Ameliorating Majority Decisiveness through Expression of Preference Intensity

Abstract

I n pairwise voting, when a simple majority rule produces a winner, that winner is robust to the minority's preferences. The typical means of protecting the minority from the decisiveness of the majority is by increasing the required majority or by augmenting the simple majority rule with constitutional constraints. In the former case the required majority q becomes larger than one-half, and this implies that the q-majority rule becomes biased in favor of one of the alternatives, usually the status quo. In the latter case the augmented rule becomes biased in favor of the minority. The main issue examined in this paper is whether the amelioration of majority decisiveness can be attained by unbiased voting rules that allow some restricted expression of preference intensities. Our results clarify that the use of scoring rules provides a positive answer to the above question when voters resort to variable degrees of coordinated strategic voting. The results are illustrated in the special cases of the plurality and the Borda rules.

Condorcet vs. Borda in Light of a Dual Majoritarian Approach

“…This rule occupies a special place among all positional scoring rules since it is less susceptible than all other rules to many unsettling possibilities and anomalies, Brams and Fishburn (2002), Nurmi (1999) and Saari (2001). Under the Borda rule a simple majority of ½ is not decisive, however, as shown by Baharad and Nitzan (2002), a special majority is decisive. 7 We measure the severity of the specialmajority decisiveness under the Borda rule, SMD B , in a similar manner to SMD, (see equation (6)):…”

“…Our analysis focuses on one of the drawbacks of these rules, namely, their disregard of the minority preferences. Baharad and Nitzan (2002) have studied this drawback clarifying how it can be ameliorated by applying unbiased scoring rules. The proposed resolution of the problem associated with majority decisiveness is, nevertheless, incomplete as argued in Baharad and Nitzan (2007).…”

Approval voting reconsidered

“…It has been shown in Baharad and Nitzan (2002) where α is assumed to be a fraction with a denominator n and S denotes the average of the scores S 2 , … ,S k-1 (that is, the average score of all the candidates but the top ranked one). Based on equations (1) and (2), the first drawback of approval voting, namely its vulnerability to majority decisiveness can be easily established:…”

The Costs of Implementing the Majority Principle: The Golden Voting Rule

“…As recently shown by Baharad and Nitzan (2002), these properties enable scoring rules to eliminate the decisiveness ('tyranny') of certain majorities, even under coordinated strategic voting. Their main result calls attention to the possible amelioration of majority decisiveness by scoring rules.…”