Single Transferable Vote Research Articles

Paradoxical oddities in two multiwinner elections from Scotland

If you were a candidate in an election, would you prefer more support from voters or less? Put another way: would you prefer that your campaign staff persuade more voters to vote for you, or fewer? These questions seem silly, because of course you would want more support from voters. Surprisingly, when using certain voting methods it is actually possible for more voter support to produce a worse result for a candidate; such an outcome is a type of monotonicity paradox. In [1], we searched for various types of monotonicity paradoxes in 1079 single-transferable vote (STV) elections from a database of Scottish local government elections. The purpose of this article is to present in detail two of the most interesting elections revealed by our search. These two elections are arguably the most paradox-riddled real-world political ranked choice elections ever documented, perhaps rivalled only by four single-winner examples from the United States: the 2009 mayoral election in Burlington, Vermont ([2, 3]); a 2021 city council race in Minneapolis, Minnesota [4]; the 2022 Special Election for US House in Alaska [5]; and the 2022 District 4 School Director election in Oakland, California [6]. The first election we present is the 2017 council election in the Buckie Ward of the Moray Council Area, which demonstrated the most extreme instance of a committee size monotonicity paradox ever observed in an actual election. The second election is the 2012 council election in the Steòrnabhagh a Tuath Ward of the Nah-Eileanan Siar Council Area, which demonstrated upward and downward monotonicity paradoxes, as well as a no-show paradox. To contextualise these elections, as part of our discussion we indicate how often these kinds of paradoxes occur in Scottish local government elections.

Going negative when spoiled for choice? Destabilizing and boomerang effects of negative political messaging in multiparty systems with multimember districts

ABSTRACT Classical electoral behaviour theories have associated possible benefits of negative campaigning with two-party plurality systems due to their zero-sum nature. Nevertheless, negative campaigning is a widely used electoral strategy outside of these contexts, despite scant evidence of its benefits for political parties and candidates who employ it. Our research question is simple – is negative campaign messaging effective for attackers in multiparty systems with multimember districts? Or does it create a ‘boomerang effect’ in this context, for which the producer of the message faces a backlash? Multiparty systems with multimember districts should, according to the literature, be scenarios where the effects of negative campaigning are most complex if not unpredictable. This paper uses Facebook political messages to inform a survey experiment design that tests the effects of negative political messaging on voters. We employ this survey in Ireland, which uses the single transferable vote, an electoral system which magnifies outcome uncertainty for attackers. Our results suggest that negative messaging in this context produces both the intended effect and a boomerang effect for the sponsor of the message. These countervailing results suggest a net null effect for the efficacy of negative messaging.

Election Laws and Electoral Reforms in India and U.K.

This paper examines the election laws and electoral reforms in India and the United Kingdom, highlighting their evolution, current frameworks, and ongoing challenges. India, the world's largest democracy, operates under a legal structure largely defined by the Representation of the People Act, 1951, and is overseen by the Election Commission of India. The Indian electoral system, based on the First-Past-The-Post (FPTP) model, has undergone significant reforms to address issues of transparency, voter fraud, and campaign finance, including the introduction of electronic voting machines (EVMs) and Voter Verifiable Paper Audit Trails (VVPATs). In contrast, the United Kingdom's electoral system, rooted in centuries-old traditions, is regulated by laws such as the Representation of the People Acts and the Political Parties, Elections and Referendums Act, 2000. While the UK also employs the FPTP system, it faces criticism for not reflecting the proportionality of votes. Recent reforms in the UK have focused on improving voter registration, addressing electoral fraud, and debating alternative voting methods like the Single Transferable Vote (STV) to enhance democratic representation. The study identifies both similarities and divergences in the electoral processes of these two democracies, emphasizing the impact of their respective legal frameworks on electoral integrity and democratic participation. It also explores ongoing debates and proposed reforms aimed at enhancing the inclusiveness, fairness, and transparency of elections in both nations.

Monotonicity anomalies in Scottish local government elections

The single transferable vote (STV) voting method is used to elect multiple candidates in ranked-choice elections. One weakness of STV is that it fails multiple fairness criteria related to monotonicity and no-show paradoxes. We analyze 1079 local government STV elections in Scotland to estimate the frequency of such monotonicity anomalies in real-world elections, and compare our results with prior empirical and theoretical research about the rates at which such anomalies occur. In 62 of the 1079 elections we found some kind of monotonicity anomaly. We generally find that anomaly rates are similar to prior empirical research and much lower than what most theoretical research has found. Most STV anomalies we find are the first of their kind to be documented in real-world multiwinner elections.

