Power, Voting, and Voting Power: 30 Years After

The relation between social power and negative freedom is examined, assuming Stoppino’s formal classification of power and a ‘pure’ negative conception of freedom. The aim is twofold: first, to clarify whether and (if so) in what ways a person’s negative freedom is diminished when others exercise power over her, thus arriving at an exhaustive analysis of the power-freedom relation on the basis of Stoppino’s classification; secondly, to correct the common misconception according to which a person’s pure negative freedom is diminished only by violence or its threat, and not by less evident forms of power.

This note examines the application of the concept of causation to the con-struction of power indices. It is argued that if the modeling of power relations should capture the causal factors of an outcome then a power index should be based only on the set of minimal winning coalitions. The argument refers to Mackie’s inus conditions.

We discuss two inter-related puzzling features of the literature on a priori voting power. First, the mathematical model used in virtually all this literature does not recognize abstention as an option distinct from both a ‘yes’ and a ‘no’ vote. Second, real-life decision rules of voting bodies—in particular the US legislature and the UN Security Council—are misrepresented as though they did not allow abstention as a

tertium quid

. We suggest that these misrepresentations may be examples of what philosophers of science call ’theory-laden observation’.

This chapter uses quantile regression to uncover variations in the strength of the relationship between the expected closeness of the outcome, size of the electorate and voter turnout in Norwegian school language referendums. Referendums with a low turnout show a weak positive effect of closeness and a strong negative effect of size, the opposite being true of referendums with a high turnout. The results substantiate the marginalist defense of the Downsian rational voter hypothesis, which asserts that, while closeness and size cannot explain the absolute level of turnout, they can account for change at the margin.

The standard democratic methods are unable to take the intensities of preferences into account. This is seen as a problem both in the theory of social choice and in the philosophy of democracy. The Borda count is sometimes defended as a rule which is able to take intensity differences into account. Here, it is argued that some defences of the Borda rule are based on the view that the basic task of voting rules is to aggregate information. In voting, however, there are two aspects which are not equally relevant other contexts: the requirements of democracy, and the interaction between the aggregation method and the input of aggregation. Voting should be conceptualized as an exercise of power. Arguments for Borda may be convincing in some contexts, but not necessarily in voting contexts.

Can fewer votes win more seats? In the 2008 local elections in the German State of Bavaria the trick worked, thirty-six times. The year 2009 invites party officials in the German States of Rhineland-Palatia, the Saarland, and Thuringia to play the game. The name of the game is

list apparentements

. We show what it is about.

The credibility of voting power theory is undermined by the lack of clarity about the precise specification of the underlying collective decision-making situation. We propose a basic distinction between two scenarios in which a committee can make decisions under a voting rule. In a ‘take-it-or-leave-it’ scenario the committee has only the choice of accepting or rejecting by vote proposals submitted from outside, while in a ‘bargaining’ committee negotiation is feasible and the voting rule conditions it by imposing which groups of voters can enforce any agreement. From these two points of view we reinterpret and critically review the foundations and normative recommendations of voting power theory.

When studying the constitutional choice of European voting rules, most power index analyses concentrate on member states’ relative decisiveness for forming winning coalitions in the Council of Ministers. These studies have two shortcomings: (a) They ignore the distribution of relative power between the Commission, the Council of Ministers and the European Parliament, as defined by the multi-cameral European legislative procedures. (b) They disregard the absolute notion of power, which is dependent on the inclusion of member states in winning coalitions under various voting rules. In this article we present our approach on member states’ constitutional choice of European voting rules with regard to the two notions of power: actors’ relative decisiveness and their absolute inclusiveness in decision making. We present an index to measure inclusiveness and apply our concept to the European multi-cameral legislature. On the basis of our study, we present a reasoned account of motives behind member states’ recent institutional reforms of legislative procedures.

The problem of seat apportionment in electoral systems turns out to be quite complex, since no apportionment method exists which succeeds in verifying all the principal fairness criteria. Gambarelli (

1999

) introduced an apportionment technique which is custom made for each case, respects Hare minimum, Hare maximum and Monotonicity and satisfies other criteria in order of preference. In this chapter a generalization of that method is proposed, in order to extend it to the multi-district election case, where criteria should be respected at a global as well as at a local level. An existence theorem and a generating algorithm are supplied.

