On the manipulability of a class of social choice functions: plurality kth rules

In this paper we introduce the plurality kth social choice function selecting an alternative, which is ranked kth in the social ranking following the number of top positions of alternatives in the individual ranking of voters. As special case the plurality 1st is the same as the well-known plurality rule. Concerning individual manipulability, we show that the larger k the more preference profiles are individually manipulable. We also provide maximal non-manipulable domains for the plurality kth rules. These results imply analogous statements on the single non-transferable vote rule. We propose a decomposition of social choice functions based on plurality kth rules, which we apply for determining non-manipulable subdomains for arbitrary social choice functions. We further show that with the exception of the plurality rule all other plurality kth rules are group manipulable, i.e. coordinated misrepresentation of individual rankings are beneficial for each group member, with an appropriately selected tie-breaking rule on the set of all profiles.

Approval voting without ballot restrictions

We axiomatically study voting rules without making any assumption on the ballots that voters are allowed to cast. In this setting, we characterize the family of “endorsement rules,” which includes approval voting and the plurality rule, via the imposition of three normative conditions. The first condition is the well known social‐theoretic principle of consistency; the second one, unbiasedness, roughly requires social outcomes not to be biased toward particular candidates or voters; the last one, dubbed no single voter overrides, demands that the addition of a voter to an electorate cannot radically change the social outcome. Building on this result, we provide the first axiomatic characterization of approval voting without the approval balloting assumption. The informational basis of approval voting as well as its aggregative rationale are jointly derived from a set of conditions that can be defined on most of the ballot spaces studied in the literature.

User Localization in an Indoor Environment by Combining Different Algorithms through Plurality Rule

User localization in an indoor environment has a wide application area including production and service systems such as factories, smart homes, hospitals, nursing homes, etc. User localization based on Wi-Fi signals has been widely studied using various classification algorithms. In this type of problem, several Wi-Fi routers placed in an indoor environment provide signals with different strengths depending on the location/room of the user. Most classification algorithms successfully make the localization with a high accuracy rate. However, in the current literature, there is no widely accepted 'best' algorithm for solving this problem. This study proposes the use of the plurality rule to combine several classification algorithms and obtain a single result. Plurality voting rule is an electoral system where the candidate that polls the most vote wins the election. We apply the plurality rule to the indoor localization problem and generate the Majority algorithm. The Majority algorithm takes the 'votes' of five different classification algorithms and provides a single result through plurality rule. Results show that the mean accuracy rate of the Majority algorithm is higher than the classification algorithms it combines. In addition, we show that proving a single accuracy rate is not sufficient for declaring that an algorithm is better than the other. Classification algorithms select the training and test data randomly and different divisions result in different accuracy rates. In this study, we show that comparing the classification algorithms through confidence intervals provides more accurate information.

The effect of two-round presidential elections on human rights

Recent research suggests that democratic presidential elections held using a runoff rule produce presidents that are more likely to protect human rights, in comparison to those elected under plurality rule; with this follow-up article, I seek to highlight the importance of advancing to a runoff round for those elections held using a runoff rule. I find that for presidential democracies that already have a runoff rule in place, country-years where the president has been elected after a runoff round are more likely to be associated with high government respect for human rights, in comparison to country-years where the president has been elected after only one round (that could have advanced to a runoff round, but did not). This article provides decision-makers with more information regarding the human rights consequences of runoff rounds, so that the costs and benefits of adopting (or retaining) variations of a runoff rule can be better weighed.

Weighted voting on the IMF Managing Director

Executive Directors of the International Monetary Fund elect the Fund’s Managing Director from a shortlist of three candidates; financial quotas of IMF members define the respective numbers of votes. The implied a priori distribution of success (preference satisfaction) is compared across different electoral procedures. The USA’s Executive Director can expect to come closer to its top preference under plurality rule than for pairwise majority comparisons or plurality with a runoff; opposite applies to everybody else. Differences of US success between voting rules dominate the within-rule differences between most other Directors, and much of the latest reform of quotas.

Recognition Under Plurality Rule and the Paradox of Recognition in Burundi

This chapter examines the adoption and effects on peace of non-recognition under minority Tutsi rule and then recognition under plurality Hutu rule in Burundi. It reviews pre-civil-war history up to 1993, arguing that non-recognition arose from a “dilemma of recognition,” given Tutsi leaders’ concerns over mobilization effects. It discusses how the ethnic power configuration changed via the political ascendance of the Conseil national pour la défense de la démocratie-Forces pour la défense de la démocratie (CNDD-FDD) during the civil war and through to the 2005 constitution. This shift toward majority ethnic rule accompanied a transition toward recognition, consistent with the book’s theory. On the question of effects, introducing quotas for Hutus and Tutsis in government, military, and other institutions reduced the political salience of ethnicity, a phenomenon the chapter calls the “paradox of recognition.” This paradox challenges conflict management theories proposing that recognition entrenches the political salience of ethnic identity.

Under What Conditions Is Recognition Adopted?

This chapter tests a theory that emphasizes ethnic power configurations to explain the adoption or non-adoption of ethnic recognition in conflict-affected countries from 1990 to 2012. The analysis focuses on the adoption of ethnic recognition in constitutions or comprehensive political settlements. The main finding is that minority ethnic rule strongly predicts non-adoption. When a country is under minority rule, recognition is adopted only 24 percent of the time, as compared to plurality rule, under which recognition is adopted 60 percent of the time. This relationship is robust to controlling for a large number of potential confounding factors related to both domestic and international conditions. The relationship is strongest in countries where ethnic fractionalization is low, in which case minority groups differ most in their demographic share from plurality groups. The findings support the idea that ethnic power configurations are crucial for understanding the adoption of ethnic recognition.

Consistency of scoring rules: a reinvestigation of composition-consistency

We consider a collective choice problem in which the number of alternatives and the number of voters vary. Two fundamental axioms of consistency in such a setting, reinforcement and composition-consistency, are incompatible. We first observe that the latter implies four conditions each of which can be formulated as a consistency axiom on its own right. We find that two of these conditions are compatible with reinforcement. In fact, one of these, called composition-consistency with respect to non-clone winners, turns out to characterize a class of scoring rules which contains the Plurality rule. When combined with a requirement of monotonicity, composition-consistency with respect to non-clone winners uniquely characterizes the Plurality rule. A second implication of composition-consistency leads to a class of scoring rules that always select a Plurality winner when combined with monotonicity.