The case for Instant Runoff Voting

Australia is the birthplace of the two main forms of preferential electoral voting - the Alternative Vote (AV) and the Single Transferable Vote (STV) methods. Accident and force of circumstances largely explain their introduction. The Hughes Government introduced the AV system in 1918 in an attempt to prevent the right-of-centre parties from splitting their support to the benefit of the ALP. In 1948 the Chifley Government moved to replace the Senate's preferential block system with the STV method in an attempt to electorally contain Menzies. Yet credit also needs be given to the deliberate efforts and clear intentions of their designers. The electoral systems proposed in 1902 were ahead of their time. Indeed, 1902 marked an important step in the design of Australia's electoral system. Once the debate had crystallized around the relative merits of preferential methods, it was only a matter of time before the Commonwealth would see their adoption.

Instant runoff voting (IRV) has recently gained popularity as an alternative to plurality voting for political elections, with advocates claiming a range of advantages, including that it produces more moderate winners than plurality and could thus help address polarization. However, there is little theoretical backing for this claim, with existing evidence focused on case studies and simulations. In this work, we prove that IRV has a moderating effect relative to plurality voting in a precise sense, developed in a 1-dimensional Euclidean model of voter preferences. We develop a theory of exclusion zones, derived from properties of the voter distribution, which serve to show how moderate and extreme candidates interact during IRV vote tabulation. The theory allows us to prove that if voters are symmetrically distributed and not too concentrated at the extremes, IRV cannot elect an extreme candidate over a moderate. In contrast, we show plurality can and validate our results computationally. Our methods provide new frameworks for the analysis of voting systems, deriving exact winner distributions geometrically and establishing a connection between plurality voting and stick-breaking processes.

This thesis consists of three chapters. In the first chapter, I investigate the effects of complexity in various voting systems on individual behavior in small group electoral competitions. Using a laboratory experiment, I observe individual behavior within one of three voting systems -- plurality, instant runoff voting (IRV), and score then automatic runoff (STAR). I then estimate subjects' behavior in three different models of bounded rationality. The estimated models are a model of Level-K thinking (Nagel, 1995), the Cognitive Hierarchy (CH) model (Camerer, et al. 2004), and a Quantal Response Equilibrium (QRE) (McKelvey and Palfrey 1995). I consistently find that more complex voting systems induce lower levels of strategic thinking. This implies that policy makers desiring more sincere voting behavior could potentially achieve this through voting systems with more complex strategy sets. Of the tested behavioral models, Level-K consistently fits observed data the best, implying subjects make decisions that combine of steps of thinking with random, utility maximizing, errors.In the second chapter, I investigate the relationship between the mechanisms used to select leaders and both measures of group performance and leaders' ethical behavior. Using a laboratory experiment, we measure group performance in a group minimum effort task with a leader selected using one of three mechanisms: random, a competition task, and voting. After the group task, leaders must complete a task that asks them to behave honestly or dishonestly in questions related to the groups performance. We find that leaders have a large impact on group performance when compared to those groups without leaders. Evidence for which selection mechanism performs best in terms of group performance seems mixed. On measures of honesty, the strongest evidence seems to indicate that honesty is most positively impacted through a voting selection mechanism, which differences in ethical behavior between the random and competition selection treatments are negligible.In the third chapter, I provide an investigation into the factors and conditions that drive behavior in dynamic innovation contests. Starting from a dynamic innovation contest model from Halac, et al. (2017), I construct a two period dynamic innovation contest game. From there, I provide a theoretical background and derivation of mixed strategies that can be interpreted as an agent's degree to which they engage in free riding behavior, namely through allowing their opponent to exert effort in order to uncover information about an uncertain state of the world. I show certain conditions must be fulfilled in order to induce free riding in equilibrium, and also analytically show the impact of changing contest prize structures on the degree of free riding. I end this paper with an experimental design to test these various theoretical conclusions in a laboratory setting while also considering the behavioral observations recorded in studies investigating similar contest models and provide a plan to analyze the data collected by this laboratory experiment.All data collected for this study consists of individual human subject data collected from laboratory experiments. Project procedures have been conducted in accordance with Purdue's internal review board approval and known consent from all participants was obtained.