A comparison of sequential ranked-choice voting and single transferable vote

A comparison of sequential ranked-choice voting and single transferable vote

Democratising Democracy: Votes-Weighted Representation

Democracy is in retreat around the world. To reduce the UK’s own democratic deficit, support is growing for some kind of proportional representation. We propose that existing versions of PR can be greatly simplified and improved on by giving each representative voting power in the assembly proportional to the number of votes they have been given by the electorate: “Votes-Weighted Representation”. Under VWR a country/region is divided into multi-member constituencies. Each voter has a single vote. Ballot papers list the candidates (each party can field several), whom voters then rank. The candidate with the fewest votes (top preferences) is eliminated, and their votes are transferred to next preferences, repeating until the number of candidates remaining equals the number to elect. Optionally, given sufficiently secure and accessible voting software, every voter can also have a 'dynamic' second vote, which they can arbitrarily split and delegate to any representatives from any constituencies, for however long and on whichever issues they wish; delegated votes are added to representatives’ vote weights. Any voter can override the delegation of their second vote on any issue, and remotely vote on it in the assembly themselves, directly. Compared with existing systems, these proposals will allow more accountable, more responsive and finer-grained coverage of the inherently multi-dimensional political space, including between elections. Fewer votes will be wasted, and better proportionality of voting power in the assembly should be achievable than under comparable Single Transferable Vote (STV) and highest averages or highest remainders methods for apportioning representatives. Also, fewer votes will be wasted compared with using electoral thresholds without vote transfers from eliminated candidates. Political fragmentation should be largely avoidable by using 6- or 7-member constituencies, without unduly compromising proportionality for bigger parties, or the diversity of elected representatives. Our proposals should help democratise democracy, improve its functioning, and reverse its global retreat.

Rank Aggregation Using Scoring Rules

To aggregate rankings into a social ranking, one can use scoring systems such as Plurality, Veto, and Borda. We distinguish three types of methods: ranking by score, ranking by repeatedly choosing a winner that we delete and rank at the top, and ranking by repeatedly choosing a loser that we delete and rank at the bottom. The latter method captures the frequently studied voting rules Single Transferable Vote (aka Instant Runoff Voting), Coombs, and Baldwin. In an experimental analysis, we show that the three types of methods produce different rankings in practice. We also provide evidence that sequentially selecting winners is most suitable to detect the "true" ranking of candidates. For different rules in our classes, we then study the (parameterized) computational complexity of deciding in which positions a given candidate can appear in the chosen ranking. As part of our analysis, we also consider the Winner Determination problem for STV, Coombs, and Baldwin and determine their complexity when there are few voters or candidates.

The Maltese single transferable vote experience: a case study of gerrymandering?

AbstractRe-drawing the electoral boundaries to provide benefit to one particular political party and thereby damaging the principle of representation in democracy has been a core issue in political science in the recent years. For years social scientists have been advocating the idea of measuring or preventing the potential for damage that may arise from the existence of the above-mentioned redistricting process. Following this discussion, we investigate the possible gerrymandering phenomenon that might have arisen, or whether there are any asymmetries or partisan biases due to boundary delimitation of the electoral constituencies in the case of the Maltese general elections. From the evidence of various statistical tests and simulations, our conclusion is that we find no evidence of gerrymandering in the 2013 and 2017 Maltese general elections.

The case for Instant Runoff Voting

Instant runoff voting (IRV) is an electoral system that produces better elections and more representative outcomes in races with three or more candidates. Used by over 50 American jurisdictions, IRV addresses the challenges of plurality voting in crowded candidate fields. It upholds majority rule, promotes voter engagement, discourages personal attacks, and minimizes strategic voting. IRV is preferable to runoff systems and other proposed single-winner methods. In comparison to runoffs, IRV produces higher, more equitable turnout and reduces costs and demands on voters. In contrast to methods based on rating candidates, voters in IRV elections have incentives to indicate their honest preferences. IRV demonstrates greater political viability and more intuitively fair outcomes than Condorcet methods. For legislative elections, IRV complements the single transferable vote, which is the best way to address the U.S.’s governance and polarization crises, end gerrymandering, and secure fairer representation for all.

