Runoff Rule Research Articles

Run-off Elections in the Laboratory

Abstract We study experimentally the properties of the majority run-off system and compare them to those of plurality rule. Our focus is on Duverger’s famous prediction that the plurality rule leads to higher co-ordination of votes on a limited number of candidates than the majority run-off rule. We find strong co-ordination forces under both systems. However, as predicted by the theory, in some cases these forces are stronger under plurality. Despite these differences in voting behaviour, we find small and mostly not significant differences in electoral outcomes and, hence, voters’ welfare.

Stress-testing the runoff rule in the laboratory

When a majority of voters has common values, but private information, then the runoff rule always admits an equilibrium that aggregates information strictly better than any equilibrium of the plurality rule. But there are cases in which the plurality rule supports equilibria that aggregate information strictly better compared to certain undominated equilibria of the runoff rule. Is there any risk with applying the runoff rule in these situations? We conduct a laboratory experiment and we show that the runoff rule consistently delivers better outcomes than the plurality rule even in such unfavorable scenarios. This establishes that the superiority of the runoff rule over the plurality rule in empirical settings outperforms its theoretical advantages.

Run-off election-based decision method for the training and inference process in an artificial neural network

Generally, the decision rule for classifying unstructured data in an artificial neural network system depends on the sequence results of an activation function determined by vector–matrix multiplication between the input bias signal and the analog synaptic weight quantity of each node in a matrix array. Although a sequence-based decision rule can efficiently extract a common feature in a large data set in a short time, it can occasionally fail to classify similar species because it does not intrinsically consider other quantitative configurations of the activation function that affect the synaptic weight update. In this work, we implemented a simple run-off election-based decision rule via an additional filter evaluation to mitigate the confusion from proximity of output activation functions, enabling the improved training and inference performance of artificial neural network system. Using the filter evaluation selected via the difference among common features of classified images, the recognition accuracy achieved for three types of shoe image data sets reached ~ 82.03%, outperforming the maximum accuracy of ~ 79.23% obtained via the sequence-based decision rule in a fully connected single layer network. This training algorithm with an independent filter can precisely supply the output class in the decision step of the fully connected network.

The effect of two-round presidential elections on human rights.

Recent research suggests that democratic presidential elections held using a runoff rule produce presidents that are more likely to protect human rights, in comparison to those elected under plurality rule; with this follow-up article, I seek to highlight the importance of advancing to a runoff round for those elections held using a runoff rule. I find that for presidential democracies that already have a runoff rule in place, country-years where the president has been elected after a runoff round are more likely to be associated with high government respect for human rights, in comparison to country-years where the president has been elected after only one round (that could have advanced to a runoff round, but did not). This article provides decision-makers with more information regarding the human rights consequences of runoff rounds, so that the costs and benefits of adopting (or retaining) variations of a runoff rule can be better weighed.

Stress-Testing the Runoff Rule in the Laboratory

When a majority of voters has common values, but private information, then the runoff rule always admits an equilibrium that aggregates information strictly better than the best equilibrium of the plurality rule. But there are cases in which the plurality rule supports equilibria that are strictly better compared to certain undominated equilibria of the runoff rule. Is there any risk with applying the runoff rule in these situations? We conduct a laboratory experiment and we show that the runoff rule consistently delivers better outcomes than the plurality rule even in such unfavorable scenarios. This establishes that the superiority of the runoff rule over the plurality rule in empirical settings outperforms its theoretical advantages.

Selecting the runoff pair

Although two-round voting procedures are common, the theoretical voting literature rarely discusses any such rules beyond the traditional plurality runoff rule. Therefore, using four criteria in conjunction with two data-generating processes, we define and evaluate nine “runoff pair selection rules” that comprise two rounds of voting, two candidates in the second round, and a single final winner. The four criteria are: social utility from the expected runoff winner (UEW), social utility from the expected runoff loser (UEL), representativeness of the runoff pair (Rep), and resistance to strategy (RS). We examine three rules from each of three categories: plurality rules, utilitarian rules and Condorcet rules. We find that the utilitarian rules provide relatively high UEW and UEL, but low Rep and RS. Conversely, the plurality rules provide high Rep and RS, but low UEW and UEL. Finally, the Condorcet rules provide high UEW, high RS, and a combination of UEL and Rep that depends which Condorcet rule is used.

