First and second best voting rules in committees

A committee of people with common preferences but different abilities in identifying the best alternative (e.g., a jury) votes in order to decide between two alternatives. The first best voting rule is a weighted voting rule that takes the different individual competences into account, and is therefore not anonymous, i.e., the voters’ identities matter. Under this rule, it is rational for the committee members to vote according to their true opinions, or informatively. This is not necessarily true for an anonymous voting rule, under which members may have an incentive to vote non-informatively. Thus, strategic, sophisticated voters may vary their voting strategies according to the voting rule rather than naively voting informatively. This paper shows that the identity of the best anonymous and monotone (i.e., quota) voting rule does not depend on whether the committee members are strategic or naive or whether some are strategic and some are naive. One such rule, called the second best rule, affords the highest expected utility in all cases.

“Wasn’t he sweet?” said Yossarian. “Maybe they should give him three votes.” Joseph Heller, Catch-22

     

Ambivalent citizenship and extraterritorial voting among Colombians in London and Madrid

In this article, we explore the nature of extraterritorial voting among Colombian migrants in the 2010 elections in London and Madrid. To address the neglected issue of why voter turnout from abroad has been so low, we take into account the views of voters and non‐voters alike to show that, while the external vote privileges the professional and well educated, this does not mean that migrants are not interested in politics back home. Drawing on Bauman (1991), we conceptualize ambivalent citizenship as the paradoxical manner in which, through the external vote, states impose hegemonic notions of citizenship from above, which people embrace in an ambivalent manner from below. We show that the workings of the state make voting a difficult process; they create structural ambivalence for migrants who, even if they practise their citizenship in other ways, exercise individual ambivalence because they find it difficult to engage with a political system back home that they do not trust. The conceptualization of ‘ambivalent citizenship’ therefore encompasses the contradictory complexities inherent in the provision of external voting rights that actively privilege and exclude migrants in mutually constitutive ways.     

The two-party system under alternative voting procedures

Countries that elect their policy-makers by means of Plurality Voting tend to have a two-party system. This observation can be explained by the strategic behavior of voters. This article derives two broad classes of voting procedures under which strategic voting behavior induces a two-party system under standard assumptions on voter preferences. One class consists of the voting procedures with unique top-score, i.e., under which a voter can cast a top-score vote for only one candidate (e.g., Plurality Voting, Borda Count). The other class consists of the voting procedures that permit truncated ballots, i.e., under which voters do not have to cast all their votes (e.g., Approval Voting). This analysis suggests that the key for strategic voting behavior to induce a two-party system is that voters can always cast a different score for the two candidates they rank first and second on their ballots.     

Voters and Values in the 2004 Election

A poorly devised exit poll question undermined meaningful analysisof voters’ concerns in the 2004 presidential election.Twenty-two percent of voters picked "moral values" from a listof "issues" describing what mattered most in their vote, morethan selected any other item. Various commentators have misinterpretedthis single data point to conclude that moral values are anascendant political issue and to credit conservative Christiangroups with turning George W. Bush’s popular vote defeatin 2000 into his three million–vote margin of victoryin 2004. We suggest, rather, that while morals and values arecritical in informing political judgments, they represent personalcharacteristics and ill-defined policy preferences far morethan any discrete political issue. First by conflating moralsand values and then by further conflating characteristics andissues, the exit poll’s "issues" list distorted our understandingof the 2004 election. In this article, we examine the flawsin the 2004 National Election Pool exit poll’s "most importantissue" question and explore the presumed rising electoral importanceof moral values and the conservative Christians who overwhelminglyselected this item. Using national exit poll data from 1980through 2004 and other national surveys, we find that the moralvalues item on the issues list cannot properly be viewed asa discrete issue or set of closely related issues; that itsimportance to voters has not grown over time; and that whencontrolled for other variables, it ranks low on the issues listin predicting 2004 vote choices. The aggregated exit poll dataalso show that the voting behavior of conservative Christiansis relatively stable over time, and these voters were not primarilyresponsible for Bush’s improvement in 2004 over 2000.     