Suitability of the Single Transferable Vote as a Replacement for Largest Remainder Proportional Representation

There are two main approaches to achieving proportional representation in elections: the single transferable vote and methods based on party lists. This paper discusses ways to use the single transferable vote while using some of the main features used with the largest remainder method, such as the electoral threshold. The investigation has shown that the Weighted Inclusive Gregory method is a suitable replacement for the largest remainder method when it is desirable to avoid wasted votes and to handle independent candidates in a straightforward way, but it is also desirable to keep the results as close to the ones achieved under the largest remainder method as possible. The investigation also led to the development of an algorithm for using the single transferable vote when preference lists are based on party lists, exploiting commonalities and symmetries between the patterns of preferences given in the votes. It has been shown that such an algorithm makes the calculations faster than the use of ordinary implementations of the single transferable vote when the numbers of seats and candidates are high, as commonly happens when methods based on party lists are used.

Complexity of shift bribery for iterative voting rules

In iterative voting systems, candidates are eliminated in consecutive rounds until either a fixed number of rounds is reached or the set of remaining candidates does not change anymore. We focus on iterative voting systems based on the positional scoring rules plurality, veto, and Borda and study their resistance against shift bribery attacks introduced by Elkind et al. [1] and Kaczmarczyk and Faliszewski [2]. In constructive shift bribery (Elkind et al. [1]), an attacker seeks to make a designated candidate win the election by bribing voters to shift this candidate in their preferences; in destructive shift bribery (Kaczmarczyk and Faliszewski [2]), the briber’s goal is to prevent this candidate’s victory. We show that many iterative voting systems are resistant to these types of attack, i.e., the corresponding decision problems are NP-hard. These iterative voting systems include iterated plurality as well as the voting rules due to Hare, Coombs, Baldwin, and Nanson; variants of Hare voting are also known as single transferable vote, instant-runoff voting, and alternative vote.

Propostas de reforma do sistema eleitoral no Brasil: o que pensa a ciência política brasileira?

The present paper maps the position of 51 Brazilian political scientists about electoral reform in the period after the 1988 Constitution. For this purpose, the research selected scientific articles, but also books, interviews and texts in newspapers. Five main streams were identified in the specialized literature on the reform of the electoral system: (1) the one that defends the proportional vote of the open list; (2) the proportional closed list voting; (3) the proportional vote of a flexible list, here also incorporated the model of “single transferable vote”; (4) the one that defends some type of majority vote; (5) and the one that seeks to mix proportional mechanisms with the majority in a system known as “mixed vote”. The paper concludes that the proportional system is preferred by most Brazilian political scientists who have intervened in the public sphere in the last twenty years, with a certain preference for the transition to the closed list model.

Simulation of the Implementation of the Single Transferable Vote in Bosnia and Herzegovina – the Case of Elections for the Parliamentary Assembly in 2000

The electoral system is deeply divided and post-conflict societies have a prominent place in the existing literature studying political and institutional regulation. One of the assumptions is that the electoral system encourages political actors to act and behave more moderately or radically. Proportional representation electoral systems are widespread and are generally considered the most suitable for the representation of social groups, although the success of their outcomes remains disputable. Two types of proportional systems – party lists and single transferable vote – stand mutually opposed from the standpoints of incentives of political actors to political moderation. The party lists system (list-PR) was criticized for encouraging more radical behavior as opposed to the single transferable vote (STV) which instigated more moderate behavior. The outcomes of the named two types of proportional systems will be compared based on the case study of the elections for the House of Representatives of the Parliamentary Assembly of Bosnia and Herzegovina which were held in 2000, using counterfactual simulation. Contrary to the expected outcomes of the STV, the electoral simulation will show that the list-PR has proven to be a more successful institutional solution in terms of encouraging political moderation. A STV would not significantly lead to an interethnic exchange of preferences, nor the representation of the small moderate parties, contrary to the list-PR that enabled their representation.

Evaluating the Effect of Optimized Voting Using Hybrid Particle Swarm and Grey Wolf Algorithm on the Classification of the Zoo Dataset

When there are numerous possible solutions for a given class in a given problem, majority voting or plurality voting is typically employed. One common technique for improving classification accuracy is bagging, which involves training many classifiers on slightly different datasets and then voting on the combined results. In this research, we examine how alternative voting procedures affect the efficiency of two distinct classification algorithms applied to datasets of varying complexity. Despite the increased computing cost associated with determining preference order, the results show that the single transferable vote can be a suitable alternative to plurality voting.

