An Empirical Comparison of the Performance of Classical Power Indices

Power indices are general measures of the relative a priori voting power of individual members of a voting body. They are useful for both positive and normative analysis of voting bodies particularly those using weighted voting. This paper applies new algorithms for computing the rival Shapley-Shubik and Banzhaf indices for large voting bodies to shareholder voting power in a cross section of British companies. Each company is a separate voting body and there is much variation in ownership between them resulting in different power structures. Because the data are incomplete, both finite and 'oceanic' games of shareholder voting are analysed. The indices are appraised, using reasonable criteria, from the literature on corporate control. The results are unfavourable to the Shapley-Shubik index and suggest that the Banzhaf index much better reflects the variations in the power of shareholders between companies as the weights of shareholder blocs vary.     

The Distribution of A Priori Voting Power in the EC Council of Ministers and the European Parliament

One of the most important decision making bodies in the EC is the Council of Ministers. In that voting body the member states have different voting weights roughly in proportion to the size of their populations. This article focuses on the voting power of current and prospective member states (Finland, Norway and Sweden) utililizing the Shapley-Shubik and Banzhaf indices of voting power. As the decision rules play a crucial role in the computation of these indices, the a priori voting power distribution is considered under various decision rules ranging from simple majority to near unanimity. We also discuss the a priori voting power distribution of various political groupings in the current European Parliament and in the hypothetical parliament which would have Finland, Norway and Sweden as new members. Although thus far the real power base in the EC is the Commission, the analysis of voting power distributions in the Council of Ministers and in the parliament sheds some light upon the relative influence that various actors might have in EC decision-making processes.     

The inevitability of the “paradox of redistribution” in the allocation of voting weights

In voting bodies, when voting weights are reallocated, it may be observed that the voting power of some members, as measured by the Shapley-Shubik and Banzhaf power indices, increases while their voting weight decreases. By a simple constructive proof, this paper shows that such a “paradox of redistribution” can always occur in any voting body if the number of voters, n, is sufficiently large. Simulation results show that the paradox is quite frequent (up to 30 percent) and increases with n (at least for small n). Examples are given where the Banzhaf and Shapley-Shubik indices are not consistent in demonstrating the paradox.     

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.     

A priori power measures and the institutions of the European Union

Abstract. The a priori voting powers of member countries in the council of ministers of the European Union have been discussed in the literature mainly from the view–point of Banzhaf and Shapley–Shubik indices. This paper discusses — in the light of these and other more recent (Colomer's, Holler's as well as Deegan and Packel's) power indices — the interaction of the council ministers and the European Parliament (EP) under the assumption that the consent of both bodies is needed to carry a motion or piece of union–wide legislation. Moreover, the double–majority principle is discussed from the view–point of voting power distribution. Finally we consider the voting power distribution in a three–chamber system consisting of Commission, Council and EP.     

REPRESENTATIVE IDEOLOGY AND THE VOTE FOR WELFARE REFORM

This article examines the congressional vote for HR3734, The Personal Responsibility and Work Opportunity Reconciliation Act of 1996. The primary concern is to identify the factors that had a significant influence over the voting decision, paying special attention to representative ideology measured by Americans for Democratic Action and American Conservative Union voting scores. An empirical model is developed and estimated using logistic regression. The model incorporates proxies for representative ideology, constituent ideology, constituent economic interests, and the potential for legislative shirking. The results indicate that representative ideology was an important factor in the vote, but that constituent ideology and interests were also influential. Knowledge of the pattern of voting on the original legislation should prove useful to policymakers as the need for further refinement of the welfare system becomes evident, as it almost surely will.     

Robust satisficing voting: why are uncertain voters biased towards sincerity?

The modern theory of voting usually regards voters as expected utility maximizers. This implies that voters define subjective probabilities and utilities for different outcomes of the elections. In real life, these probabilities and utilities are often highly uncertain, so a robust choice, immune to erroneous assumptions, may be preferred. We show that a voter aiming to satisfice his expected utility, rather than maximize it, may present a bias for sincere voting, as opposed to strategic voting. This may explain previous results which show that strategic voting is not as prevalent as would be expected if all voters were expected utility maximizers.     

Politics, Economics and the Measurement of Power

To what extent is political power fundamentally different from or, alternatively, comparable to economic power? While it is true that the basic institutions of democratic political life - the electoral arena and the sovereign representative assembly - differ from such capitalist economic institutions as the market and the joint-stock company, the logic of the power game which takes place in both settings is quite similar. In both institutions power will be a function of the capacity to enter decisive coalitions with other players: individuals, political parties, stockholders or groups of stockholders. Power indices may therefore be employed in order to reveal aspects of the strategic gaming that takes place both in representative assemblies and at yearly stockholders' meetings. This article discusses and compares various quantitative measures of voting power in the two kinds of voting bodies.     

A note on calculating Condorect probabilities

Probability voting models arrive at important conclusions on the paradox of voting. The computation of the probabilities uses the Selby relations for sums of powers of integers. The integers are essentially the number of voters with linear preference orderings. With an ordered set of integers the equation implicit in these calculations may have to be amended.     