Strategic, sincere, and heuristic voting under four election rules: an experimental study

We report on laboratory experiments on voting. In a setting where subjects have single-peaked preferences, we find that the rational choice theory provides very good predictions of actual individual behavior in one-round and approval voting elections but fares poorly in explaining vote choice under two-round elections. We conclude that voters behave strategically as far as strategic computations are not too demanding, in which case they rely on simple heuristics (under two-round voting) or they just vote sincerely (under single transferable vote).     

Reconsidering Explanations for Regional Convergence in Voter Registration and Turnout in the United States, 1956–20001

In the United States, voter turnout rates have been declining for the last 4 decades; however, this pattern differs substantially by region. Southern states have actually seen a fairly dramatic increase in turnout since the 1950s and currently the South and non‐South have almost identical rates of voter registration and turnout. Using a series of Heckman probit models, which examine voting as a two‐step process of registering and casting a vote, we systematically investigate differences in rates of registering and voting across regions and test explanations for regional convergence over time. Using data from the American National Election Studies (1956–2000), we find that regional convergence in voter registration is primarily due to the removal of formal and informal barriers to registration and voting in the South and declining efforts to mobilize potential voters in the non‐South. In addition, we find some fairly distinct differences in which predictors are important to each stage of the voting process; for example, race is a better predictor of registering to vote than voting. We conclude with a discussion of the implications of these results.     

CAMPAIGN SPENDING IN CONGRESSIONAL ELECTIONS

Past research of the effects of campaign spending in Congressional elections has found, contrary to expectations, that incumbent spending lowers votes he or she receives. Our model simultaneously determines votes and spending and eliminates this anomaly. A measure comparing the incumbent's voting record to constituent preferences aids model identification. Using two-stage least squares, we find that both incumbent and challenger spending are signficant determinants of the popular vote received. Tenure and spending appear to have diminishing returns, and voters appear to punish incumbents who vote against their wishes.     

Unlikelihood of Condorcet’s paradox in a large society

We provide intuitive, formal, and computational evidence that in a large society Condorcet’s paradox (the intransitivity of social preference obtained by pairwise vote) can hardly occur. For that purpose, we compare two models of social choice, one based on voting and another one based on summing individual cardinal utilities, expressed either in reals, or integers. We show that in a probabilistic model with a large number of independent individuals both models, almost surely, provide the same decision results. This implies that Condorcet’s and Borda’s methods tend to give the same decisions as the number of voters increases. Therefore, in the model with a large number of voters, the transitivity of the Borda preference is inherent in a majority preference as well. Received: 26 June 1998/Accepted: 16 April 1999     

Pre-election polling and third party candidates

I analyze voters’ incentives in responding to pre-election polls with a third party candidate. Third party supporters normally have an incentive to vote strategically in the election by voting for one of the major candidates. But these voters would vote third party if the third party candidate is doing surprisingly well in the polls. Because voters are more likely to vote third party if the third party candidate is doing well in polls, voters who like the third party candidate best have an incentive to claim they will vote third party in the polls so that more voters will ultimately vote third party in the election. The differing incentives faced during polls and elections accounts for why third party candidates do better in polls than in elections.     

Voting power: an information theory approach

In recent years, there has been increasing awareness of the importance of formal measures of voting power and of the relevance of such measures to real life political issues. Nevertheless, existing measures have been criticized, especially because of their dependence on the unrealistic assumption that different coalitions have equal probabilities. In this paper we show that the classical problem of measuring voting power can be naturally embedded in information theory. This perspective on voting power allows us to extend measures of voting power to cases in which there are dependencies among voters. In doing so, we distinguish between two different notions of a given voter’s power—‘control’ and ‘informativeness’—corresponding, respectively, to the average uncertainty regarding the outcome of a vote that remains when all others have voted and the average uncertainty that is eliminated when only the given voter has voted. This distinction settles a number of well-known paradoxes and enables the study of voting power on the basis of actual political behavior at all levels.     

