Condorcet efficiency: A preference for indifference

The Condorcet winner in an election is the candidate who would be able to defeat all other candidates in a series of pairwise elections. The Condorcet efficiency of a voting procedure is the conditional probability that it will elect the Condorcet winner, given that a Condorcet winner exists. The study considers the Condorcet efficiency of weighted scoring rules (WSR's) on three candidates for large electorates when voter indifference between candidates is allowed. It is shown that increasing the proportion of voters who have partial indifference will increase the probability that a Condorcet winner exists, and will also increase the Condorcet efficiency of all WSR's. The same observation is observed when the proportion of voters with complete preferences on candidates is reduced. Borda Rule is shown to be the WSR with maximum Condorcet efficiency over a broad range of assumptions related to voter preferences. The result of forcing voters to completely rank all candidates, by randomly breaking ties on candidates that are viewed as indifferent, leads to a reduction in the probability that a Condorcet winner exists and to a reduction in the Condorcet efficiency of all WSR's. Received: 31 July 1999/Accepted: 11 February 2000     

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.     

Condorcet efficiencies under the maximal culture condition

The Condorcet winner in an election is a candidate that could defeat each other candidate in a series of pairwise majority rule elections. The Condorcet efficiency of a voting rule is the conditional probability that the voting rule will elect the Condorcet winner, given that such a winner exists. The study considers the Condorcet efficiency of basic voting rules under various assumptions about how voter preference rankings are obtained. Particular attention is given to situations in which the maximal culture condition is used as a basis for obtaining voter preferences. Received: 4 February 1998/Accepted: 13 April 1998     

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.     

A Signaling Model of Repeated Elections

I develop a two period model of elections in which voters’ first period actions affect candidates’ estimates of voter preferences and thus affect second period electoral and policy outcomes. I find an equilibrium in which centrist voters abstain in the first election, despite facing zero costs of voting and having a strict preference between the alternatives before them. The reason centrists abstain is to signal their preferences to future candidates and thereby promote future policy moderation.For helpful discussions and comments I thank David Austen-Smith, Tim Feddersen, Roger Myerson, Tom Palfrey, Ronny Razin, two anonymous reviewers, and seminar participants at Kellogg, NYU, and the 2000 World Congress of the Game Theory Society.     

An Elite View of the Polls

This research note examines the views of election polls of asample of political activists: delegates elected to the 1980state conventions of the Oklahoma Democratic and Republicanparties. Findings show that although just l3 percent of thedelegates overall place high levels of trust in the resultsof major national polls, nearly a majority (45 percent) feelthat poll results affect voter behavior. Both trust in electionpolls and perception of their impact on voters are found toincrease with involvement or interest in electoral politics.     

Symmetry extensions of “neutrality” I: Advantage to the condorcet loser

This is the first of three papers introducing a theory for positional voting methods that determines all possible election rankings and relationships that ever could occur with a profile over all possible subsets of candidates for any specified choices of positional voting methods. As such, these results extend to all positional voting systems what was previously possible only for the Borda Count and the plurality voting systems. In this first part certain mathematical symmetries based on neutrality are used 1) to generalize the basic properties that cause the desired features of the Borda Count and 2) to describe classes of positional voting methods with new types of election relationships among the election outcomes. Some of these relationships generalize the well-known results about the positioning of a Condorcet winner/loser within a Borda ranking, but now it is possible for the Condorcet loser, rather than the winner, to have the advantage to win certain positional elections. Included among the results are axiomatic characterizations of many positional voting methods.This research was supported in part by NSF Grant IRI-9103180.     

Likely (and Unlikely) Voters and the Assessment of Campaign Dynamics

Only in recent years has the "likely voter" technology beenextended to polls well in advance of an election. In the caseof the 2000 U.S. presidential election, CNN/USA Today/Galluptracking polls indicated considerable fluctuations in likelyvoter preferences, greater than among the larger pool of registeredvoters surveyed. This article explores how Gallup’s likelyvoter model exaggerates the reported volatility of voter preferencesduring the campaign. Much of the reported variation in candidatepreference reported by Gallup in that election is not due toactual voter shifts in preference but rather to changes in thecomposition of Gallup’s likely voter pool. The findingshighlight dangers of relying on samples of likely voters whenpolling well before Election Day.     

