A comparison of Dodgson's method and the Borda count

Summary. In an election without a Condorcet winner, Dodgson's Method is designed to find the candidate that is “closest” to being a Condorcet winner. In this paper, we show that the winner from Dodgson's Method can occur at any position in the ranking obtained from the Borda Count, the plurality method, or any other positional voting procedure. In addition, we demonstrate that Dodgson's Method does not satisfy the Independence of Irrelevant Alternatives axiom. Received: January 12, 2001; revised version: June 7, 2001     

Manipulation through political endorsements

We study elections with three candidates under plurality voting. A candidate is a Condorcet loser if the majority of the voters place that candidate at the bottom of their preference rankings. We first show that a Condorcet loser might win the election in a three-way race. Next we introduce to the model an endorser who has private information about the true probability distribution of the preferences of the voters. Observable endorsements facilitate coordination among voters who may otherwise split their votes and lead to the victory of the Condorcet loser. When the endorser has an ideological bias towards one of the candidates, the coordination impact of endorsements remains unaltered, moreover the endorser successfully manipulates the outcome of the election in favor of his bias, even if his ideological bias is known by the voters. The results are true for any endorsement cost and any magnitude of bias as long as the electorate is large enough.     

The likelihood of dubious election outcomes

Summary. A disturbing phenomenon in voting, which causes most of the problems as well as the interest in the field, is that election outcomes (for fixed preferences) can change with the way the ballots are tallied. This causes difficulties because with each possible choice, some set of voters can be dubious about whether it is the “correct” one. But, how likely are these settings allowing multiple election outcomes? By combining properties of the geometry of voting developed by Saari with a analytic-geometric technique created by Schlafli, we determine the likelihood that a three candidate election can cause these potentially dubious outcomes. Received: April 11, 1997; revised version: November 12, 1997     

Decisiveness of contributors’ perceptions in elections

We consider a model of two-candidate elections with a one-dimensional policy space. Spending on campaign advertisements can directly influence voters’ preferences, and contributors give the money for campaign spending in exchange for promised services if the candidate wins. We find that the winner of the election depends crucially on the contributors’ beliefs about who is likely to win and the contribution market tends toward nonsymmetric equilibria in which one of the two candidates has no chance of winning. If the voters are only weakly influenced by advertising or if permissible campaign spending is small, then the candidates choose policies close to the median voter’s ideal point, but the contributors still determine the winner. Uncertainty about the Condorcet winning point (or its nonexistence) can change these results and generate equilibria in which both candidates have substantial probabilities of winning.     

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.     

The Borda method is most likely to respect the Condorcet principle

Summary We prove that in the class of weighted voting systems the Borda Count maximizes the probability that a Condorcet candidate is ranked first in a group election. A direct result is that the Borda Count maximizes the probability that a transitive, binary ranking of the candidates is preserved in a group election. A preliminary result, but one of independent interest, is that the Borda Count maximizes the probability that a majority outcome betweenany two candidates is reflected by the group election. All theorems are valid when there is a uniform probability distribution on the voter profiles and can be generalized to other uniform-like probability distributions. This work extends previous results of Fishburn and Gehrlein from three candidates to any number of candidates.This work is a portion of my doctoral dissertation The Geometric Investigation of Voting Techniques: A Comparison of Approval Voting, Positional Voting Techniques and the Borda Count written under Don Saari at Northwestern University, Evanston, Illinois.     

Counterexamples on the Superiority of Approval versus Plurality

We present a simple voting environment with three candidates where the Condorcet winner exists. Under plurality rule, the derived game has a stable set where such a candidate is elected with probability one. However, no stable set of the approval game elects the Condorcet winner with positive probability. We also analyze the robustness of such an example to changes in the number of voters and their preferences. To conclude, we present a generic four‐candidate voting environment with the same properties.     

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.     

A strategy-proofness characterization of majority rule

Summary. A feasible alternative x is a strong Condorcet winner if for every other feasible alternative y there is some majority coalition that prefers x to y. Let (resp., denote the set of all profiles of linear (resp., merely asymmetric) individual preference relations for which a strong Condorcet winner exists. Majority rule is the only non-dictatorial and strategy-proof social choice rule with domain , and majority rule is the only strategy-proof rule with domain . Received: August 29, 2000; revised version: November 13, 2002 RID="*" ID="*"We are grateful to Wulf Gaertner and our two referees for insightful comments on a previous draft. Correspondence to: D. E. Campbell     

Economic theory and econometric dynamics in modelling wages and prices in the United Kingdom

We show that a “competing claims” model of imperfect competition can explain the movements of wages and prices in the United Kingdom, using quarterly data covering 1976–93. We argue that careful attention both to economic theory and to the interaction between dynamics and identification is crucial in the building of the model and to dynamic econometric models in general. We use a small numerical example with simulated cointegrated data to illustrate the potential pitfalls. First version received: January 1998/final version received: November 1998     

The Borda rule,Condorcet consistency and Condorcet stability

Summary. The Borda rule is known to be the least vulnerable scoring rule to Condorcet inconsistency, Saari (2000). Such inconsistency occurs when the Condorcet winner (the alternative which is preferred to any other alternative by a simple majority) is not selected by the Borda rule. This note exposes the relationship between the Borda rule and the Condorcet q-majority principle as well as the Condorcet q-majority voting rule. The main result establishes that the Borda rule is Condorcet q-majority consistent when where k is the number of alternatives. The second result establishes that is the minimal degree of majority decisiveness corresponding to the Borda rule under sincere voting. The same majority is required to ensure decisiveness under the Borda rule and to ensure that a q-rule (the generalized q-majority Condorcet rule) is a voting rule. Received: April 8, 2002; revised version: July 17, 2002 Correspondence to:S. Nitzan     

Comparison of Scoring Rules in Poisson Voting Games

Scoring rules are compared by their equilibria in simple voting games with Poisson population uncertainty, using new techniques for computing pivot probabilities. Best-rewarding rules like plurality voting can generate discriminatory equilibria where the voters disregard some candidate as not a serious contender, although he may be universally liked, or may be symmetric to other candidates as in the Condorcet cycle. Such discriminatory equilibria are eliminated by worst-punishing rules like negative voting, but then even a universally disliked candidate may have to be taken seriously. In simple bipolar elections, equilibria are always majoritarian and efficient under approval voting, but not other scoring rules. Journal of Economic Literature Classification: D72.     

