The uncovered set in spatial voting games

In a majority rule voting game, the uncovered set is the set of alternatives each of which can defeat every other alternative in the space either directly or indirectly at one remove. Research has suggested that outcomes under most reasonable agenda processes (both sincere and sophisticated) will be confined to the uncovered set. Most research on the uncovered set has been done in the context of voting games with a finite number of alternatives and relatively little is known about the properties of the uncovered set in spatial voting games.We examine the geometry of the uncovered set in spatial voting games and the geometry of two important subsets of the uncovered set, the Banks set and the Schattschneider set. In particular, we find both general upper and lower limits on the size of the uncovered set, and we give the exact bounds of the uncovered set for situations with three voters. For situations with three voters, we show that the Banks set is identical to the uncovered set.     

The potential of iterative voting to solve the separability problem in referendum elections

In referendum elections, voters are often required to register simultaneous votes on multiple proposals. The separability problem occurs when a voter’s preferred outcome on one proposal depends on the outcomes of other proposals. This type of interdependence can lead to unsatisfactory or even paradoxical election outcomes, such as a winning outcome that is the last choice of every voter. Here we propose an iterative voting scheme that allows voters to revise their voting strategies based on the outcomes of previous iterations. Using a robust computer simulation, we investigate the potential of this approach to solve the separability problem.     

Reliability of Information Aggregation with Regional Biases: A Note

Is there a rationale for an electoral college system or do these voting systems always waste useful information? This paper studies this question in a setup in which voting is supposed to aggregate decentralized information about individual preferences for two candidates. Individual perceptions may be affected by regional information. When such regional information plays a major role, an electoral college system may be superior to simple majority voting.     

Making statements and approval voting

We assume that people have a need to make statements, and construct a model in which this need is the sole determinant of voting behavior. In this model, an individual selects a ballot that makes as close a statement as possible to her ideal point, where abstaining from voting is a possible (null) statement. We show that in such a model, a political system that adopts approval voting may be expected to enjoy a significantly higher rate of participation in elections than a comparable system with plurality rule.     

A Special Case of Penrose’s Limit Theorem When Abstention is Allowed

In general, analyses of voting power are performed through the notion of a simple voting game (SVG) in which every voter can choose between two options: ‘yes’ or ‘no’. Felsenthal and Machover [Felsenthal, D.S. and Machover, M. (1997), International Journal of Game Theory 26, 335–351.] introduced the concept of ternary voting games (TVGs) which recognizes abstention alongside. They derive appropriate generalizations of the Shapley–Shubik and Banzhaf indices in TVGs. Braham and Steffen [Braham, M. and Steffen, F. (2002), in Holler, et al. (eds.), Power and Fairness, Jahrbuch für Neue Politische Ökonomie 20, Mohr Siebeck, pp. 333–348.] argued that the decision-making structure of a TVG may not be justified. They propose a sequential structure in which voters first decide between participation and abstention and then between ‘yes’ or ‘no’. The purpose of this paper is two-fold. First, we compare the two approaches and show how the probabilistic interpretation of power provides a unifying characterization of analogues of the Banzhaf (Bz) measure. Second, using the probabilistic approach we shall prove a special case of Penrose’s Limit Theorem (PLT). This theorem deals with an asymptotic property in weighted voting games with an increasing number of voters. It says that under certain conditions the ratio between the voting power of any two voters (according to various measures of voting power) approaches the ratio between their weights. We show that PLT holds in TVGs for analogues of Bz measures, irrespective of the particular nature of abstention.     

Distance,Turnout, and the Convenience of Voting*

Objectives. This research examines how distance factors into the costs associated with political participation. We hypothesize that the political geography of a voter's residence affects not only the likelihood that he or she will vote, but whether the voter will choose between traditional Election Day voting or nontraditional means, such as casting an absentee ballot by mail, or going to an early‐voting site. Methods. Using a geographic information system (GIS), we calculate Manhattan‐block distances between voter residences and their respective precinct and nearest early‐voting sites in Clark County, NV for the 2002 mid‐term election. We then use these calculated distances to predict, with multinomial logistic regression, the likelihood of nonvoting, precinct voting, and nontraditional voting. Results. Our evidence suggests that the cost of traveling to reach a traditional voting site is associated with nonvoting to a point, but the relationship between distance and participation is nonlinear. Distance to traditional voting sites is also highly associated with choosing to vote by mail. Would‐be nonvoters are more inclined to use proximate election‐day sites than proximate early‐voting sites, probably because they decide to vote so late in the campaign. Conclusions. Our findings have important implications for democratic theory, ongoing efforts to reform the electoral process, and the practice of voter mobilization.     