Formal work on the electoral model often suggests that parties or candidates should locate themselves at

the electoral center (or origin)

. Recent research has found no evidence of such convergence. In order to explain non-convergence, the stochastic electoral model is extended by including various kind of

valences

, some of which are based on individual and electoral

perceptions

. These electoral perceptions can be influenced by the contributions made by activist groups to the various parties. We present this formal activist model and then discuss the US presidential election in 2008 and the midterm US election in 2010 in order to evaluate the influence of activist groups, such as the so-called “Tea Party.” As an application of the model, we discuss the continuing realignment of US politics that has that has occurred since the end of the nineteenth century as a result of conflict between activist coalitions.

In this chapter, we provide a review of some recent results on power indices related to work done by the research group SaGaTh. We review axiomatic characterizations of several of the most important indices in the literature. Furthermore, we include a power index based on a desirability relation and two new power indices based on quasi-minimal winning coalitions. Finally, we summarize some results in other areas related with power indices.

We introduce an allocation rule for measuring power in voting situations defined by a TU-game, a cooperation index and a coalition structure, and characterize it axiomatically. This rule is an extension of the Owen coalition value; in fact, also a variety of previously studied game situations is embodied and unified by our model. Two numerical examples illustrate the application of the new value.

Traditional power indices are not suited to take account of explicit preferences, strategic interaction, and particular decision procedures. This chapter studies a new way to measure decision power, based on fully specified spatial preferences and strategic interaction in an explicit voting game with agenda setting. We extend the notion of inferior players to this context, and introduce a power index which—like the traditional ones—defines power as the ability to have pivotal influence on outcomes, not as the (often just lucky) occurrence of outcomes close to a player’s ideal policy. Though, at the present state, formal analysis is based on restrictive assumptions, our general approach opens an avenue for a new type of power measurement.

This paper argues that the nucleolus can compete with the Shapley value as a measure of P-power. It currently has more solid noncooperative foundations for majority games. It also identifies a set of attractive coalitions that are expected to form (unlike the Shapley value, which is based on the values of all coalitions) and does better than the Shapley value at some postulates of voting power. On the negative side, it may give the same payoff to players of different types or/and give a payoff of zero to players that are not dummies, though this behavior is ruled out for constant-sum weighted majority games.

In games with a coalition structure, players organize themselves in coalitions that form a partition of the set of players. In games with a coalition configuration, the union of the coalitions is the whole set of players but the coalitions are not necessarily disjoint. We introduce two variations of the Public Good Index for games with a coalition configuration, provide axiomatic characterizations of them, and apply them to a real world example.

Two measures of circumstantial or local power are introduced here. In our approach we focus on the viewpoint of an external observer who tries to evaluate the probability of a proposal to be passed by a certain committee. According to this local point of view we analyze the changes in the probability to pass the issue at hand obtained by modifying a voters’ perception about the proposal. In particular, we are interested in finding optimal persuadable voters and optimal bribable voters. To this end three preorderings on the set of voters are considered which are proved to be useful to identify these optimal voters.

The literature on power indices is very large, but it has had little impact on public debate regarding various aspects of constitutional reform and the design of electoral and voting systems. The need for such an impact is very substantial, as illustrated by three recent examples drawn from New Zealand and the UK. But researchers who use power indices seem to prefer to be scholars (working in ‘ivory towers’) rather than technocrats or emancipators who might engineer or stimulate informed change: their research has very little wider impact.

In simple weighted committees with a finite number of members, fixed weights, and changing quota there exist a finite number of different quota intervals of stable power with the same sets of winning coalitions for all quotas from each of them. If in a committee the sets of winning coalitions for different quotas are the same, then the power indices based on pivots, swings, or minimal winning coalitions are also the same for those quotas. If the fair distribution of voting weights is defined, then the fair distribution of voting power means to find a quota that minimizes the distance between relative voting weights and relative voting power (optimal quota). The problem of the optimal quota has an exact solution via the finite number of quotas from different intervals of stable power.

In certain bodies, like the Council of the EU, the member states have a voting weight which depends on the population of the respective state. In this article we ask the question which voting weight guarantees a ‘fair’ representation of the citizens in the union. The traditional answer, the square-root law by Penrose, is that the weight of a state (more precisely: the voting power) should be proportional to the square-root of the population of this state. The square root law is based on the assumption that the voters in every state cast their vote independently of each other. In this chapter we concentrate on cases where the independence assumption is not valid.