Social choice by majority rule with rational participation

This paper explores the social choice properties of majority rule when voters rationally participate in elections. Employing the basic model of voter behavior developed originally by Ledyard (1984) and Palfrey and Rosenthal (1985), we show that when the electorate is sufficiently large, a participation equilibrium exists and is unique. The main result of the paper shows that under these conditions the social preference ordering induced by majority rule is identical to that given by the expected utility of a randomly selected voter, implying the existence of a Condorcet point in the proposal space. A final section provides intuition for the main theorems and relates the equilibrium of this majority rule game to the median voter result.     

An extension of the Moulin No Show Paradox for voting correspondences

In this article, we analyse the possibility of extending the Moulin theorem to Condorcet voting correspondences. Moulin (1988) established that every Condorcet voting function suffers from the No Show Paradox, or Abstention Paradox, which means that in some voting situations some voters would achieve a better result by abstaining (in other words, could manipulate the election by abstaining). This problem is similar to that of extending the Gibbard–Satterthwaite theorem on voting manipulation through casting an insincere ballot to voting correspondences. The main result of the paper states that for every Condorcet voting correspondence there are situations in which every optimistic or pessimistic voter with some preferences could manipulate the election by abstaining. Another result states, by counterexample, that some Condorcet voting correspondences are free from the Abstention Paradox from the point of view of other types of voters.     

The Relative Irrelevance of Candidate Sex

Abstract

This study tests the relevance of candidate sex to electoral contests. We predict that voters, in general, will use issue or party cues to select between candidates and not the sex of the candidate. This will not hold under two conditions: party or issue cues are unavailable or candidate sex is likely to be particularly salient to the voter. Data were collected from a random sample of registered voters who were presented with hypothetical elections featuring candidates who were systematically varied by party, position on abortion, and sex. The results are consistent with the line of research that suggests that the majority of voters do not use candidate sex as a cue for choice, but candidate sex does affect choice among those for whom gender equality issues are particularly salient. Although generally irrelevant, candidate sex can have significant implications for the outcome of particular contests.     

On removing Condorcet effects from pairwise election tallies

Condorcet profiles are responsible for a number of well known preference aggregation paradoxes. It is reasonable to claim that these profiles represent complete ties between the candidates and should therefore be excluded to determine election outcomes. Established profile decomposition techniques are of limited usefulness in extracting and removing Condorcet effects, because of the computational complexity involved, even if complete knowledge of voters’ rankings of all candidates are available. The paper discusses an easily implementable method of removing or reducing Condorcet effects from pairwise scores. Pairwise scores (and not complete knowledge of voters’ rankings) are often the only available data based on which an election winner has to be determined.     

A Review and Proposal for a New Measure of Poll Accuracy

This article proposes a new measure of the predictive accuracy(A) of election polls that permits examination of both accuracyand bias, and it applies the new measure to summarize the resultsof a number of preelection polls. We first briefly review pastmeasures of accuracy, then introduce the new measure. Afterthe new measure is described, the general strategy is to applyit to three presidential elections (1948, 1996, and 2000) andto compare the results derived from it to the results obtainedwith the Mosteller measures. Then, the new measure is appliedto the results of 548 state polls from gubernatorial and senatorialraces in the 2002 elections to illustrate its application toa large body of preelection polls conducted in "off-year" raceswith different outcomes. We believe that this new measure willbe useful as a summary measure of accuracy in election forecasts.It is easily computed and summarized, and it can be used asa dependent variable in multivariate statistical analyses ofthe nature and extent of biases that affect election forecastsand to identify their potential sources. It is comparable acrosselections with different outcomes and among polls that varyin their treatment or numbers of undecided voters.     