Borda and Condorcet: Some Distance Results

This paper provides a distance based analysis of the Borda rule with respect to Condorcet’s criterion. It shows that the minimal Condorcet consistency present in the Borda rule, whenever a Condorcet winner (the alternative that wins against every other alternative in a pairwise contest) exists, disappears in the case of voting cycles. First, it is shown that for certain preference profiles the Borda winner is furthest from being a Condorcet winner. Second, it is shown that there exist preference profiles for which the Borda winner is closest from being a Condorcet loser (the alternative that loses against every other alternative in a pairwise contest).     

Sophisticated voting under the plurality procedure: A test of a new definition

The Niemi-Frank definition of sophisticated voting can now be evaluated on two grounds. First, we can compare our definition to Farquharson's. For the most part, the two definitions yield identical outcomes. Both pickCondorcet winners a very high proportion of the time and prevent the selection of Condorcet losers. The major differences are in the logic underlying the two definitions and in the rate of determinacy of outcomes. Here there is a tradeoff. The logic underlying the Farquharson model is especially persuasive, although it is our feeling that the Niemi-Frank definition comes closer to mirroring the way in which voters might actually analyze a plurality situation. In any case, the price paid by the Farquharson definition for its ironclad logic is a much higher rate of indeterminacy. In over half of the cases, the Farquharson logic fails to lead to any conclusion whatsoever. The Niemi-Frank definition yields many more determinate situations, with mostly Condorcet winners and with strategies that make good, if not completely unassailable sense. A second way of evaluating the Niemi-Frank definition is in comparison with sincere voting. A commonly-cited shortcoming of plurality voting is that often fails to choose a Condorcet winner. As we notedearlier, sophisticated plurality voting, unlike binary voting, is imperfect in this respect. Nonetheless, even taking account of the indeterminacy thatremains in the Niemi-Frank definition, sophisticated voting picked a Condorcet winner about 10 percent more frequently than did sincere voting as well as eliminating the possibility of a Condorcet loser being chosen. By this measure, the Niemi-Frank definition is not only acceptable but suggests that this form of strategic behavior actually leads tobetter outcomes. By proposing and now by testing a new definition of sophisticated voting under plurality rule, we have begun to make some headway on understanding strategic behavior and its effects in an outwardly simple yet deceptively complex voting system. We are, of course, far from finished. Most significantly, our definition applies to only three alternatives, and Farquharson's (even if one is willing to live with its high indeterminacy) becomes extraordinarily cumbersome with more than three alternatives? In any event, the results of this foray into sophisticated nonbinary voting suggests once again that strategic behavior, rather than making things worse, improves the chances that the outcome will be the one most favored by the majority criterion.     

Approval voting and strategy analysis: A Venetian example

The author presents a historic reconstruction of the single-member constituency election system known as approval voting which was used to elect Venetian dogi for over 500 years. An interesting procedure theoretically, concurrent approval voting is the only sincere single-winner election system. Central issues concerning strategy choice under uncertainty are investigated using a contingency-dependent framework of individual behavior given prior probability distributions over decision relevant propositions. Extensions are then proposed for the use of approval procedures in modern elections and other collective decision-making situations. Finally the advantages of trichotomous preferences in decision and strategy analysis are argued.Masculine personal pronouns are used when discussing doge elections, otherwise feminine pronouns are used.     

Calculable Power: A Case Study of IMF Quotas and Voting Rights Reform*

Voting procedure is an important mechanism for public choice in collective bodies such as international organizations. This paper measures and compares IMF member countries’ voting power before the 2008 reform and after the 2010 reform on the basis of datasets on IMF quotas and voting rights distribution provided by IMF. Our study verifies that IMF’s quotas and voting rights reforms do help to reduce the voting power gap among member countries. The 2008 and 2010 reforms produce a greater improvement in emerging members’ voting power under the 70 percent majority rule than the 85 percent rule; the 70 percent majority rule means the United States would lose its absolute veto. Moreover, the paper disproves the underlying assumption that regards a member’s voting power as proportional to its voting rights. Countries with different amounts of voting rights can still have the same voting power.     

Positionalist voting functions

Positionalist voting functions are those social choice functions where the positions of the alternatives in the voter's preference orders crucially influence the social ordering of the alternatives. An important subclass consists of those voting functions where numbers are assigned to the alternatives in the preference orders and the social ordering is computed from these numbers. Such voting functions are called representable. Various well-known conditions for voting functions are introduced and it is investigated which representable voting functions satisfy these conditions. It is shown that no representable voting function satisfies the Condorcet criterion. This condition and Arrow's independence condition, which are typical non-positionalist conditions, are shown to be incompatible. The Borda function, which is a well-known positionalist voting function, is studied extensively, conditions uniquely characterizing it are given and some modifications of the function are investigated.My thanks are due to professor Bengt Hansson for encouragement and several helpful suggestions.     

