Would letting people vote for multiple candidates yield policy moderation?

We investigate whether letting people vote for multiple candidates would yield policy moderation. We do so in a setting that takes three key features of elections into account, namely, strategic voting, endogenous candidacy and policy motivation on the part of the candidates. We consider two classes of voting rules. One class consists of the voting rules where each voter casts several equally-weighed votes for the different candidates. The other class consists of the voting rules where each voter rank-orders the candidates. We identify conditions under which these voting rules yield policy moderation. We also show that these voting rules may yield policy extremism instead of policy moderation if one (or several) of the conditions is not satisfied! Finally, we find that amongst these voting rules the extent of policy moderation is maximal under the Borda Count if we consider only equilibria where all candidates are serious contenders. However, this result does not carry over to spoiler equilibria, where Approval Voting can yield more moderate policy outcomes than the Borda Count.     

Multi-stage voting, sequential elimination and Condorcet consistency

A class of voting procedures based on repeated ballots and elimination of one candidate in each round is shown to always induce an outcome in the top cycle and is thus Condorcet consistent, when voters behave strategically. This is an important class as it covers multi-stage, sequential elimination extensions of all standard one-shot voting rules (with the exception of negative voting), the same one-shot rules that would fail Condorcet consistency. The necessity of repeated ballots and sequential elimination are demonstrated by further showing that Condorcet consistency would fail in all standard voting rules that violate one or both of these conditions.     

Formal and real voting power

The so-called power indices are considered valuable tools for the analysis of various kinds of collective choice. Their applicability for the understanding of legislative decision-making has been demonstrated. If a distinction between formal voting power and real voting power is introduced, then the power index approach to the analysis of ongoing processes of social choice becomes more relevant. The concept of real voting power implies an extension of the power index approach to take into account how actors behave in order to restrict the coalition possibilities. Thus, in a legislative setting it is more suitable for the measurement of actual power, whereas the formal power indices measure constitutional power. The differences between formal and real voting power may be quite substantial as is shown in an application of these concepts to data concerning the Swedish Riksdag during the seventies.     

Electoral fraud and voter turnout: An experimental study

In this paper we experimentally investigate the consequences of electoral fraud on voter turnout. The experiment is based on a strategic binary voting model where voters decide whether to cast a costly vote in favour of their preferred candidate or to abstain. The electoral process is illicitly influenced by applying ballot-box stuffing. In the experiment we implement two different framings: we compare voter turnout in a neutral environment and with framed instructions to explicitly replicate elections. This approach enables us to both test the model's predictions and to estimate the framing effects of voting and fraud. Comparison of experimental results with theoretical predictions reveals over-voting, which is exacerbated when fraud occurs. Turnout increases as predicted with a moderate level of fraud while, with higher levels of electoral fraud, voters fail to recognize that the existence of a relatively larger number of “agents” voting with certainty considerably decreases the benefits of voting. Importantly, framing matters, as revealed by the higher turnout of those in the majority group, against which the fraud is applied.     

A Coalition-Form Analysis Of The “One Country - One Vote” Rule In The Governing Council Of The European Central Bank *

This paper analyses the “one country—one vote” rule for monetary policy decision

making of the Governing Council of the European Central Bank in a framework of cooperative game theory. The Shapley value is used as a solution concept. In contrast to former papers analysing the allocation of abstract "voting power" in committees of international organisations, preferences for monetary policy are modelled to obtain a prediction about potential transfers implied by an equal allocation of voting rights when countries are of different size. It is shown that if the number of countries participating to a currency union grows and the weight of the largest country within the currency union becomes small, the allocation of voting rights becomes irrelevant in the sense that transfers per country tend in any case to zero. [C71, E5, F02]     

Nominal bargaining power, selection protocol, and discounting in legislative bargaining

The comparative static predictions of the Baron and Ferejohn [Baron, D.P., and Ferejohn, J.A., (1989). Bargaining in legislatures, American Political Science Review 83 (4), 1181-1206] model better organize behavior in legislative bargaining experiments than Gamson's Law. Regressions similar to those employed in field data produce results seemingly in support of Gamson's Law (even when using data generated by simulating agents who behave according to the Baron-Ferejohn model), but this is determined by the selection protocol which recognizes voting blocks in proportion to the number of votes controlled. Proposer power is not nearly as strong as predicted in the closed rule Baron and Ferejohn model, as coalition partners refuse to take the small shares given by the continuation value of the game. Discounting pushes behavior in the direction predicted by Baron and Ferejohn but has a much smaller effect than predicted.     

