Alternative forms of the Shapley value and the Shapley-Shubik index

We prove the validity of an alternative representation of the Shapley-Shubik (1954) index of voting power, based on the following model. Voting in an assembly consisting of n voters is conducted by roll-call. Every voter is assumed to vote "yea" or "nay" with equal probability, and all n! possible orders in which the voters may be called are also assumed to be equiprobable. Thus there are altogether 2 ⁿ n! distinct roll-call patterns. Given a simple voting game (a decision rule), the pivotal voter in a roll-call is the one whose vote finally decides the outcome, so that the votes of all those called subsequently no longer make any difference. The main result, stated without proof by Mann and Shapley (1964), is that the Shapley-Shubik index of voter a in a simple voting game is equal to the probability of a being pivotal. We believe this representation of the index is much less artificial than the original one, which considers only the n! roll-calls in which all voters say "yea" (or all say "nay"). The proof of this result proceeds by generalizing the representation so that one obtains a value for each player in any coalitional game, which is easily seen to satisfy Shapley's (1953) three axioms. Thus the generalization turns out to be an alternative representation of the Shapley value. This result implies a non-trivial combinatorial theorem.     

Looking for Locals: Voter Information Demands and Personal Vote-Earning Attributes of Legislators under Proportional Representation

Proportional representation systems affect the extent to which elected legislators exhibit various attributes that allow them to earn a personal vote. The sources of variation in personal vote-earning attributes (PVEA) lie in informational shortcuts voters use under different electoral rules. List type (closed or open) and district magnitude (the number of legislators elected from a district) affect the types of shortcuts voters employ. When lists are closed, legislators' PVEA are of decreasing usefulness to voters as magnitude (and hence the number of candidates on a list) increases. When lists are open, legislators' PVEA are increasingly useful to voters as magnitude increases, because the number of candidates from which voters must choose whom to give a preference vote increases. As predicted by the theory, the probability that a legislator will exhibit PVEA—operationalized as local birthplace or lower-level electoral experience—declines with magnitude when lists are closed, but rises with magnitude when lists are open .     

Tacit co-operation in three-alternative non-cooperative voting games: A new model of sophisticated behaviour under the plurality procedure

Two models, one due to Farquharson and the other to Niemi-Frank, attempt to account for sophisticated voting behaviour when the voters' preference orderings are common knowledge and communication among Voters is impossible. Having subjected these two models to experimental testing, we have found them lacking. Hence, we propose a new model of sophisticated voting for 3-alternative n-person non-cooperative games under the plurality procedure, which can be extended to other voting procedures and more than three alternatives.The model assumes that voters whose first preference is (one of) the Condorcet winner(s) will (tacitly) co-ordinate their strategies and vote for their first preference, and specifies the conditions under which voters whose second preference is (one of) the Condorcet winner(s) will vote for their second (rather than their first) preference. Consequently, our model predicts that: (i) if there is a single Condorcet winner he or she will be elected; (ii) if there is more than one Condorcet winner the final outcome will be a tie between them; and (iii) when there are cyclical majorities with a single maximin alternative, this alternative will be elected.     

The impact of cuing candidate quality on female candidates

How can parties improve the electoral prospects of traditionally under-represented women? We argue that if a party signals that a single female candidate is of high quality, other women appearing on the ballot with her will receive a boost in support. More specifically, if a female candidate heads a party's list in the district, other women from her party will be rewarded with more votes. We test our reasoning by examining the nomination and election of women in three Free-List Proportional Representation systems where voters can cast multiple preference votes for individual candidates. We find robust support for the finding that when voters receive a signal that women can be quality candidates, they tend to reward additional women with preference votes regardless of their rank on the ballot.     

Accounting for Voter Heterogeneity within and across Districts with a Factor-Analytic Voter-Choice Model