This chapter places ranked choice voting (RCV) within the context of electoral systems. Preferential voting elections include the alternative vote (AV) for choosing a single winner and the single transferable vote (STV) to select multiple winners. Electoral systems for parliamentary elections in Australia and Ireland provide the rationale and history of these forms of RCV. Plurality or first-past-the-post elections serve as the benchmark for comparisons, and other broad electoral systems such as proportional representation and mixed-member proportional systems are introduced and contrasted with ranked choice. Similar electoral systems with complementary goals are discussed. Cousins to RCV include the supplementary vote, approval voting, cumulative voting, and the Borda count. Examples are introduced and compared to preferential systems. The philosophical origins of STV and RCV from Thomas Hare forward are outlined. RCV may lead to computational paradoxes such as Condorcet cycling and violations of fundamental assumptions such as monotonicity.

The alternative vote (AV) is a preferential electoral system that tends to reward political moderation and compromise. Fraenkel and Grofman have modeled the likely effects of AV in severely divided societies, in order to impugn AV as a tool of interethnic accommodation. In this response, I show that Fraenkel and Grofman’s model is based on extreme assumptions that bear no relation to party and voter behavior in such societies. Models based on realistic assumptions about strategic behavior and cross-national experience with AV both demonstrate that AV generally provides centripetal incentives that can contribute to interethnic coalition-building and accommodation.

An election audit is risk-limiting if the audit limits (to a pre-specified threshold) the chance that an erroneous electoral outcome will be certified. Extant methods for auditing instant-runoff voting (IRV) elections are either not risk-limiting or require cast vote records (CVRs), the voting system’s electronic record of the votes on each ballot. CVRs are not always available, for instance, in jurisdictions that tabulate IRV contests manually.We develop an RLA method (AWAIRE) that uses adaptively weighted averages of test supermartingales to efficiently audit IRV elections when CVRs are not available. The adaptive weighting ‘learns’ an efficient set of hypotheses to test to confirm the election outcome. When accurate CVRs are available, AWAIRE can use them to increase the efficiency to match the performance of existing methods that require CVRs.We provide an open-source prototype implementation that can handle elections with up to six candidates. Simulations using data from real elections show that AWAIRE is likely to be efficient in practice. We discuss how to extend the computational approach to handle elections with more candidates.Adaptively weighted averages of test supermartingales are a general tool, useful beyond election audits to test collections of hypotheses sequentially while rigorously controlling the familywise error rate.

Starting in 1758, elections have been held in various Canadian jurisdictions using first past the post. The same system is now used everywhere in Canada, even though the country ceased a long time ago to be a British colony. Whether constituencies should elect one member or more remained an issue for a long time, but single-member constituencies now prevail for federal, provincial, and territorial elections. For limited periods of time, a few provinces have experienced with alternative voting, the single transferable vote, or the limited vote, but all later reverted to plurality. The debate on the appropriate electoral system remains lively. Many Canadians support proportional representation, and in recent years, mixed-member proportional has emerged as the option most preferred by reformers. However, all attempts in that direction have failed so far, including the process launched by Prime Minister Justin Trudeau in 2015.

: Many organizations have turned to alternative voting systems such as instant-runoff voting for determining the outcome of single-winner elections. It is our position in this paper that the increasing deployment of such alternative systems necessitate the study and development of risk-limiting audits for these systems. We initiate this study. We examine several commonly used single-winner voting systems and provide risk-limiting auditing procedures for them. In many cases the methods from auditing plurality contests can be applied with minor changes and little loss in efficiency. For instant-runoff voting (IRV), the situation is markedly different. We describe an algorithm for auditing the candidate elimination order using plurality methods which is risk-limiting. Standard risk-limiting methods can be employed if the margin of the election can be efficiently calculated or bounded. We provide efficiently computable upper and lower bounds on the margin and, when known, compare them to the exact margins. Both auditing algorithms are potentially far less efficient than the methods to audit other types of voting systems.