Information transmission in coalitional voting games

A core allocation of a complete information economy can be characterized as one that would not be unanimously rejected in favor of another feasible alternative by any coalition. We use this test of coalitional voting in an incomplete information environment to formalize a notion of resilience. Since information transmission is implicit in the Bayesian equilibria of such voting games, this approach makes it possible to derive core concepts in which the transmission of information among members of a coalition is endogenous. Our results lend support to the credible core of Dutta and Vohra [Incomplete information, credibility and the core, Math. Soc. Sci. 50 (2005) 148-165] and the core proposed by Myerson [Virtual utility and the core for games with incomplete information, Mimeo, University of Chicago, 2005] as two that can be justified in terms of coalitional voting.     

Bargaining in committees as an extension of Nash's bargaining theory

This paper addresses the following issue: if a set of agents bargain on a set of feasible alternatives ‘in the shadow’ of a voting rule, that is, any agreement can be enforced if a ‘winning coalition’ supports it, what general agreements are likely to arise? In other words: what influence can the voting rule used to settle (possibly nonunanimous) agreements have on the outcome of consensus? We model the situation as an extension of the Nash bargaining problem in which an arbitrary voting rule replaces unanimity. In this setting a natural extension of Nash's solution is characterized.     

Condorcet Jury Theorem: An example in which informative voting is rational but leads to inefficient information aggregation

Recent research on the Condorcet Jury Theorem has proven that informative voting (that is, voting according to one’s signal) is not necessarily rational. With two alternatives, rational voting typically leads to the election of the correct alternative, in spite of the fact that not all voters vote informatively. We prove that with three alternatives, there are cases in which informative voting is rational and yet leads to the election of a wrong alternative.     

Protecting Minorities through the Average Voting Rule

In the average voting rule, the outcome is some weighted average of votes. The unique average voting outcome is characterized by a median formula, which depends on voters' preferred allocations and some parameters constructed from voters' weights. A minority is said to be protected by a switch in voting rule if the outcome becomes closer to the median bliss point of the minority. Sufficient conditions for minority protection are that, either the minority's weight is sufficiently large or the majority outcome is too unfavorable to the minority. Applications to the composition of public goods and to public expenditures level are considered. We explore the combined use of average and majority voting in a two‐stage procedure for determining the level and the composition of public expenditures.     

The geometry of voting power: Weighted voting and hyper-ellipsoids

Suppose legislators represent districts of varying population, and their assembly's voting rule is intended to implement the principle of one person, one vote. How should legislators' voting weights appropriately reflect these population differences? An analysis requires an understanding of the relationship between voting weight and some measure of the influence that each legislator has over collective decisions. We provide three new characterizations of weighted voting that embody this relationship. Each is based on the intuition that winning coalitions should be close to one another. The locally minimal and tightly packed characterizations use a weighted Hamming metric. Ellipsoidal separability employs the Euclidean metric: a separating hyper-ellipsoid contains all winning coalitions, and omits losing ones. The ellipsoid's proportions, and the Hamming weights, reflect the ratio of voting weight to influence, measured as Penrose–Banzhaf voting power. In particular, the spherically separable rules are those for which voting powers can serve as voting weights.     

European corporate governance: Trading off liquidity against control

Ownership dispersion is a pre-requisite for liquid stock markets, but it entails a collective action problem: individual investors have no incentives to engage in direct monitoring. Legal devices can provide solutions along three dimensions. One, they can concentrate or dilute voting power. Two, they can affect liquidity. Three, they can give the right or wrong monitoring incentives. This paper shows how these devices are used and how they can depress liquidity. Legal constraints aimed at strengthening minority protection can reduce the scope for monitoring, destroy liquidity and even create incentives for minority abuse: for example one-share-one-vote restrictions encourage the formation of pyramidal holding companies. The search for solutions that concentrate voting power, provide liquidity and protect minorities continues.     

Party voting discipline and the power of parties, legislators and states

We examine the distribution of decision-making power among the principal actors of a federal legislative system; parties, legislators, and constituencies. We are especially interested in how the balance of power between legislators and constituencies depends on the voting discipline exercised by the parties.We derive power measures that are related to the Banzhaf-Coleman index of decision-making power and illustrate with a simple example. Our power measures are novel because they are based on an explicit representation of party voting discipline as well as the structural properties of the decision-making process, whereas previous analyses concentrate on structurally determined power alone.     