José Afonso Mazzon Faculdade de Administração e Economia, University of São Paulo, Ave. Prof. Luciano Gualberto, 908, CEP 0558-900 São Paulo, Brazil. e-mail: jamazzon{at}usp.br e-mail: kamakura{at}duke.edu (corresponding author) In this study, we propose a model of individual voter behaviorthat can be applied to aggregate data at the district (or precinct)levels while accounting for differences in political preferencesacross districts and across voters within each district. Ourmodel produces a mapping of the competing candidates and electoraldistricts on a latent "issues" space that describes how politicalpreferences in each district deviate from the average voterand how each candidate caters to average voter preferences withineach district. We formulate our model as a random-coefficientsnested logit model in which the voter first evaluates the candidatesto decide whether or not to cast his or her vote, and then choosesthe candidate who provides him or her with the highest value.Because we allow the random coefficient to vary not only acrossdistricts but also across unobservable voters within each district,the model avoids the Independence of Irrelevant AlternativesAssumption both across districts and within each district, therebyaccounting for the cannibalization of votes among similar candidateswithin and across voting districts. We illustrate our proposedmodel by calibrating it to the actual voting data from the firststage of a two-stage state governor election in the Brazilianstate of Santa Catarina, and then using the estimates to predictthe final outcome of the second stage.     

Making votes count in parliament or government?

Several scholars have sought to elucidate voting strategies in proportional representation (PR) systems. The argument is that the existence of coalition governments forces voters to consider potential alliances and to vote in order to maximize their chances of influencing the outcome. In this paper, we argue that this vision is incomplete as PR, just as single-member district plurality, also creates incentives for voters to desert parties that have little chances of obtaining a seat in their district. We validate this theoretical claim using two different surveys conducted during the 2014 Belgian federal and regional elections. Our results show that both government and district viability have a substantial and distinct effect on vote choice.     

The vulnerability of point-voting schemes to preference variation and strategic manipulation

This essay measures and analyzes for a special class of point-voting schemes (the Borda method, plurality rule and the unrestricted point-voting scheme) sensitivity to preference variation (a simple change in the socially winning alternative resulting from alteration of a single voter's preferences) and vulnerability to individual strategic manipulation (a change in the winning alternative that benefits the voter whose preferences are altered). Assuming that society (n voters with linear preference orders on a finite set of m alternatives) satisfies the impartial-culture assumption, that is, each randomly selected voter is equally likely to hold any one of the randomly picked possible preference orders on the alternatives, we demonstrate:

1. for a given rule and a fixed number of voters, the sensitivity to individual preference variation and the vulnerability to individual strategic manipulation are greater, the larger the total number of alternatives.
2. For a given rule and a fixed number of alternatives, the vulnerability to individual strategic manipulation, in general, is not greater the smaller the total number of voters. Such a relationship does hold, however, if n is sufficiently large.
3. For any given combination of number of voters and number of alternatives, the unrestricted point-voting scheme is more sensitive to preference variation than the Borda method, which, in turn, is more exposed to such variation relative to the plurality rule. A similar conclusion does not hold with respect to vulnerability to individual strategic manipulation, unless the number of voters is sufficiently small.

     

Small changes, big results: Legislative voting behavior in the presence of new voters

Changes in district boundaries in small magnitude electoral systems can have substantive consequences for representation. In the U.S., each decennial redistricting cycle infuses House districts with a large number of new voters, changing personal representation for many citizens. What effect does the influx of these new voters exert on member behavior? By assessing the extent of this change in constituencies in conjunction with member voting behavior on roll calls, we can determine if significant changes to a congressional district impact post-redistricting legislative behavior. Using panel data estimators and various measures of legislator behavior, we show evidence that supports this claim. Our findings have notable implications for debates over representation and electoral accountability in legislative assemblies.     

Political Coase Theorem

This article considers theapplicability of the Coase theorem (in bothits positive and normative formulations) tothe political market. The articleanalogizes the choice of decision rules inthe political market to the choice of legalrules in the traditional Coase theorem andfurther analogizes alternative initialcoalitions to the different initialallocations of entitlements considered byCoase (1960). On the basis of theseanalogies, the paper examines the relevance(or lack thereof) of alternative votingrules and initial coalitions on the finalpolitical outcome. The article furthershows that, if all voters are allowed toenter into Coasian bargaining over thepolicy outcome to be adopted by themajority coalition (i.e., if politicalbargains are possible and are enforceable),uniqueness and stability are obtained. Theanalysis of the axiomatic Nash bargainingequilibrium yields an interesting geometricintuition. If voters have similar utilityfunctions centered around different idealpolicy points, the Coasian bargaining willbe conducive to the ``center of mass'' of thepolicy space, which weighs the agents'preferences as revealed in the bargainingprocess. Such ideal equilibrium satisfiesmost criteria of social welfare. Thearticle concludes considering the variouspractical limits of this ideal politicalmarket, whenever collective action andagency problems affect the politicalbargaining in a representative or directdemocracy. With all side payments prohibited,there is no assurance that collectiveaction will be taken in the most productiveway. (James M. Buchanan and Gordon Tullock, 1962)     

