibility Theorem establishes bounds on what we can require from voting systems. Given satisfaction of a small collection of "fairness" axioms, it shows votes can only exist as dictatorships in which one voter determines all…
To the best of our knowledge, a complete characterization of the domains that escape the famous Arrow's impossibility theorem remains an open question. We believe that different ways of proving Arrovian theorems illuminate this problem.…
We propose a quantum voting system, in the spirit of quantum games such as the quantum Prisoner's Dilemma. Our scheme enables a constitution to violate a quantum analog of Arrow's Impossibility Theorem. Arrow's Theorem is a claim proved…
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…
Let X be a finite set of alternatives. A choice function c is a mapping which assigns to nonempty subsets S of X an element c(S) of S. A rational choice function is one for which there is a linear ordering on the alternatives such that c(S)…
There is an extensive literature in social choice theory studying the consequences of weakening the assumptions of Arrow's Impossibility Theorem. Much of this literature suggests that there is no escape from Arrow-style impossibility…
Arrow's Impossibility Theorem states that any constitution which satisfies Independence of Irrelevant Alternatives (IIA) and Unanimity and is not a Dictator has to be non-transitive. In this paper we study quantitative versions of Arrow…
We generalize the Arrow's impossibility theorem--a key result in social choice theory--to the setting where the arity $k$ of the relation under consideration is greater than $2$. Some special but natural properties of $k$-ary relations are…
This paper presents some fundamental collective choice theory for information system designers, particularly those working in the field of computer-supported cooperative work. This paper is focused on a presentation of Arrow's Possibility…
Arrow's Impossibility Theorem states that any constitution which satisfies Transitivity, Independence of Irrelevant Alternatives (IIA) and Unanimity is a dictatorship. Wilson derived properties of constitutions satisfying Transitivity and…
Judgment aggregation studies how to combine individual judgments on logically related propositions into a collective judgment. Classical impossibility results show that sufficiently strong logical interconnections force dictatorship under…
We develop a framework that leverages the smoothed complexity analysis by Spielman and Teng to circumvent paradoxes and impossibility theorems in social choice, motivated by modern applications of social choice powered by AI and ML. For…
In social choice theory with ordinal preferences, a voting method satisfies the axiom of positive involvement if adding to a preference profile a voter who ranks an alternative uniquely first cannot cause that alternative to go from winning…
Revised proofs of Kenneth Arrow's impossibility theorem have been presented in prose form, incorporating novel ideas such as decisive sets and pivotal voters. This study develops another approach to proving the theorem. Using a proof…
This paper provides a general framework to explore the possibility of agenda manipulation-proof and proper consensus-based preference aggregation rules, so powerfully called in doubt by a disputable if widely shared understanding of Arrow's…