The Strong No Show Paradoxes are a common flaw in Condorcet voting correspondences

The No Show Paradox (there is a voter who would rather not vote) is known to affect every Condorcet voting function. This paper analyses two strong versions of this paradox in the context of Condorcet voting correspondences. The first says that there is a voter whose favorite candidate loses the election if she votes honestly, but gets elected if she abstains. The second says that there is a voter whose least preferred candidate gets elected if she votes honestly, but loses the election if she abstains. All Condorcet correspondences satisfying some weak domination properties are shown to be affected by these strong forms of the paradox. On the other hand, with the exception of the Simpson-Cramer Minmax and the Young rule, all the Condorcet correspondences that (to the best of our knowledge) are proposed in the literature suffer from these two paradoxes. Received: 30 November 1999/Accepted: 27 March 2000     

Out of Step? Voters and Social Issues in U.S. Presidential Elections

Recent political commentary has argued that the Republican Party is “out of step” with voters on social issues, costing Republicans the 2012 presidential election. This dramatic claim is deserving of scrutiny in its own right and also for the way it offers new perspective on long‐standing controversies concerning the role of social issues in U.S. national elections. We present results that seek to advance established scholarship on electoral politics as well as journalistic claims concerning the rising importance of social issues for elections. Using data from the American National Election Study, we find that social issues mattered to voters in presidential elections from 1992 through 2012. The influence of social issues on voter choice rivals those of attitudes toward defense spending and government provision. We find further evidence that liberalizing trends in social issue opinion consistently benefited Democratic candidates in presidential elections. We consider the relevance of these results for scholarship on voter choice and elections, noting further implications for commentary on the 2012 presidential election.     

THE EMERGENCE OF BANDWAGON EFFECTS: A THEORY

Previous explanations of bandwagons from election polls have exclusively emphasized conformity causes. We propose, in addition, "indirect' causes, in which election predictions first affect key actors, influencing their decisions concerning financial support, volunteer work, or endorsements. These decisions then produce major campaign alterations that influence the voters and alter the election outcome. Our addition clarifies anomalous bandwagon research findings and directs attention to the possibility of bandwagon feedback on subsequent elections. If the same forecasters create frequent bandwagon effects, their credibility should increase as a result of enhanced accuracy. But increased credibility should in turn increase the self-fulfilling tendency of their subsequent forecasts. Such deviation-amplifying feedback would permit polls to produce a highly significant, and expanding, influence on elections.     

Simple plurality versus plurality runoff with privately informed voters

This paper compares two voting methods commonly used in presidential elections: simple plurality voting and plurality runoff. In a situation in which a group of voters have common interests but do not agree on which candidate to support due to private information, information aggregation requires them to split their support between their favorite candidates. However, if a group of voters split their support, they increase the probability that the winner of the election is not one of their favorite candidates. In a model with three candidates, due to this tension between information aggregation and the need for coordination, plurality runoff leads to higher expected utility for the majority than simple plurality voting if the information held by voters about the candidates is not very accurate. Received: 12 September 2000/Accepted: 8 November 2001     

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.     

The sensitivity of weight selection for scoring rules to profile proximity to single-peaked preferences

Niemi (Am Polit Sci Rev 63:488–497, 1969) proposed a simple measure of the cohesiveness of a group of n voters’ preferences that reflects the proximity of their preferences to single-peakedness. For three-candidate elections, this measure, k, reduces to the minimum number of voters who rank one of the candidates as being least preferred. The current study develops closed form representations for the conditional probability, PASW(n,IAC|k), that all weighted scoring rules will elect the Condorcet winner in an election, given a specified value of k. Results show a very strong relationship between PASW(n,IAC|k) and k, such that the determination of the voting rule to be used in an election becomes significantly less critical relative to the likelihood of electing the Condorcet winner as voters in a society have more structured preferences. As voters’ preferences become more unstructured as measured by their distance from single-peakedness, it becomes much more likely that different voting rules will select different winners.A preliminary version of this paper was presented at the European Public Choice Society Conference in Berlin, Germany, April 15–18, 2004.     

Sequential elections with limited information

We develop an incomplete information model of a sequence of elections in a one-dimensional policy space, where voters have no contemporaneous information about candidate positions, and candidates have no information about voter preferences. The only source of information is contemporaneous endorsement data and historical data on the policy positions of previous winning candidates. We define a notion of stationary rational expectations equilibrium, and show that such an equilibrium results in outcomes which are equivalent to those that would occur under full information.We acknowledge support from ISF Grant #SES 82-08184 and #SES84-09654