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.

     

Whether one votes and how one votes

The aim of this paper is to determine if whether one votes effects the vote that is cast. Using an economic model of voting and observed voting results on nuclear power referenda, the answer is a resounding yes. Overcoming registration, turnout, and “roll off” hurdles dramatically increases the odds of voting against nuclear power. Indeed, participation swamps both economic and preference variables in the explanation of nuclear power voting outcomes. The lesson is that there is a structure to participation at the polls that should not be ignored by those interested in analyzing voting outcomes.     

The ideological component of Senate voting: Different principles or different principals?

Evidence exists on both sides of the question of whether or not legislator-specific, ideologically-driven shirking of constituent interest occurs. In this paper, we use a well-known model of such shirking by senators as our point of departure and add measures of inter-state constituent interests, the role of campaign contributions and, hence, the importance of whether or not senators are up for reelection. We find some evidence that the model provides a stronger explanation for senators up for reelection than for those who are not and that campaign contributions help determine voting decisions by these legislators. Finally, accounting for inter-state constituent interests, shirking is not a significant variable in the voting decisions of senators facing reelection. Thus, it appears that the reelection interests of some senators have been mistaken for ideologically-driven shirking.     

Probabilistic Voting and Equilibrium: An Impossibility Result

The introduction of voters' uncertainty alone is in no way sufficient to guarantee an equilibrium outcome of a voting process. What is needed in addition is the assumption that the voting probabilities depend strictly convex respectively concave of the utility losses caused by the proposed policies of the different parties. This assumption is, however, not compatible with an unrestricted policy space, and it has to be rejected for theoretical as well as empirical reasons. Thus, using models of probabilistic voting we still have to accept that cycles can arise and electoral outcomes are prone to manipulation via agenda setting.     

A Priori Voting Power: What Is It All About?

We explain the meaning of a priori voting power and outline how it is measured. We distinguish two intuitive notions as to what voting power means, leading to two approaches to measuring it. One conception, I-power, focuses on a voter's potential influence over the outcome of decisions by a voting body. The second conception, P-power, focuses on voters' payoff, their expected share of a fixed winning 'prize'. We discuss and rebut some philosophical and pragmatic objections, according to which a priori (as distinct from actual) voting power is worthless or inapplicable.     

Explanations of protectionism in international trade votes

In this study, we analyze the voting records of U.S. senators on three recent international trade bills. Our objective is to assess the importance of ideology and constituent interest as forces that influence protectionist vs. free trade voting behavior. The methodology uses discriminant analysis supplemented with expert judgement. The first conclusion is that ideology is the more important force in generic protectionism issues, and local constituent interests are more important for commodity-specific issues. Second, we find that protectionism is especially associated with liberal ideology, high import impact, and low export dependence. Although the discriminant analysis outperforms expert judgement in classifying protectionist vs. free trade votes in two of the three bills studied, the best explanation is obtained by using both methods together.We are indebted to Dennis Quinn, Tom Brewer, Michael Czinkota, Karen Gaertner, Annette Shelby, and Melanie Hayes. Errors remain our responsibility.     

Donald Trump,contempt, and the 2016 GOP Iowa Caucuses

ABSTRACT

Theories of discrete emotions distinguish contempt from other negative emotions, and recent evidence shows that contempt toward candidates played a major role in two US Senate races in 2014. Contempt felt by respondents was the most significant emotion predicting voting against three of the four major party candidates, and had effects independent of other emotions, such as anger, anxiety, and hope. In the present paper, the 2016 Republican Iowa Caucus provides the opportunity to examine contempt in a different context: an intra-party primary campaign, where candidates share the important characteristic of party affiliation. We find that while voters perceived all leading GOP candidates as expressing at least some contempt, Donald Trump was seen as expressing the most contempt by far. Voters also felt contempt for at least some candidates of their own party. When they did so, it predicts significantly lowered probabilities of voting for Cruz, Trump, and Rubio, and increased probabilities of voting for one or more of their opponents. Implications of these findings for theory and research on the role of contempt and other specific emotions in voting behavior are discussed.     

Flexible Integration,EMU and Relative Voting Power in the EU

This paper studies the implications offlexible integration in the European Union. Itanalyses the voting power of member states in theCouncil of Ministers when differently sized subgroupsof the EU are set up. European Monetary Union isreferred to as the most important example of flexibleintegration. The Banzhaf-Index is calculated to studythe distribution of voting power in the decisionmaking process according to the stability and growthpact. The results show considerable fluctuations,especially for smaller countries, in relative votingpower, the latter being defined as the relationbetween voting power and relative voting weight.     

How elections matter: A study of U.S. senators

Policy representation implies not only congruence between constituent and representative preferences, but also the ability of representatives to perceive and adjust to changing constituent preferences. This paper examines the extent of such representation among U.S. senators. It shows that a senator's voting behavior strongly affects his chances of election, but that senators demonstrate only a limited ability to adapt to changing constituent preferences.