Do Absentee Voters Differ from Polling Place Voters?: New Evidence from California

In the 2003 California gubernatorial recall election 2,775,785absentee ballots were cast, representing about 30 percent ofall voters statewide. Given the number of absentee ballots andthe increasing propensity for voters in California and elsewhereto choose this voting method, we some basic questions: Who areabsentee voters, and are they different from polling place voters?To answer these questions, we fielded a statewide survey ofabsentee voters in the days before the October 7 recall election,asking respondents why they voted absentee, their partisan andideological preferences, demographic characteristics, and otherrelevant questions. We find that absentee voters do not differsignificantly from the overall state electorate in terms oftheir vote preferences, despite being older and better educated.For example, 56 percent of absentee voters in our survey voted"yes" on the recall, compared with 55 percent for the entirestate, according to official returns. Further, absentee votersfavored Arnold Schwarzenegger over Cruz Bustamante by a considerablemargin, similar to the overall election results. We found partyregistration among absentee voters to be nearly identical tostatewide partisan registration.     

Enlargement and the balance of power: an experimental study

Theoretical analysis suggests that enlargement of a voting body may affect the balance of power between the original members even if their number of votes and the decision rule remain constant. Some of the existing voters may actually gain, a phenomenon known as the paradox of new members. We test for this effect using laboratory experiments. Participants propose and vote on how to divide a budget according to weighted majority voting rules, and we measure the voting power of a player by his average payoff in the experiment. By comparing voting power across voting bodies of varying size, we find empirical support for the paradox of new members.     

Alienation,indifference and the choice of ideological position

In this paper we describe a simple model of individual voting behavior and present its implications for the candidate positioning problem under both vote and plurality maximization. Under our assumptions, some voters at the extremes of the ideological spectrum typically will not vote because they are alienated by the equilibrium location of candidates. There will also be some voters in the middle of the ideological spectrum who will not vote because they are indifferent between the equilibrium locations of the candidates. Both the abstention from alienation and from indifference arise explicitly from utility maximization. Once we allow for alienation and indifference, the two alternative candidate objective functions (vote maximization and plurality maximization) yield different outcomes. In particular, we show that under vote maximization the Median Voter (or Minimum Differentiation) outcome will not arise. On the other hand, under plurality maximization, the Median Voter outcome may or may not hold, depending on the distribution of voter preferences.We should like to thank Jerry Fusselman, Jon Hamilton, Mel Hinich, Charlie Holt and participants at seminars at the University of Virginia, Northwestern University and the 1989 Meetings of the Public Choice Society and the Economic Science Association for their helpful comments.     

DECEPTION AND POLITICAL PARTICIPATION: THEORY AND LABORATORY EVIDENCE

We model two‐candidate elections in which (1) voters are uncertain about candidates' attributes; and (2) candidates can inform voters of their attributes by sending advertisements. We compare between political campaigns with truthful advertising and campaigns in which there is a small chance of deceptive advertising. Our model predicts that voters should vote in‐line with an advertisement's information. We test our model's predictions using laboratory elections. We find, in the presence of even a small probability that an advertisement is deceptive, voters become substantially more likely to elect a “low‐quality” candidate. We discuss implications of this for existing models of voting decisions. (JEL C92, D72, D82)     

Is it ever safe to vote strategically?

There are many situations in which mis-coordinated strategic voting can leave strategic voters worse off than they would have been had they not tried to strategise. We analyse the simplest of such scenarios, in which a set of strategic voters all have the same sincere preferences and all contemplate casting the same strategic vote, while all other voters are not strategic. Most mis-coordinations in this framework can be classified as instances of either strategic overshooting (too many voted strategically) or strategic undershooting (too few). If mis-coordination can result in strategic voters ending up worse off than they would have been had they all just voted sincerely, we call the strategic vote unsafe. We show that under every onto and non-dictatorial social choice rule there exist circumstances where a voter has an incentive to cast a safe strategic vote. We extend the Gibbard–Satterthwaite Theorem by proving that every onto and non-dictatorial social choice rule can be individually manipulated by a voter casting a safe strategic vote.     

