Majority Runoff Elections: Strategic Voting and Duverger's Hypothesis

The majority runoff system is widely used around the world, yet our understanding of its properties and of voters’ behavior is limited. In this paper, we fully characterize the set of strictly perfect voting equilibria in large three-candidate majority runoff elections. Considering all possible distributions of preference orderings and intensities, we prove that only two types of equilibria can exist. First, there are always equilibria in which only two candidates receive votes. Second, there may exist an equilibrium in which three candidates receive votes. Its characteristics challenge common beliefs: (i) neither sincere voting by all voters nor pushover tactics (i.e., supporters of the front-runner voting for a less preferred candidate so as to influence who will face the front-runner in the second round) are supported in equilibrium, and (ii) the winner does not necessarily have democratic legitimacy since the Condorcet winner may not even participate in the second

Strategic Voting in Two-Party Legislative Elections

We study the voting game where agents' preferences are endogenously decided by the information they receive, and they can collaborate in a group. We show that strategic voting behaviors have a positive impact on leading to the "correct" decision, outperforming the common non-strategic behavior of informative voting and sincere voting. Our results give merit to strategic voting for making good decisions.

Numerous studies investigate how personality traits and individual characteristics influence vote choice. However, the effect of risk attitudes on the proclivity to cast a strategic vote has not been tested yet. This article tests whether the likelihood of defecting from one’s preferred party is influenced by attitudes towards risk. I argue that the utility stemming from expressing a preference by opting for the favored party is a sure thing, whereas the utility stemming from an instrumental choice depends on some probabilities, and consequently that strategic voting is riskier than sincere voting. Using survey data from the United Kingdom and Canada, I find that risk-averse voters are less likely to vote strategically than risk-acceptant ones.

Approval voting (AV) has been defended and criticized from many different viewpoints. In this paper, I will concentrate on two topics: preference intensities and strategic behavior. A voter is usually defined as voting sincerely under AV if he or she gives a vote to all candidates standing higher in his or her ranking than the lowest-ranking candidate for whom he or she gives a vote. There are no ‘holes’ in a voter’s approval set.1 Since this kind of behavior is extremely rare, it has been claimed that approval voting makes strategic voting unnecessary (Brams and Fishburn 1978). On the other hand, Niemi (1984) has argued (see also van Newenhizen and Saari 1988a,b), that even though strategic voting may be rare under AV, even incere voting may require a considerable amount of strategic thinking under this rule. If strategic voting is defined by the fact that a voter gives his or her vote to a candidate who is lower in his or her ranking than some candidate for whom he or she does not vote (see, e.g., Brams and Sanver 2006), I will be studying strategic behavior but not strategic voting under AV here.KeywordsPublic ChoiceVote RuleStrategic BehaviorVote ShareSincere BehaviorThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

How widespread is strategic voting in two-round electoral systems, and which types of voters are most likely to engage in such behavior? While runoff elections are common in presidential systems around the world, research on strategic voting in these settings remains limited. This paper explores four different types of strategic behavior that are possible in two-round systems, including some types, such as “strong-to-weak” strategic voting, which are not possible in single-shot elections. We use a nationwide survey to assess the incidence and correlates of strategic voting in Brazil’s 2018 presidential election, where thirteen candidates competed in the first round. We find evidence of “weak-to-strong” strategic voting at a similar rate to that documented in single-round elections in other countries. We find little evidence of other types of strategic voting. Furthermore, we show that voters’ confidence in their predictions of the likely electoral outcome and their ideological preferences strongly predict strategic voting. These results point to the importance of accounting for voter beliefs and attitudes in addition to objective voter characteristics to explain strategic voting.

The literature on agendas with sincere and strategic voting represents an important contribution to our understanding of committees, of institutions, and of the opportunities to manipulate outcomes by the manipulation of institutions. That literature, though, imposes an assumption that may be unrealistic in many situations; namely, that everyone knows the preferences of everyone else. In this essay we apply Bayesian equilibrium analysis to show that the properties of agendas that others derive by assuming complete information do not hold necessarily under incomplete information. First, a Condorcet winner need not be selected, even if nearly everyone on the committee most prefers it. Second, the two-step theorem, that any outcome reachable in n voting stages via some amendment agenda is reachable in two stages under sophisticated voting, need not hold. Third, nonbinding votes, such as straw polls, can critically affect final outcomes.

Approval Voting is analyzed in a context of large elections with strategic voters: the Myerson’s Large Poisson Games. We first establish the Magnitude Equivalence Theorem which substantially reduces the complexity of computing the magnitudes of the pivot outcomes. Furthermore, we show that the Condorcet Winner need not be the Winner of the election in equilibrium under Approval Voting. Indeed, a ‘paradoxical’ example is provided where a candidate ranked first by more than half of the voters is not the Winner of the election.

