How Borda voting rule can respect Arrow IIA and avoid cloning manipulation

Abstract. This paper proposes a new formulation of the Borda rule in order to deal with the problem of cloning manipulation. This new Borda voting specification will be named: Dynamic Borda Voting (DBV) and it satisfies Arrow's IIA condition. The calculations, propositions with proof and explanations are made to show the effectiveness of this method. From DBV, the paper presents a method to measure and quantify the magnitude of the shock due to change in irrelevant alternatives over a scale moving from 0 to 100.Keywords. Voting rules, Arrow IIA, Cloning manipulation.JEL. C60, D70, D80

The effects of closeness on the election of a pairwise majority rule winner

Some studies have recently examined the effect of closeness on the probability of observing the monotonicity paradox in three-candidate elections under Scoring Elimination Rules. It has been shown that the frequency of such paradox significantly increases as elections become more closely contested. In this paper we consider the effect of closeness on one of the most studied notions in Social Choice Theory: The election of the Condorcet winner, i.e., the candidate who defeats any other opponent in pairwise majority comparisons, when she exists. To be more concrete, we use the well known concept of the Condorcet efficiency, that is, the conditional probability that a voting rule will elect the Condorcet winner, given that such a candidate exists. Our results, based on the Impartial Anonymous Culture (IAC) assumption, show that closeness has also a significant effect on the Condorcet efficiency of different voting rules in the class of Scoring and Scoring Elimination Rules

How Borda voting rule can respect Arrow IIA and avoid Cloning manipulation

This paper proposes a new formulation of the Borda rule in order to deal with the problem of cloning manipulation. This new Borda voting specification will be named: Dynamic Borda Voting (DBV) and it satisfies Arrow's IIA condition. The calculations, propositions with proof and explanations are made to show the effectiveness of this method. From DBV, the paper presents a method to measure and quantify the magnitude of the shock due to change in irrelevant alternatives over a scale moving from 0 to 100

How Borda voting rule can respect Arrow IIA and avoid Cloning manipulation

This paper proposes a new formulation of the Borda rule in order to deal with the problem of cloning manipulation. This new Borda voting specification will be named: Dynamic Borda Voting (DBV) and it satisfies Arrow's IIA condition. The calculations, propositions with proof and explanations are made to show the effectiveness of this method. From DBV, the paper presents a method to measure and quantify the magnitude of the shock due to change in irrelevant alternatives over a scale moving from 0 to 100

Monotonicity paradoxes in three-candidate elections using scoring elimination rules

International audienceScoring elimination rules (SER), that give points to candidates according to their rank in voters’ preference orders and eliminate the candidate(s) with the lowest number of points, constitute an important class of voting rules. This class of rules, that includes some famous voting methods such as Plurality Runoff or Coombs Rule, suffers from a severe pathology known as monotonicity paradox or monotonicity failure, that is, getting more points from voters can make a candidate a loser and getting fewer points can make a candidate a winner. In this paper, we study three-candidate elections and we identify, under various conditions, which SER minimizes the probability that a monotonicity paradox occurs. We also analyze some strategic aspects of these monotonicity failures. The probability model on which our results are based is the impartial anonymous culture condition, often used in this kind of study