VOTING EXPRESSIVELY

We address a common criticism directed toward models of expressive voting that they are ad hoc in nature. To that end, we propose a foundation for expressive behavior that is based on a novel theory of social preferences under risk. Under our proposal, expressive considerations in behavior arise from the particular way in which risky social prospects are assessed by decision‐makers who want to interpret their choices as moral. To illustrate the scope of our framework, we use it to address some key questions in the literature on expressive voting: why, for expressive considerations, might voters vote against their self‐interest in large elections and why might such elections exhibit a moral bias. Specifically, we consider an electoral set‐up with two alternatives and explain why, when the size of the electorate is large, voters may want to vote for the alternative they deem morally superior even if this alternative happens to be strictly less preferred, in an all‐inclusive sense, than the other. (JEL D01, D03, D81, D72, A13)     

Simple manipulation-resistant voting systems designed to elect Condorcet candidates and suitable for large-scale public elections

This article focuses on voting systems that (i) aim to select the Condorcet candidate in the common case where one exists and (ii) impede manipulation by exploiting voter knowledge of electorate preferences. The systems are relatively simple, both mathematically and for voter understanding, and are fully workable for large-scale elections. Their designated equilibrium strategies, under which voters vote sincerely, involve discerning the top one or two candidates in the preference ordering of the electorate. One set of systems uses its ballot to obtain voters’ preference rankings plus approval votes, and tallies the latter if no Condorcet winner exists. It offers solid advantages vis-à-vis instant-runoff voting, which uses a kindred ballot and has attracted recent reformers. Another set of systems uses only approval voting, which is examined from a new angle.     

The power of a cohesive subgroup within a voting body

We examine the power of a subgroup within a voting body as a function of its size and cohesiveness. The measure of cohesiveness is the probability that an arbitrary member of the subgroup will vote the same way as the leader of the subgroup. All voters are assumed to vote independently, and those not in the subgroup vote for or against with probability 1/2 in each case. The power of the subgroup is the probability that its vote differential exceeds the vote differential of the members of the body not in the subgroup. Tradeoffs between relative subgroup size and its follow-the-leader probability are considered.     

The power of a collectivity to act in weighted voting games with many small voters

We analyze the propensity to approve a random proposal of a large committee that makes decisions by weighted voting. The approach is a generalized version of James Coleman’s “power of a collectivity to act”. Throughout the paper it is assumed that the voters are of two kinds: a fixed (possibly empty) set of “major” (big) voters with fixed weights, and an ever-increasing number of “minor” (small) voters, whose total weight is also fixed, but where each individual’s weight becomes negligible. As our main result, we obtain that asymptotically many minor voters act like a modification of the quota for the vote among major voters. The paper estimates the rate of convergence which turns out to be very high if the weight distribution among the small voters is not too skewed. The results obtained are illustrated by evaluating the decision rules for the Council of Ministers of the EU for various scenarios of EU enlargement. I wish to thank Matthew Braham, Sidartha Gordon, Maurice Koster, Moshé Machover, Guillermo Owen and two anonymous referees for helpful comments.     

Optimal voting rules for two-member tenure committees

A tenure committee first votes on whether to hire a candidate; if it does, it receives an informative performance signal, and then votes on whether to tenure the candidate; rejection at either stage returns the committee to a candidate pool, endogenising the value of the outside option. A candidate’s fate depends only on the behaviour of two ‘weather-vane’ committee members. Committee members may vote against favoured candidates if the weather-vane is opposed; enthusiastic assessments by one of these weather-vanes may harm a candidate’s chances by increasing others’ thresholds for hiring him; sunk time costs may lead voters who voted against hiring to vote for tenuring him, even after a poor probationary performance. For two member committees that are patient and perceptive, the optimal voting rule is a (weak) majority at the hiring stage and unanimity at the tenure stage; when such committees are impatient or imperceptive, the double (weak) majority rule is optimal. Perversely, the performance of a patient, imperceptive committee improves as its perceptiveness further declines. Consistent with practice, falling threshold rules are not optimal. Results on optimal voting rules are also presented in limit cases as committee members’ beliefs become more correlated. Finally, we compare the model to a discrete-time European options model.