Voting with abstention

Most voting models in the literature neglect abstention, but is such a simplification justified? I investigate this question in a model with outside pressure on voters. For sequential voting (e.g., roll call votes), with and without an abstention option, there is a unique subgame perfect equilibrium, which implies that true majorities always succeed. Abstention can be an equilibrium strategy for some voters, in particular under complex decision rules (e.g., weighted voting, double majorities). Simultaneous voting often has a unique pure strategy equilibrium but also a plethora of mixed and pure/mixed strategy equilibria. Therefore, only with equilibrium selection, can we evaluate the consequences of neglecting abstention. For equal weight voting, equilibria selected by the procedure of Harsanyi and Selten change completely with an abstention option, even if abstention itself is not or rarely used. With small enough outside pressure, however, the selected equilibrium honors true majorities in both cases.     

Weighted approval voting

To allow society to treat unequal alternatives distinctly we propose a natural extension of Approval Voting by relaxing the assumption of neutrality. According to this extension, every alternative receives ex-ante a strictly positive and finite weight. These weights may differ across alternatives. Given the voting decisions of every individual (individuals are allowed to vote for, or approve of, as many alternatives as they wish to), society elects the alternative for which the product of total number of votes times exogenous weight is maximal. If the product is maximal for more than one alternative, a pre-specified tie-breaking rule is applied. Our main result is an axiomatic characterization of this family of voting procedures.      

Shareholders’ agreements and voting power: evidence from Italian listed firms

This work provides an empirical investigation of shareholders’ agreements signed in Italy over the past decade. The evidence shows that agreements produce a remarkable reshuffling of voting power (Shapley value) among participants. In particular, the first owner gains much voting power at low levels of ownership concentration, and his gain is decreasing in his ownership stake; the opposite happens for the other participants. In addition, the likelihood that a supermajority rule is included in an agreement contract is increasing in the first owner's share of equity. These findings are consistent with the hypothesis that agreements are used to correct situations where the first owner's power is at one of the two extremes: either too low (leading to insufficient monitoring over managers and gridlocks in decision-making) or too high (enabling him to extract large private benefits of control).     

Endogenous Firm Objectives

We analyze the behavior of a monopolistic firm in general equilibrium when the firm's decisions are taken through shareholder voting. We show that, depending on the underlying distribution, rational voting may imply overproduction as well as underproduction, relative to the efficient level. Any initial distribution of shares is an equilibrium, if individuals do not recognize their influence on voting when trading shares. However, when they do, and there are no short–selling constraints, the only equilibrium is the efficient one. With short–selling constraints typically underproduction occurs. It is not market power itself causing underproduction, but the inability to perfectly trade the rights to market power.     

Control rights, pyramids, and the measurement of ownership concentration

The recent corporate governance literature has emphasised the distinction between control and cash-flow rights but has disregarded measurement issues. Control rights may be measured by immediate shareholder votes, the voting rights as traced through ownership chains, or voting power indices that may or may not trace ownership through chains. We compare the ability of various measures to identify the effects of ownership concentration on share valuation using a German panel data set. The widely used weakest-link principle does not perform well in this comparison. Furthermore, measures that trace control through ownership chains do not outperform those that rely on immediate ownership, thus questioning the role of pyramids in the separation of control and cash-flow rights. The paper emphasises that there is a distinction between these two aspects of ownership even without pyramids or preferred stock, identification of which requires measures that, like the Shapley–Shubik index, do not simply equate control rights with voting rights.     

Demand bargaining and proportional payoffs in majority games

We study a majoritarian bargaining model in which players make payoff demands in decreasing order of voting weight. The unique subgame perfect equilibrium outcome is such that the minimal winning coalition of the players that move first forms with payoffs proportional to the voting weights. This result advances previous analysis in terms of one or more of the following: a) the simplicity of the extensive form (finite horizon with a predetermined order of moves); b) the range of the majority games covered; c) the equilibrium concept (subgame perfect equilibrium is sufficient for a unique prediction).     

Noncooperative foundations of bargaining power in committees and the Shapley–Shubik index

In this paper we explore the noncooperative foundations of the bargaining power that a voting rule gives to each member of a committee that bargains in search of consensus over a set of feasible agreements under a voting rule. Assuming complete information, we model a variety of bargaining protocols and investigate their stationary subgame perfect equilibria. We show how the Shapley–Shubik index and other power indices can be interpreted as measures of ‘bargaining power’ that appear in this light as limit cases.