By classic results in social choice theory, any reasonable preferential voting method sometimes gives individuals an incentive to report an insincere preference. The extent to which different voting methods are more or less resistant to such strategic manipulation has become a key consideration for comparing voting methods. Here we measure resistance to manipulation by whether neural networks of varying sizes can learn to profitably manipulate a given voting method in expectation, given different types of limited information about how other voters will vote. We trained over 100,000 neural networks of 26 sizes to manipulate against 8 different voting methods, under 6 types of limited information, in committee-sized elections with 5-21 voters and 3-6 candidates. We find that some voting methods, such as Borda, are highly manipulable by networks with limited information, while others, such as Instant Runoff, are not, despite being quite profitably manipulated by an ideal manipulator with full information. For the three probability models for elections that we use, the overall least manipulable of the 8 methods we study are Condorcet methods, namely Minimax and Split Cycle.

Is plurality or majority electoral reform a sensible option in Germany’s muddled electoral system debate? Yes, it is. Since Germany’s mixed-member proportional system fails to concentrate the party system in a sufficient way, Peggy Matauschek searches for a suitable alternative to the principle of proportional representation. She discusses the following options according to their contextual conditions: single-member plurality and majority electoral systems—like the alternative vote system—, parallel systems, proportional representation systems with a low district magnitude and majority bonus systems. In light of its balanced performance, the study advocates the introduction of a system with a majority bonus for a coalition.

The alternative vote: Do changes in single-member voting systems affect descriptive representation of women and minorities?

Declaring a winner by adopting the Simple majority criterion is a fundamental mistake. The outcome could be in deep contrast with both Condorcet’s and Borda’s methods. A better result can be obtained with Run-off voting or with Instant run-off voting. Though the ranking could not comply with Condorcet’s method, yet the outcome is not as flawed as that provided by the Simple majority criterion.

If instant runoff voting (IRV) mitigates strategic voting, is that because the rules of the system mechanically reduce strategic opportunities, or because of other more indirect effects? In single-vote plurality elections, a voter can be pivotal if adding one vote to a candidate would cause that candidate to win. In IRV, it is more complicated to identify when one voter can be pivotal. This letter derives all the ways that a single ballot can change the result of an IRV election, for any number of candidates and voters. I obtain an expression for the probability of casting a pivotal vote in IRV by phrasing the probability that any pivotal event occurs as a function of all the rankings cast by other voters. This expression facilitates modeling vote choice in IRV, and enables the estimation of voters’ strategic opportunities in IRV contests between any number of candidates. I present some illustrative simulations estimating pivotal probabilities in both IRV and Single-Member District Plurality for stylized electorates with identical preference structures. These simulations produce similar estimated pivotal probabilities in the two systems, suggesting that these systems may provide similar opportunities to strategically cast a decisive vote.

Dans cet article nous présentons les résultats d’une expérience électorale réalisée durant l’élection présidentielle de 2007 qui avait pour objectifs de confronter le vote préférentiel transférable à deux critères : la simplicité et la sélection du vainqueur de Condorcet. À partir du profil des préférences des électeurs qui ont participé à cette expérience électorale, nous montrons que cette procédure de vote peut conduire à la désignation d’un vainqueur différent suivant la méthode de dépouillement employée. Avec la méthode de Hare, le vainqueur est N. Sarkozy, tandis que la méthode de Coombs conduit à l’élection de F. Bayrou. Pour ces deux méthodes, les modalités pratiques du scrutin restent les mêmes et l’expérience a montré que ce processus répond bien au critère de simplicité. Par contre, au regard du principe de Condorcet, seule la méthode de Coombs, pour ce profil des préférences a conduit à l’élection du vainqueur de Condorcet, à savoir F. Bayrou.

In an election which uses preference ballots, there exist many different voting methods for choosing a winner of the election given the voters’ preference data. We analyse the extent to which the choice of voting method matters in American ranked-choice elections. To this end, we compiled a database of over 200 American elections which used preference ballots and, for each election, calculated the winner under the methods of plurality, instant runoff voting, plurality runoff, Condorcet, Bucklin voting, and two versions of Borda count. We find that the choice of voting method matters less frequently than what is suggested by much of the theoretical literature.