Parliament the Mirror of the Nation: Representation, Deliberation, and Democracy in Victorian Britain, by Gregory Conti

Reviewed by: Parliament the Mirror of the Nation: Representation, Deliberation, and Democracy in Victorian Britain by Gregory Conti Philip Harling (bio) Parliament the Mirror of the Nation: Representation, Deliberation, and Democracy in Victorian Britain, by Gregory Conti; pp. xi + 408. Cambridge and New York: Cambridge University Press, 2019, $120.00, $34.99 paper. Thomas Hare is one of those eminent Victorians you have probably never heard of. A barrister and sometime assistant commissioner of London Charities, his hobby was to make the British electoral system perfect, and Hare scribbled a lot in pursuit of this goal. His magnum opus was Treatise on the Election of Representatives (1859). This was a formidably dense tome that nevertheless spoke to John Stuart Mill, who teamed up with Henry Fawcett to write a pamphlet that sought to translate Hare’s ideas into plainer English. The biggest of those ideas involved proportional representation (PR) and the single transferable vote (STV). PR was an electoral system in which the preferences among voters were intended to be reflected more proportionately within the elected body than could be achieved via pluralities or bare majorities within a winner-take-all [End Page 452] system, which “wasted” the votes of losing candidates (203). STV was Hare’s prescription for achieving PR in a way that made every vote count toward the electoral outcome. Today, STV is popular in Australia and Ireland, while PR—usually the party-list variety, and simpler than STV—is in wide use in Europe and far beyond, from Austria to Argentina, Italy, and Indonesia. There is therefore no doubting the global impact of this Hare-brained scheme. And while Hare’s home country still clings to the winner-take-all, first-past-the-post system, the debate about its relative virtues and vices compared with the PR alternatives continues to this day. If that debate within Britain remains vigorous now, it was even more so in Hare’s day. In Parliament the Mirror of the Nation: Representation, Deliberation, and Democracy in Victorian Britain, Gregory Conti guides us through this Victorian conversation with skill and erudition. His book is a history of political thought and, as such, some of us who are not chiefly political thinkers will get lost from time to time within the denser thickets of that erudition. But Conti convinces that even this sort of reader should care about Victorian debates about STV and PR, in part because they are germane to our growing contemporary anxieties that the composition of our political bodies inadequately reflects the diversity and divisions within our societies. Even more, we should care because those debates show that the Victorians believed deeply, a lot more deeply than we do, in what Conti calls “the transformative, world-altering character of political deliberation” (364). They felt a moral urgency to get their electoral system right, as they did about so much else. Like his admirers and critics, and virtually all mid-Victorians, Hare thought that the British people were the greatest on earth. The proof of their greatness lay in the soundness of their democratic political institutions, which held firm while the Continent veered between bloody revolution and bloodier reaction. The British Parliament has never been held in higher esteem than it was in the third quarter of the nineteenth century. There was nevertheless much talk of improvement. How could Parliament be made a more accurate image of the society for which it made laws? How could it be made a proper mirror of the nation? This was the ruling theoretical question, Conti convincingly argues. The most common answer involved improving upon the 1832 electoral settlement by increasing suffrage. Thus Whig-Liberals like Walter Bagehot and Henry Davis Pochin could agree with Conservatives such as Henry Warwick Cole that parliamentary seats needed to be redistributed and consolidated so as to bring so-called respectable workingmen more squarely into the political nation. Free-thinking radicals like G. J. Holyoake could likewise concur with Tories such as Augustus Stapleton that corporate interests needed better representation within the post-1832 British Parliament, even if they disagreed about which of those interests merited better access to the House of Commons. Arrayed against these varieties-of-suffrage...

Variants of Ranked-Choice Voting from a Strategic Perspective

Ranked-choice voting has come to mean a range of electoral systems. Broadly, they can facilitate (a) majority winners in single-seat districts, (b) majority rule with minority representation in multi-seat districts, or (c) majority sweeps in multi-seat districts. Further, such systems can combine with rules to encourage/discourage slate voting. This article describes five major versions used, abandoned, and/or proposed for US public elections: alternative vote, single transferable vote, block-preferential voting, the bottoms-up system, and alternative vote with numbered posts. It then considers each from the perspective of a ‘political strategist.’ Simple models of voting (one with two parties, another with three) draw attention to real-world strategic issues: effects on minority representation, importance of party cues, and reasons for the political strategist to care about how voters rank choices. Unsurprisingly, different rules produce different outcomes with the same sets of ballots. Specific problems from the strategist’s perspective are: ‘majority reversal,’ serving ‘two masters,’ and undisciplined third-party voters (or ‘pure’ independents). Some of these stem from well-known phenomena, e.g., ranking truncation and ‘vote leakage.’ The article also alludes to ‘vote-management’ tactics, i.e., rationing nominations and ensuring even distributions of first-choice votes. Illustrative examples come from American history and comparative politics. A running theme is the two-pronged failure of the Progressive Era reform wave: with respect to minority representation, then ranked voting's durability.