The weighted voting system used by the International Monetary Fund creates problems of democratic legitimacy since each member’s influence or voting power is not in general equal to its voting weight. Using voting power analysis to analyse both the Board of Governors and the Executive Board, we show that it tends to enhance the power of the United States at the expense of all other members. We investigate the constituency system as a form of representative democracy, idealizing it as a compound voting body, and find that it gives disproportionately large power to some smaller European countries, particularly Belgium and Netherlands. We also find that many countries are effectively disenfranchised. Separate analyses are done for 2006 and 2012, before and after recent reforms, which have been billed as being radical, enhancing the voice of the poor and emerging markets, but the effects are disappointingly small.

This chapter uses the Banzhaf power measure to calculate the

a priori

voting power of individual voters under the existing Electoral College system for electing the President of the United States, as well as under variants of this system in which electoral votes are either apportioned among the states in a different manner or cast by the states in a different manner. While the present winner-take-all manner of casting state electoral gives a substantial advantage to voters in the largest states, this advantage is diluted by the small-state advantage in apportionment. Moreover, most of the alternative Electoral College plans that have been proposed to remedy this large-state advantage give an equally substantial voting power advantage to voters in small states. Direct popular election of the President uniquely maximizes and equalizes individual voting power.

In this chapter, we view the party charged with forming a governing coalition immediately following an election as attempting to put together a coalition that will, with some compromise, promote its ability to implement its legislative agenda and to influence the legislative outcome in this direction. We thus view the problem of the coalition leader as one of maximizing its influence as measured by the Penrose measure of absolute voting power and subject this hypothesis and three variants to empirical testing using election data from nine countries. Two variants, namely: restricting the maximization process to the set of closed winning coalitions, or likewise but with a further requirement that the winning coalition selected be of minimal range, achieved levels of predictive success comparable to the Leiserson-Axelrod minimal range theory, suggesting that a closer examination of the role of a priori measures of power in political coalition formation may be useful.

Several power indices were introduced in order to account for different aspects of decisional situations. In this note we analyze how to deal with those situations, commonly arising in politics, in which the agents have some incompatibilities. We present some comments on existing power indices and discuss how communication structures and restricted games may allow a better evaluation of the power of the parties when incompatibilities play a relevant role. Also the question of the probability of a coalition to form is discussed.

The pattern of ownership and control of British industry is unusual compared with most other countries in that ownership is relatively dispersed. Typically the largest shareholder in any large listed company is likely to own a voting minority of the shares. Majority ownership by a single shareholder is unusual. It is not uncommon for the largest shareholding to be under 20 % and in many cases it is much less than that. A broadly similar pattern is observed in the USA. Two inferences about corporate governance are conventionally drawn from this, following the early work of Berle and Means: (1) All but the very largest shareholders are typically too small to have any real

incentive

to participate in decision making; (2) All but the very largest shareholdings are too small to have any real voting

power

. The question of voting power is the focus of this chapter.

The

a priori

voting powers of the 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. In this article we shall, in the spirit of the voter calculus outlined by Buchanan and Tullock in

Calculus of Consent

, use also other indices to give a richer picture of the possibilities and limitations of the member states in this weighted voting body. We shall also discuss the evolution of the powers to act of the body as a whole. Moreover, the fragmentation and concentration of the council are dealt with. Some implications of the—at the time of this writing hypothetical—enlargements are traced.

Which governments of European Union (EU) member states were most effective in the intergovernmental negotiations on the establishment of the European Economic and Monetary Union (EMU)? Did Germany, France or the UK come out as losing or winning parties compared to their original priorities? Such questions are certainly relevant, not least currently—in a time in which EMU faces challenges and its original setup may be adapted (notably by strengthening its fiscal underpinnings). A small data set on government preferences regarding the EMU provides more insights into such questions. On the basis of negotiation analytic tools, utilizing information on preferences and preference intensities, this chapter shows that the German government obtained outcomes on EMU that were fairly close to its initial priorities. France also faired well. By comparison, a number of smaller EU states were not as successful and had to concede on quite a number of points.

A solution, based on power measures, is proposed to the problem of assigning seats to new countries applying for membership of the European Parliament. This solution, simpler than many others, is obtained by weighting the populations and GDPs of all members. A strategy of optimization for each single country is suggested.

In this paper, we evaluate the distribution of power within the Council of Ministers (CM) in the EU’s most used legislative procedure, the

codecision procedure

or

ordinary legislative procedure

. Although our main emphasis is on the power distribution inside CM, we do

not

make the assessment in isolation from the European Parliament (EP) because it ‘co-decides’ on the respective policy outcomes. We investigate aprocedural non-cooperative model of codecision, in which members of CM and EP act strategically. CM and EP are thus evaluated as integrated parts of EU decision making. We relate our findings to studies that disregard the effects of inter-institutional interaction on the intra-institutional distribution of power. Previous analysis of the inter-institutional balance of power between CM and EP is extended by explicitly accounting for weighted voting.