Pareto improvements by Pareto strategic voting under majority voting with risk loving and risk avoiding voters — A note

Voters satisfy maximin or maximax in their choices between sets of alternatives and secure a Pareto improvement by all voting strategically under simple majority voting for particular sincere preferences. Thus the assumption that strategic voting is a bad thing is challenged and the idea that we should reject voting because of the possibility of misrepresentation dismissed.     

Strict proportional power in voting bodies

It is a widely known fact among game theorists as well as political scientists that the distribution of voting weights in a voting body is generally a poor proxy for the distribution of voting power within the body. It has been proposed to equate the distribution of a priori voting power and actual seat distribution by randomizing the decision rule of the voting body over various majority rules. In this paper, some implications of this procedure will be discussed.     

On the stability of a triplet of scoring rules

When choosing a voting rule to make subsequent decisions, the members of a committee may wish this rule to be self-selected when it is the object of a choice among a menu of different possible voting rules. Such concepts have recently been explored in Social Choice theory, and a menu of voting rule is said to be stable if it contains at least one self-selective voting rule at each profile of preferences on voting rules. We consider in this article the menu constituted by the three well-known scoring rules {Borda, Plurality, and Antiplurality}. Under the Impartial Culture assumption, which proposes an a priori model to estimate the likelihood of the profiles, we will derive a probability for the stability of this triplet of voting rules.     

One person/one vote is not efficient given information on factions

This paper argues that if we have any information about special interest groups in a society, then one person/one vote is not the most efficient voting system. Instead weighted voting is appropriate where the weights assigned to the various individuals depend on the correlation between different individual utilities. The reason why one person/one vote is inefficient is that the correlation between individual utilities allows us to get some estimates of preference intensities from the individual votes.After proving this thesis in general, we illustrate it with a three person example. In the example, we find that moderately correlated individuals get the greatest weight.     

The Welfare Consequences of Strategic Voting in Two Commonly Used Parliamentary Agendas

This paper studies the welfare consequences of strategic voting in two commonly used parliamentary agendas by comparing the average utilities obtained in simulated voting under two behavioural assumptions: expected utility maximising behaviour and sincere behaviour. The average utility obtained in simulations is higher with expected utility maximising behaviour than with sincere voting behaviour under a broad range of assumptions. Strategic voting increases welfare particularly if the distribution of preference intensities correlates with voter types.      

Media exposure and the engaged citizen: How the media shape political participation

Media exposure is widely known to increase institutional forms of political participation such as voting. Less well understood is whether media exposure also affects protest, a less institutional form of engagement. This paper examines the mechanics through which this relationship operates by considering the media's direct and indirect effect on voting and protesting, via political trust, efficacy, and knowledge. We make these comparisons by analyzing the unique Jennings panel dataset that collects information on respondents at three separate points. The results show that media exposure affects voting more than protesting and that these relationships operate through different mechanisms. While media exposure leads to voting because it increases political knowledge, it is associated with protest via external political efficacy. Furthermore, while this relationship is causal for voting it is only correlational for protest. The results illustrate the importance of disentangling forms of political engagement when considering media effects.     

试论我国宪法的完善

宪法是国家的根本法。我国现行宪法在宪法的解释制度、修宪程序以及全国人大及其常委会的表决制度等方面存在一些问题。我们应借鉴西方国家宪法的经验并结合本国的实际情况 ,将宪法的解释权赋予人民法院 ,确立宪法的司法解释制度 ;修正宪法的第六十四条 ,改进修改宪法的方式 ;在表决原则、表决的法定人数和意愿表示项方面进一步完善全国人大及其常委会的表决制度。     

Expected frequency and mean size of the paradox of new members

The paradox of new members occurs when the addition of one or more new members to a weighted voting body increases, rather than decreases, the voting power of some of the old members. Extending the computational work of Brams and Affuso (1976), the mean size of the paradox and the relative frequency of its occurrence are presented for small and moderate-size weighted voting bodies. Computational results are presented and conclusions are drawn for the two power indices of Shapley-Shubik and Banzhaf, three different decision rules, and voting bodies with or without dictator. Although the paradox cannot be dismissed as either contrived or improbable, its mean size in moderatesize voting bodies is sufficiently small to question its practical significance.     

Voting by Mail: Turnout and Institutional Reform in Oregon*

Objectives. I test the impact of Oregon's vote‐by‐mail system on voter turnout. Methods. To determine the impact, I create a cross‐sectional time‐series regression model of state turnout in presidential elections from 1980 to 2004 and mid‐term elections from 1982 to 2006. Results. I find that Oregon's turnout increases by around 10 percentage points of registered voters in both presidential and mid‐term elections due to the voting‐by‐mail reform. Conclusions. These results suggest that one of the reasons that the United States has comparatively lower turnout is due to its more onerous voting procedures.