Measuring majority power and veto power of voting rules

We study voting rules with respect to how they allow or limit a majority from dominating minorities: whether a voting rule makes a majority powerful and whether minorities can veto the candidates they do not prefer. For a given voting rule, the minimal share of voters that guarantees a victory to one of the majority’s most preferred candidates is the measure of majority power; and the minimal share of voters that allows the minority to veto each of their least preferred candidates is the measure of veto power. We find tight bounds on such minimal shares for voting rules that are popular in the literature and used in real elections. We order the rules according to majority power and veto power. Instant-runoff voting has both the highest majority power and the highest veto power; plurality rule has the lowest. In general, the greater is the majority power of a voting rule, the greater its veto power. The three exceptions are: voting with proportional veto power, Black’s rule and Borda’s rule, which have relatively weak majority power and strong veto power, thus providing minority protection. Our results can shed light on how voting rules provide different incentives for voter participation and candidate nomination.

     

Voting power and voting blocs

We investigate the method of power indices to study voting power of members of a legislature that has voting blocs. Our analysis is theoretical, intended to contribute to a theory of positive political science in which social actors are motivated by the pursuit of power as measured by objective power indices. Our starting points are the papers by Riker (Behavioural Science, 1959, “A test of the adequacy of the power index”) and Coleman (American Sociological Review, 1973, “Loss of Power”). We argue against the Shapley–Shubik index and show that anyway the Shapley–Shubik index per head is inappropriate for voting blocs. We apply the Penrose index (the absolute Banzhaf index) to a hypothetical voting body with 100 members. We show how the power indices of individual bloc members can be used to study the implications of the formation of blocs and how voting power varies as bloc size varies. We briefly consider incentives to migrate between blocs. This technique of analysis has many real world applications to legislatures and international bodies. It can be generalised in many ways: our analysis is a priori (assuming formal voting and ignoring actual voting behaviour) but can be made empirical with voting data reflecting behaviour; it examines the consequences of two blocs but can easily be extended to more.     

The product paradox of voting power

We consider a system made up of two committees, with overlapping membership but with different rules for passing decisions; the passage of a joint resolution requires separate approval by each committee. We show that it is possible for one voter a to be stronger (have greater voting power) than another voter b in both of the two committees, while in the two-committee system (considered as a single composite entity) b is stronger than a. We argue that this apparently paradoxical phenomenon is inherent in the structure of the decision-making system in question, rather than being an artefact of any particular index used to measure voting power.     

A critical reappraisal of some voting power paradoxes

Power indices are meant to assess the power that a voting rule confers a priori to each of the decision makers who use it. In order to test and compare them, some authors have proposed ‘natural’ postulates that a measure of a priori voting power ‘should’ satisfy, the violations of which are called ‘voting power paradoxes.’ In this paper two general measures of success and decisiveness based on the voting rule and voters' behavior and some of these postulates/paradoxes test each other. As a result serious doubts are cast on the discriminating power of most voting power postulates.     

Efficacy,power and equity under approval voting

Approval voting allows each voter to vote for as many candidates as he wishes in a multicandidate election. Previous studies show that approval voting compares favorably with other practicable election systems. The present study examines the extent to which votes for different numbers of candidates can affect the outcome. It also considers generic powers of voters and the extent to which approval voting treats voters equitably. If there are three candidates, votes for one or two candidates are equally efficacious in large electorates. For four or more candidates, votes for about half the candidates are most efficacious. Although inequities among voters can arise under approval voting, the common plurality voting system is considerably less equitable than approval voting.     

A mathematical one-man one-vote rationale for Madisonian presidential voting based on maximum individual voting power

North Carolina state election law gives county election boards broad authority to determine the form of the ballot used in federal, state, and local races. This paper examines the extent to which ballot formats appear to be strategically chosen and the impact of ballot design on 1992 North Carolina elections. Our results indicate that the form of the ballot influenced the decisions of some voters in statewide races in 1992 and that the design of the ballot may have been chosen strategically by county election boards dominated by the members of one party.     

The effects of technical parties and partisan election management bodies on voting outcomes

Research on election integrity has noted the important role of election administration in facilitating free and fair practices. However, limited research has assessed how the staffing of polling station level election commissions may influence voting. Using extensive personnel and election data from Ukraine, this article investigates how partisanship and liberal registration rules permit major parties to “stack” election commissions with sympathetic officials. The empirical analysis demonstrates that the placement of representatives from major parties, or affiliated parties, in leadership positions on polling station commissions is associated with improved election outcomes.     

Class voting and left voting in Scandinavia

Abstract. This article examines the effects of different definitions of the working class on the measurement of class voting and left voting in Denmark, Norway and Sweden. First, the similarities and differences in how the working class has been operationalized in the three countries are summarized. To determine the effects of different operationalizations, Swedish election survey data are recoded to conform more closely to the classification procedures used in Danish and Norwegian studies. The analysis shows that if a similar operationalization is used, the level of left voting in both the Swedish working and middle classes increases and the Alford index of class voting declines. Class voting and left voting in the younger and older generations and among women and men are also discussed. Dissimilar patterns of class voting and left voting among women in the three countries are largely a product of different classification schemes. The concluding discussion points to a number of problems in using the Alford index as a summary statistic in cross-national comparisons.     

Is the allocation of voting power among EU states fair?

It has often been claimed that the current allocation of votes among EU states is not fair. In this paper we verify this assertion by carrying out an evaluation of the distribution of power among the member states. The results show that the current distribution of votes for the qualified majority does not lead to a fair distribution of power whatever definition of the EU is considered. It can not be claimed however that the current voting process has a systematic bias in favor of certain states. We also present a simple method to derive voting weights which lead to a fair allocation of power.     

Robust voting

The formal equivalence between social choice and statistical estimation means that criteria used to evaluate estimators can be interpreted as features of voting rules. The robustness of an estimator means, in the context of social choice, insensitivity to departures from majority opinion. In this paper we consider the implications of substituting the median, a robust, high breakdown estimator, for Borda's mean. The robustness of the median makes the ranking method insensitive to outliers and reflect majority opinion. Among all methods that satisfy a majority condition, median ranks is the unique one that is monotonic. It is an attractive voting method when the goal is the collective assessment of the merits of alternatives.     

Approval voting in practice

Several leading professional associations have recently decided to use approval voting (AV). The largest of them, The Institute of Electrical and Electronics Engineers, Inc. (IEEE), with more than 300,000 members, adopted AV in response to practical political problems with conventional plurality elections of precisely the sort that AV was designed to solve. This paper analyzes results of the first three multicandidate elections conducted by the IEEE using the new system. Issues examined include participation rates, use of multiple votes, patterns of shared support, majority rule, AV-dominance, effects on outcomes, and encouragement of candidate entry. In general, AV appears to have had a successful test.