The problem of designing an optimal weighted voting system for the two-tier voting, applicable in the case of the Council of Ministers of the European Union (EU), is investigated. Various arguments in favor of the square root voting system, in which voting weights of member states are proportional to the square root of their population. It is known that the voting power of every member state is approximately equal to its voting weight, if the threshold

$$q$$

q

for the qualified majority in the voting body is optimally chosen. We analyze the square root voting system for a generic ‘union’ of

$$M$$

M

states and derive in this case an explicit approximate formula for the level of the optimal threshold:

$$q\simeq 1/2+1/\sqrt{\pi M}$$

q

≃

1

/

2

+

1

/

π

M

.

We analyse the projected future evolution of the distribution of voting power and related quantities under the qualified majority (QM) decision rule for the Council of Ministers of the EU, prescribed by the Nice and Lisbon Treaties. Our projections are based on the demographic changes forecast by Eurostat (2008) for the period stretching from the year 2008 to the year 2061. We use a method similar to the one we used in Felsenthal and Machover (2001, 2004a, 2004b, 2007).

For centuries, cycles and other anomalies have hindered the use of paired comparisons, whether it be in decision theory, voting, economics, engineering, statistics, and on and on. It is shown here how all of these problems, along with ways to find solutions, can be completely understood in terms of what is called a “ranking wheel.”

Among many other topics, Hannu Nurmi has worked on voting paradoxes and how to deal with them. In his work he often uses a geometric approach developed by Don Saari for the analysis of paradoxes of preference aggregation such as the Condorcet paradox or Arrow’s general possibility theorem. In this chapter this approach is extended to other paradoxes analysed by Nurmi and the recent work in judgment aggregation. In particular we use Saari’s representation cubes to provide a geometric representation of profiles and majority outcomes.

The article transfers an argument of Pattanaik and Xu on ranking opportunity sets to tragic choices and the so called “numbers problem”. We characterize conditions that make the numbers count. This in itself will not resolve any problem relevant to the ongoing ethical debate but should shed some fresh light on it by forcing participants to state specifically which of the assumptions (axioms) should give way for what reasons.

Multi-choice games and fuzzy games, both of which are generalizations of cooperative games, enable us to deal with more than two participation levels. We consider generalized Shapley values for both type of games which are called a multi-choice value and a fuzzy value, respectively. By constructing a fuzzy game from a multi-choice game using a piecewise multilinear function, we can confirm that the multi-choice value converges to the fuzzy value when the number of levels is sufficiently large.

Pure bargaining problems with transferable utility are considered. By associating a quasi-additive cooperative game with each one of them, a

Shapley rule

for this class of problems is derived from the Shapley value for games. The analysis of this new rule includes axiomatic characterizations and a comparison with the proportional rule.

In legislative bargaining of the Baron-Ferejohn type, veto players either hold all of the overall power of 1 and share proportional to their recognition probabilities, or hold no power at all. Hence, in this setting, it is impossible to provide non-cooperative support for power indices that do not assign all or no power to veto players. This highlights problems in the interpretation of results of Valenciano (2008a, b) which are taken as support for the Shapley-Shubik index and other normalized semi-values.

In a large population, the first mover advantage causes only a vanishingly small distortion to the unanimity bargaining outcome. However, if the bargainers form parties through which bargaining takes place—as is the case in representative democracies—the first mover distortion remains significant. The main result of the chapter is that the distortion-free allocation can be restored under a party system if the first proposer right is allocated via a logrolling mechanism (an auction where the winning bid is added to the pool of resources) prior to the actual bargaining. Thus logrolling can be justified as a mechanism that corrects the distortion inherent to representative democracy.

This chapter surveys the results in general equilibrium theory based on dynamical models, and emphasizes the role of structural stability. In this context it is natural to consider a

preference field H

for the society, combining economic fields, associated with the preferred changes wrought by agents in the economic market place, together with fields of preferred changes in the polity. A preference field specifies at each point

$$ x\in $$

x

∈

the space of states,

X

, a set of feasible vectors of change. A condition called

half-openness

of

H

is sufficient to guarantee existence of a

local direction gradient, d

, for the society, and thus of a social choice. when half openness fails then the dynamical system so defined can be

chaotic

. We apply some of these abstract ideas to the question of dealing with climate change.