Partially Binding Platforms: Campaign Promises vis‐à‐vis Cost of Betrayal

This study examines and models the effects of partially binding campaign platforms in a political competition. Here, a candidate who implements a policy that differs from the platform must pay a cost of betrayal, which increases with the size of the discrepancy. I also analyse endogenous decisions by citizens to run for an election. In particular, the model is able to show two implications that previous frameworks have had difficulty with. First, candidates with different characteristics have different probabilities of winning an election. Second, even knowing that he/she will lose an election, a candidate will still run, hoping to make an opponent's policy approach his/her own policy.     

Self-Selection Consistent Functions

This paper studies collective choice rules whose outcomes consist of a collection of simultaneous decisions, each one of which is the only concern of some group of individuals in society. The need for such rules arises in different contexts, including the establishment of jurisdictions, the location of multiple public facilities, or the election of representative committees. We define a notion of allocation consistency requiring that each partial aspect of the global decision taken by society as a whole should be ratified by the group of agents who are directly concerned with this particular aspect. We investigate the possibility of designing efficient allocation consistent rules. We also explore whether such rules may in addition respect the Condorcet criterion. Journal of Economic Literature Classification Numbers: D7, D71.     

Condorcet Jury Theorem or Rational Ignorance

We analyze a symmetric model of an election in which voters are uncertain about which of two alternatives is desirable for them. Each voter must incur some cost to acquire information about the alternatives. We show that by focusing on unbiased voting strategies, general symmetric signal structures can be degenerated to a two‐signal model. In addition, we show that for any sequence of unbiased voting equilibria, if the second‐order derivative of the information cost function at no information is zero, then the probability of electing the desirable alternative converges to one, that is, the Condorcet Jury Theorem is valid. Otherwise, this probability converges to some value less than one; that is, the “rational ignorance” hypothesis is valid.     

SEQUENTIAL VOTING WHEN LONG ELECTIONS ARE COSTLY

This paper analyzes sequential voting in binary elections when voters are motivated by a desire both to elect their preferred candidate and to avoid a long and costly election. I find a unique equilibrium in which a voter's action depends both on the intensity of the voter's preferences as well as how well the candidates have done in earlier voting rounds. This equilibrium results in momentum in which voters are more likely to vote for the candidate currently in the lead. Furthermore, the probability a voter votes for a candidate is increasing in the size of the candidate's lead. As a consequence, a candidate is more likely to win the election if the candidate's stronger supporters vote earlier in the election.     

Candidate quality and US Senate elections

We find that candidate quality is a key determinant of US Senate election outcomes. We model the results for the last 10 US Senate election cycles, from 2012 back to 1994, for a total of 345 election contests. For the contests where an incumbent seeks re-election, a quality challenger can significantly diminish the advantage that usually attaches to incumbency. For the open-seat contests, which tend to be more competitive, candidate quality can swing a close election. Governors who seek election to the US Senate receive the largest boost, as indicated by our candidate-quality variables vector. Wave effects and presidential coattail effects are also shown to be contributing factors in certain cases.     

Dominance solvable approval voting games

This work provides necessary and sufficient conditions for the dominance solvability of approval voting games. Our conditions are very simple since they depend just on the number of possible winners when voters play weakly undominated strategies. If there are at most two possible winners, then the game is dominance‐solvable and the outcome coincides with the Condorcet winner. If every candidate is a possible winner, the game is not dominance‐solvable. If none of the previous conditions holds, then the game need not be dominance‐solvable, and the outcome need not coincide with the Condorcet winner.     

Information and strategic voting

We theoretically and experimentally study voter behavior in a setting characterized by plurality rule and mandatory voting. Voters choose from three options. We are interested in the occurrence of strategic voting in an environment where Condorcet cycles may occur and focus on how information about the preference distribution affects strategic behavior. We also vary the relative importance of the second preferred option. Quantal response equilibrium analysis is used to analyze the game and derive predictions. Our results indeed show that strategic voting arises. Its extent depends on (i) information availability; (ii) the relative importance of the intermediate candidate; (iii) the electorate’s relative support for one’s preferred candidate; (iv) the relative position of the plurality-supported candidate in one’s preference ordering. Our results show that information serves as a coordination device where strategic voting does not harm the plurality-preferred candidate’s chances of winning.     

Are PACs Trying to Influence Politicians or Voters?

Political Action Committees (PACs) can affect public policies in either of two ways: altering legislators' roll-call voting behavior, or influencing election outcomes. This paper develops a dynamic model demonstrating that the relative importance of the election-influencing channel is easily underestimated. A one-time contribution to a candidate who supports the PAC's position that alters an election outcome yields benefits to the PAC as long as that candidate holds office. In contrast, roll-call vote buying is likely to operate on a quid-pro-quo basis, limiting the PAC's return on investment. Empirical tests based on the theoretical model suggest that PACs value the election-influencing aspect of contributions at least as much as the roll-call vote-buying channel.