Split-voting in the Federal Republic of Germany: An analysis of the federal elections from 1953 to 1987

This article is about split-voting in the Federal Republic of Germany. Since 1953 each voter has had two votes. Although only the second vote is of importance for the distribution of the mandates, the voters increasingly make use of split-voting. The reasons for this increase of the split-vote are multiple: one being an expression of the rising need for participation. This split-vote' has nothing to do with the candidate of the electoral district, but very much with coalition preference. Considerable discrepancy between the first and the second vote can especially be observed among the Liberals. They profit from the fact that there is a widespread ignorance of the electoral system. The gains of the FDP are made at the expense of the current coalition partner.     

Personal vote‐seeking in flexible list systems: How electoral incentives shape Belgian MPs' bill initiation behaviour

It is well known that different types of electoral systems create different incentives to cultivate a personal vote and that there may be variation in intra‐party competition within an electoral system. This article demonstrates that flexible list systems – where voters can choose to cast a vote for the list as ordered by the party or express preference votes for candidates – create another type of variation in personal vote‐seeking incentives within the system. This variation arises because the flexibility of party‐in‐a‐district lists results from voters' actual inclination to use preference votes and the formal weight of preference votes in changing the original list order. Hypotheses are tested which are linked to this logic for the case of Belgium, where party‐in‐a‐district constituencies vary in their use of preference votes and the electoral reform of 2001 adds interesting institutional variation in the formal impact of preference votes on intra‐party seat allocation. Since formal rules grant Belgian MPs considerable leeway in terms of bill initiation, personal vote‐seeking strategies are inferred by examining the use of legislative activity as signalling tool in the period between 1999 and 2007. The results establish that personal vote‐seeking incentives vary with the extent to which voters use preference votes and that this variable interacts with the weight of preference votes as defined by institutional rules. In addition, the article confirms the effect of intra‐party competition on personal vote‐seeking incentives and illustrates that such incentives can underlie the initiation of private members bills in a European parliamentary system.     

Policy representation

This paper examines the extent to which conditions for the 'representative party government' model of representation exist in the EU. It suggests that, although application of the model is obviously limited, there is some support for its relevance. Using surveys of voters and candidates for the European Parliament the paper shows that some policy positions of representatives are constrained more by their party group than their nationality, and to some degree there is obvious congruence between the opinions of candidates and their voters. This is particularly so with respect to left–right orientation; far less with respect to European Monetary Union where elites appear much more enthusiastic than their electorates.     

Votes for Sale: The Logic of Power in Joint-Stock Companies

The joint-stock company as an institution rests on two major principles. On the one hand, it embodies the logic of collective choice. The ultimate rights to power are vested in a constituency composed of the stockholders. The constituency elects a board which in turn appoints an executive. Decisions are usually taken by majority rule. In these respects, the joint-stock company resembles the democratic polity. On the other hand, it also includes important elements of market exchange. Unlike many other instances in which the logic of collective choice applies, the rights to power can be freely exchanged on a stock market. This paper examines the power implications of this combination of principles using illustrations drawn from the corporate world of Sweden. It argues that although there are similarities between the situation of stockholders and that of voters, the incentives to participate in the exercise of control are rather different. Whereas a model based solely on instrumental rationality is insufficient to explain the participation of voters, it does well in accounting for that of stockholders. Further, the prerequisites of the emergence and maintenance of participatory norms are favorable with respect to voters but unfavorable with regard to stockholders. The paper concludes by considering the implications of the results for the alleged autonomy of managers vis-à-vis the owners and by examining the importance of the exit mechanism as a means of power for minor stockholders.     

Are leftist or rightist voters better substantively represented? The effects of variance in district magnitude on party-voter ideological congruence

How does the variation in district magnitude in districted proportional representation systems affect congruence between a voter and their party of choice? I argue that voters in large-magnitude districts will have higher levels of party-voter congruence than voters in small-magnitude districts, due to stronger strategic incentives and reduced party options in small-magnitude districts. Furthermore, I argue that this relationship will be stronger among leftist voters compared to rightist voters, due to the concentration of rightist voters in rural, small-magnitude districts and leftist voters in urban, high-magnitude districts. These expectations are tested using data that from 45 elections in 12 districted proportional representation systems included in the Comparative Study of Electoral Systems (CSES). The results support the expectation that party-voter ideological congruence will be higher for voters in larger electoral districts, and lower for voters located within smaller districts. Leftist voters do appear to suffer a congruence penalty in smaller districts, whereas the congruence of rightist voters is less affected by district magnitude. An examination of the mechanisms behind this finding suggests that leftist-voters in small-magnitude districts are faced with a smaller and more right-leaning set of party options.     