Forecasting government support in Irish general elections: Opinion polls and structural models

Election forecasting is a cottage industry among pollsters, the media, political scientists, and political anoraks. Here, we plow a fresh field in providing a systematic exploration of election forecasting in Ireland. We develop a structural forecast model for predicting incumbent government support in Irish general elections between 1977 and 2020 (the Iowa model). We contrast this structural model with forecasts from opinion polls, the dominant means of predicting Ireland’s elections to date. Our results show that with appropriate lead-in time, structural models perform similarly to opinion polls in predicting government support when the dependent variable is vote share. Most importantly, however, the Iowa model is superior to opinion polls in predicting government seat share, the ultimate decider of government fate in parliamentary systems, and especially significant in single transferable vote (STV) systems where vote and seat shares are not always in sync. Our results provide cumulative evidence of the potency of structural electoral forecast models globally, with the takeaway that the Iowa model estimating seat share outpaces other prediction approaches in anticipating government performance in Irish general elections.

Ballot structure, district magnitude and descriptive representation: the case of New Zealand local council elections

ABSTRACT It is sometimes claimed that the use of preferential voting facilitates more effective representation of under-represented groups than that generated by the first-past-the-post (FPP) system, particularly in combination with higher district magnitude. This claim is tested using unique observational data. Local government elections in New Zealand are conducted using either the single transferable vote (STV) or first-past-the-post, providing the opportunity to compare representation of women and Indigenous Māori across the two sets of councils. When combined with higher district magnitude, STV may sometimes promote the election of women, but has no effects on the election of Māori. The advantages of high district magnitude STV in promoting descriptive representation are counteracted by lack of coordination in candidate nomination and voting because these local electoral contests are predominantly nonpartisan.

The incumbency advantage in second-order PR elections: Evidence from the Irish context, 1942–2019

Do candidates in local elections benefit from an incumbency advantage? And which factors moderate the strength of this incumbency bonus? Analyzing seven decades of Irish local elections (1942–2019) conducted under proportional representation through the single transferable vote, we reassess and extend the mixed evidence on the incumbency advantage under proportional representation and in second-order elections. By applying the Regression Discontinuity Design, we find that the incumbency advantage is at least as strong in Irish local as in general elections, which are conducted under the identical electoral system. We also show that marginally elected candidates in local elections have much higher reelection probabilities when they do not face a high-quality candidate in their local electoral area after getting elected. The findings point to the importance of name recognition as a major driver of the incumbency advantage in local elections.

Alberta’s forgotten experiment with electoral reform: the hybrid single transferable vote/alternative vote and the quasi-party system

A persistent yet understudied aspect of Alberta’s “quasi-party system” is the role of the electoral system. While many authors have rightly pointed out that a majoritarian single-member plurality system has helped Alberta’s ruling parties produce disproportionate majorities, the province has not always operated under this electoral arrangement. From 1926 until 1955, Alberta had a “hybrid” system, consisting of the Single Transferable Vote in multi-member constituencies in Edmonton and Calgary and the Alternative Vote in single-member constituencies in the rest of Alberta. This unusual attempt at electoral reform played an important role in the dominance of the United Farmers of Alberta and the early Social Credit Party (until 1955). AV acted as an essentially majoritarian system in rural Alberta, producing statistically indistinguishable results from FPTP. This contrasts the Albertan case with other attempts at implementing the Alternative Vote. On the other hand, STV benefited the UFA and Social Credit in two distinct ways. STV increasing proportionality in Edmonton and Calgary, as it has in many other jurisdictions. However, due the hybrid system, the urban opposition in Edmonton and Calgary to the UFA was fragmented by a proportional system like STV. Social Credit, with its larger urban base, used STV to maximize its urban vote through a process of voter transfers. Finally, rural malapportionment is a key feature in both the hybrid system and the subsequent return to single-member plurality. Rural seats, operating under both AV and FPTP, have been the electoral bedrock for Alberta’s long lived political dynasties. The unique case of Alberta’s hybrid electoral system serves as an important potential case study in debates surrounding electoral reform in Canada and around the world. Please be aware that a revision to this article was submitted on April 30, 2021. Therefore, there may be some differences between the online version of this submission and the print version.