Reevaluating the presidential runoff rule: Does a provision promote the protection of human rights?

In recent years, an increasing number of democracies have adopted a runoff rule to elect their president. Some have argued, however, that the benefits of such a rule are dubious at best. In this article, I seek to counter this claim, as I posit that a runoff rule promotes the protection of human rights by reducing outcomes that are negatively associated with high government respect for human rights. Using ordered logistic regression and an analysis of predicted probabilities, I find that democratic presidential elections held using a runoff rule produce presidents that are less likely to be associated with lower government respect for human rights, and more likely to be associated with greater government respect for human rights. I conclude by suggesting that politicians should consider embracing a presidential runoff rule, as its adoption could be a relatively easy way to reduce repression.

An Informational Basis for Voting Rules

This paper presents a novel combinatorial approach for voting rule analysis. Applying reversal symmetry, we introduce a new class of preference profiles and a new representation (bracelet representation). By applying an impartial, anonymous, and neutral culture model for the case of three alternatives, we obtain precise theoretical values for the number of voting situations for the plurality rule, the run-off rule, the Kemeny rule, the Borda rule, and the scoring rules in the extreme case. From enumerative combinatorics, we obtain an information utilization index for these rules. The main results are obtained for the case of three alternatives

Measuring Majority Tyranny: Axiomatic Approach

We study voting rules with respect to how they allow or limit a majority to dominate minorities. For this purpose we propose a novel quantitative criterion for voting rules: the qualified mutual majority criterion (q, k)-MM. For a fixed total number of m candidates, a voting rule satisfies (q, k)-MM if whenever some k candidates receive top k ranks in an arbitrary order from a majority that consists of more than q ∈ (0, 1) of voters, the voting rule selects one of these k candidates. The standard majority criterion is equivalent to (1/2, 1)-MM. The standard mutual majority criterion (MM) is equivalent to (1/2, k)-MM, where k is arbitrary. We find the bounds on the size of the majority q for several important voting rules, including the plurality rule, the plurality with runoff rule, Black’s rule, Condorcet least reversal rule, Dodgson’s rule, Simpson’s rule, Young’s rule and monotonic scoring rules; for most of these rules we show that the bound is tight.

Computational aspects of strategic behaviour in elections with top-truncated ballots

Understanding when and how computational complexity can be used to protect elections against different manipulative actions has been a highly active research area over the past two decades. Much of this literature, however, makes the assumption that the voters or agents specify a complete preference ordering over the set of candidates. There are many multiagent systems applications, and even real-world elections, where this assumption is not warranted, and this in turn raises a series of questions on the impact of partial voting on the complexity of manipulative actions. In this paper, we focus on two of these questions. First, we address the question of how hard it is to manipulate elections when the agents specify only top-truncated ballots. Here, in particular, we look at the weighted manipulation problem—both constructive and destructive manipulation—when the voters are allowed to specify top-truncated ballots, and we provide general results for all scoring rules, for elimination versions of all scoring rules, for the plurality with runoff rule, for a family of election systems known as Copeland\(^{\alpha }\), and for the maximin protocol. The second question we address is the impact of top-truncated voting on the complexity of manipulative actions in electorates with structured preference profiles. In particular, we consider electorates that are single-peaked and we show how, for many voting protocols, allowing top-truncated voting reimposes the \(\mathcal {NP}\)-hardness shields that normally vanish in such electorates.