Campaign contributions as valence

I study how the possibility of voters contributing to candidates in response to the candidates’ policy proposals affects the equilibrium policy in winner-take-all political competition. More specifically, I allow each partisan voter to contribute to her preferred candidate where the amount contributed depends on the relative positions of the two candidates. Candidates then use the donations to build valence through campaigning, which in turn affects the voting decision of impressionable voters. Since candidates are concerned with raising money as well as picking a policy position preferred by the median voter, I show that campaign contributions may lead to divergent equilibria in winner-take-all elections when politicians are policy-motivated, albeit only under stylized utility functions and donor densities. Further, under symmetric voter and donor densities, if either the donor density is single-peaked or the voter utility is concave, a unique equilibrium exists in which both candidates propose the ideal policy of the median voter.     

Policy representation

Abstract This paper examines the extent to which conditions for the 'representative party government' model of representation exist in the EU. It suggests that, although application of the model is obviously limited, there is some support for its relevance. Using surveys of voters and candidates for the European Parliament the paper shows that some policy positions of representatives are constrained more by their party group than their nationality, and to some degree there is obvious congruence between the opinions of candidates and their voters. This is particularly so with respect to left–right orientation; far less with respect to European Monetary Union where elites appear much more enthusiastic than their electorates.     

Sincere and strategic voters: An Israeli study

The theoretical literature on voting behavior has shown that a rational voter may sometimes decide to vote for a candidate or party that does not constitute his or her first preference. Such voters are traditionally called strategic voters, in contrast to voters who act sincerely, i.e., those who always vote for their first preference regardless of how others are likely to vote. After discussing some of the problems associated with the definition of these two types of voters and suggesting a new operational definition, some attitudes and characteristics of these two types of voters are investigated. It was found that strategic voters constitute a very small percentage of the entire electorate, that their education level is significantly higher than that of sincere voters, that they tend more often to believe that polls influence voters' decisions and hence tend to delay their own final voting decision, that they tend more often than sincere voters to support small parties but do not tend more often than sincere voters to switch the party they decide to support from one election to the next, and that there is no significant difference between them and sincere voters regarding which governing coalition should/will form following an election.     

Finnish parties’ positions in 2007: A matter of equilibrium or voters’ projection?

According to the Finnish National Election Studies (FNES) the positions of Finnish parties in the years 2003 and 2007 were almost identical. In FNES, party placement is based on the voters’ perceptions and therefore it is assumed that either the voters have correctly guessed the positions of the parties or they have been wrong in their judgments. In the first case, the Finnish parties are likely to have reached a state of equilibrium where no party has an incentive for unilaterally changing its optimal position. On the other hand, if the voters are incorrect, it is likely that they have projected their own positions to the parties. The results reject the equilibrium hypothesis and confirm the projection hypothesis.     

The Representative Roles of MPs: A Citizen Perspective

From the normative point of view, there is a general agreement that representatives should act in line with the interests of those being represented. The knowledge about citizens' preferences for representation is very limited, however. This study examines MP's representative roles from the perspective of the citizens. It utilises a task definition approach in the Finnish institutional setting, which substantially differs from the context of earlier investigations in terms of open‐list electoral systems with mandatory preferential voting. Based on the 2007 Finnish National Election Study (n = 1,422), voters' preferences concerning four different representational roles are analysed: as representatives pursuing the interests of their electoral district, party, individual voters or being independent actors. Next, voters' preferences are accounted for by the factors related to each type of representation: citizens' regional electoral context, party attachment and electoral supply, political engagement and political competence, respectively. The results show that citizens living in electoral districts located far away from the political centre or in constituencies where it is more difficult for small parties to win political representation are most prone to prefer regional representation. Similarly, voters who have closer ties with political parties prefer party‐centred representation while those who feel less politically efficient favour close ties with their MPs. Education in turn increases the support for a political representative to act independently from the electorate or the party.