From the perspective of some common criteria for evaluating voting procedures, the results we offer in this essay will almost certainly be interpreted as inditments of STV. Even if we restrict preferences with conditions R1 and R2, STV is not necessarily incentive compatible. Moreover, strategic voting does not ensure the selection of Condorcet winning candidates or of Condorcet outcomes. This fact, moreover is not dependent on the existence of “bogus” equilibria — outcomes that exclude Condorcet candidates cannot be avoided under all circumstances even if we limit our analysis to strong or to individually stable equilibria. It is not the case, though, that the Condorcet criterion is the unique or even the most important criterion with which to evaluate election procedures. For example, we have not examined the extent to which STV ensures proportionality and we have not compared STV to other procedures. Despite the apparent deficiencies described in this essay, STV may yet prove to be a viable alternative to systems that seek to ensure proportionality by other means.

The history of political theory can shed light on the question of what political contexts are and are not appropriate for Quadratic Voting (QV), and the methods by which extra votes might be distributed when QV is appropriate. Ancient Greek and contemporary political thought draws attention to the connections between the assumed equality of moral worth among citizens and systems of voting, and to the relationship between equality or inequality of standing to the bases of dessert and the fair distribution of political influence in a democratic state. These matters in turn bear directly on democratic legitimacy, and thus on the stability of the social order. Some issues that must be decided in a democratic community concern common interests. Common-interest issues, based on widely held conceptions of equal moral worth, are not appropriately determined by preference intensity, and thus are inappropriate for a QV voting system. Real-money versions of QV risk undermining respect for law and democratic legitimacy. The costs of system-threatening civil conflict attendant upon loss of legitimacy outweighs any efficiency gains within the system. Token-currency versions of QV, which do not threaten democratic legitimacy, are a more plausible option for the application of QV to political issues in which correlating unequal influence with preference intensity does not conflict with assumptions of equal moral worth.

A Condorcet method for a single-seat preferential election is defined by the way it handles cases without a Condorcet winner. Such cases are described in terms of cyclic candidate triples. Sometimes election theory considers intricate patterns of intersecting cyclic triples. In practice, cyclic triples are rare, but they may be created as part of strategic voting against a Condorcet winner. This strategy, often called burying, is difficult to apply, but critics will detect a missed opportunity and regard it as a punishment for honest voting. A new Condorcet method, SV, lets a cyclic triple be won by the candidate with the smallest opportunity to defeat a Condorcet winner this way. A new geometric model allows visual comparison of the opportunities under various methods.

This paper seeks to prove that under a large class of group decision rules some sincere voting situations will be unstable because of strategic manipulation by single individuals. The concept of stability used is weaker than the stability concepts figuring in many earlier contributions in this area, insofar as under the concept used here any individual, while disrupting a given voting situation, considers the possibility of retaliation by other individuals. DUMMETT AND FARQUHARSON [2], Murakami [7], Farquharson [3], Sen [14], Gibbard [4], Satterthwaite [13], and Pattanaik [10, 11, and 12] have discussed various aspects of the problem of stability in voting. The general conclusion which emerges from these writings seems to be that stability of all possible sincere voting situations (which implies the absence of strategic distortion of preferences by voters) is an extremely rare feature of democratic group decision procedures. However, the notion of stability or equilibrium underlying many of these contributions is a simple one and does not take into account several phenomena usually associated with strategic voting such as the possibility of counter-coalitions when a coalition (of one or more individuals) threatens to disrupt a voting situation. The purpose of this paper is twofold. First, it introduces a less demanding notion of stability which takes into account the possibility of formation of countercoalitions when an individual seeks to influence the outcome in his own favor by strategic manipulations in voting. Secondly, using this very weak notion of stability, it is shown that, while under the changed definition the possibility of having unstable sincere voting situations because of strategic voting by single individuals is somewhat reduced, invulnerability of all possible sincere voting situations to voting maneuvres of single individuals still remains a very rare property among democratic group decision rules based on pairwise comparisons. We lay down the basic notation and some preliminary definitions in Section 1. In Section 2 we introduce a notion of stability taking into account the possibility of counter-coalitions. Using this very weak definition of stability, in Section 3 we show that under most democratic group decision rules based on pairwise comparisons, there is the danger of having unstable sincere voting situations owing to strategic manipulations by single individuals. We conclude in Section 4.

Condorcet's paradox for weak preference orderings

We introduce incomplete information to a multiparty election under proportional representation: each voter knows her preferences and votes strategically to maximize her payoffs, but is uncertain about the number and the preferences of the other voters. Parties are assumed to be purely office motivated and, hence, the resulting governments are always minimum winning. In this framework, we prove (a) generic existence of equilibria where only two parties receive a positive fraction of the votes and therefore lead to single-party governments and (b) generic inexistence of equilibria that lead to coalition governments. That is, contrary to common wisdom, a proportional rule is found not to promote sincere voting and to be favorable towards single-party governments. The existence of two-party equilibria that lead to single-party governments is robust to parties having ideological concerns.

From Ballot-Boxes to Barracks: Votes, Institutions, and Post-Election Coups