Miscounts, Duverger's Law and Duverger's Hypothesis

In real-life elections, vote-counting is often imperfect. We analyze the consequences of such imperfections in plurality and runoff rule voting games. We call a strategy profile a robust equilibrium if it is an equilibrium if the probability of a miscount is positive but small.All robust equilibria of plurality voting games satisfy Duverger's Law: In any robust equilibrium, exactly two candidates receive a positive number of votes. Moreover, robustness (only) rules out a victory of the Condorcet loser.All robust equilibria under runoff rule satisfy Duverger's Hypothesis: First round votes are (almost always) dispersed over more than two alternatives. Robustness has strong implications for equilibrium outcomes under runoff rule: For large parts of the parameter space, the robust equilibrium outcome is unique.

Strong and coalition-proof political equilibria under plurality and runoff rule

We analyze the effects of voter coordination on the equilibrium of voting games. Specifically, we analyze the concepts of strong equilibrium and coalition-proof equilibrium for plurality rule and runoff rule elections. We characterize these equilibria in the three candidate case, and provide results for important special cases in the general multicandidate case.

Strong and Coalition - Proof Political Equilibria under Plurality and Runoff Rule

We analyze the effects of voter coordination on the equilibrium of voting games. Specifically, we analyze the concepts of strong equilibrium and coalition - proof equilibrium for plurality rule and runoff rule elections. We characterize these equilibria in the three candidate case, and provide results for important special cases in the general multicandidate case.

Robust Political Equilibria Under Plurality and Runoff Rule

A central problem for the game theoretic analysis of voting is that voting games have very many Nash equilibria. In this paper, we consider a new refinement concept for voting games that combines two ideas that appear reasonable for voting games: First, trembling hand perfection (voters sometimes make mistakes when casting their vote) and second, coordination of voters with similar interests. We apply this refinement to an analysis of multicandidate elections under plurality rule and runoff rule. For plurality rule, we show that our refinement implies Duverger's law: In all equilibria, (at most) two candidates receive a positive number of votes. For the case of 3 candidates, we can completely characterize the set of equilibria. Often, there exists a unique equilibrium satisfying our refinement; surprisingly, this is even true, if there is no Condorcet winner. We also consider the equilibria under a runoff rule and analyze when plurality rule and runoff rule yield different outcomes.

Duverger's Hypothesis, the Run-Off Rule, and Electoral Competition

I analyze a model of electoral competition with entry under the run-off rule. I consider both two- and multiple-party systems. The principal result is that two-party systems may prove stable under the run-off rule: I show that a continuum of equilibria exists in which only two parties enter and subsequent entry is deterred. This finding conflicts with the accepted wisdom on the run-off rule encapsulated by Duverger's Hypothesis. The results of the model are then reconciled with Duverger's Hypothesis and a more precise formulation is proposed.

ASSESSING THE LEVEL OF COMPROMISE IN REAL CHOICE MODELS

We analyze the plurality runoff rule often used in national elections and prove that the corresponding choice function is Borda-rational. The compromise level attained in real voting systems is defined. The corresponding measures are calculated for the case of plurality runoff with three main candidates. We investigate the influence of the axiom of independence of irrelevant alternatives on the rationality type of choice functions realized in multicriterion choice systems.

Strategic Voting under Plurality and Runoff Rules

Choosing a method of electing a president is often a contentious constitutional issue for newly emerging democracies. The debate focuses largely on two alternative electoral procedures: plurality rule and plurality rule with a runoff. Duverger (1954) argues that plurality rule has a consolidating influence on parties that a runoff rule lacks. This paper focuses on the `psychological effect' identified by Duverger as the principal basis of consolidation, and studies the conditions under which strategic voting can change the sincere voting outcome and identifies the types of voters who should vote strategically under plurality and runoff rules. Three interesting findings can be drawn from the theoretical results. First, strategic voting is needed more often under plurality rule than under runoff rule to render the Condorcet winner the voting outcome. Second, under the plurality rule, strategic voting cannot ensure that a Condorcet winner will win and cannot even preclude a Condorcet loser from winning. Under the runoff rule, however, strategic voting ensures that the Condorcet winner will win, if one exists. Third, it is easier for a third candidate to enter the election and win the race under the plurality rule than under the runoff rule even if the third candidate is not a Condorcet winner.