Related papers: A Quantitative Arrow Theorem
The well-known Condorcet Jury Theorem states that, under majority rule, the better of two alternatives is chosen with probability approaching one as the population grows. We study an asymmetric setting where voters face varying…
It is shown that, since an ultrafilter over an operator-algebraically finite (i.e. isomorphic to the lattice of projectors of a finite Von Neumann algebra) quantum logic is not necessarily principal, Arrow's Impossibility Theorem doesn't…
We consider the social welfare function a la Arrow, where some voters are not qualified to evaluate some alternatives. Thus, the inputs of the social welfare function are the preferences of voters on the alternatives that they are qualified…
The classic Gibbard-Satterthwaite theorem says that every strategy-proof voting rule with at least three possible candidates must be dictatorial. Similar impossibility results hold even if we consider a weaker notion of strategy-proofness…
The well-known Condorcet's Jury theorem posits that the majority rule selects the best alternative among two available options with probability one, as the population size increases to infinity. We study this result under an asymmetric…
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…
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 critique the formulation of Arrow's no-dictator condition to show that it does not correspond to the accepted informal/intuitive interpretation. This has implications for the theorem's scope of applicability.
We consider a voting model, where a number of candidates need to be selected subject to certain feasibility constraints. The model generalises committee elections (where there is a single constraint on the number of candidates that need to…
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…
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…
The classical Arrow's Theorem answers "how can $n$ voters obtain a collective preference on a set of outcomes, if they have to obey certain constraints?" We give an analogue in the judgment aggregation framework of List and Pettit,…
The electoral criterion of independence of irrelevant alternatives, or IIA, states that a voting system is unacceptable if it would choose a different winner if votes were recounted after one of the losers had dropped out. But IIA confuses…
In 1950 Arrow famously showed that there is no social welfare function satisfying four basic conditions. In 1976, on the other hand, Gibbard and Sonnenschein showed that there does exist a unique probabilistic social welfare method that…
This paper builds upon the work of Dougherty and Heckelman (2020) by determining the frequency that 13 voting systems violate Arrow's social choice criteria with up to six alternatives. These results determine which of the 13 voting…
May's classical theorem states that in a single-winner choose-one voting system with just two candidates, majority rule is the only social choice function satisfying anonimity, neutrality and positive responsiveness axiom. Anonimity and…
We study the phenomenon of intransitivity in models of dice and voting. First, we follow a recent thread of research for $n$-sided dice with pairwise ordering induced by the probability, relative to $1/2$, that a throw from one die is…
One of quantum theory's salient features is its apparent indeterminism, i.e. measurement outcomes are typically probabilistic. We formally define and address whether this uncertainty is unavoidable or whether post-quantum theories can offer…
The Gibbard-Satterthwaite theorem states that no unanimous and non-dictatorial voting rule is strategyproof. We revisit voting rules and consider a weaker notion of strategyproofness called not obvious manipulability that was proposed by…
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…