Instant runoff voting (IRV) is an increasingly-popular alternative to traditional plurality voting in which voters submit rankings over the candidates rather than single votes. In practice, elections using IRV often restrict the ballot length, the number of candidates a voter is allowed to rank on their ballot. We theoretically and empirically analyze how ballot length can influence the outcome of an election, given fixed voter preferences. We show that there exist preference profiles over k candidates such that up to k-1 different candidates win at different ballot lengths. We derive exact lower bounds on the number of voters required for such profiles and provide a construction matching the lower bound for unrestricted voter preferences. Additionally, we characterize which sequences of winners are possible over ballot lengths and provide explicit profile constructions achieving any feasible winner sequence. We also examine how classic preference restrictions influence our results—for instance, single-peakedness makes k-1 different winners impossible but still allows at least Ω(√k). Finally, we analyze a collection of 168 real-world elections, where we truncate rankings to simulate shorter ballots. We find that shorter ballots could have changed the outcome in one quarter of these elections. Our results highlight ballot length as a consequential degree of freedom in the design of IRV elections.
more »
« less
This content will become publicly available on June 18, 2024
Most Expected Winner: An Interpretation of Winners over Uncertain Voter Preferences
It remains an open question how to determine the winner of an election given incomplete or uncertain voter preferences. One solution is to assume some probability space for the voting profile and declare that the candidates having the best chance of winning are the (co-)winners. We refer to this interpretation as the Most Probable Winner (MPW). In this paper, we focus on elections that use positional scoring rules, and propose an alternative winner interpretation, the Most Expected Winner (MEW), according to the expected performance of the candidates.
We separate the uncertainty in voter preferences into the generation step and the observation step, which gives rise to a unified voting profile combining both incomplete and probabilistic voting profiles. We use this framework to establish the theoretical hardness of MEW over incomplete voter preferences, and then identify a collection of tractable cases for a variety of voting profiles, including those based on the popular Repeated Insertion Model (RIM) and its special case, the Mallows model. We develop solvers customized for various voter preference types to quantify the candidate performance for the individual voters, and propose a pruning strategy that optimizes computation. The performance of the proposed solvers and pruning strategy is evaluated extensively on real and synthetic benchmarks, showing that our methods are practical.
more »
« less
- NSF-PAR ID:
- 10377586
- Date Published:
- Journal Name:
- Proceedings of the '23 International Conference on the Management of Data (ACM SIGMOD 2023)
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
In many real world situations, collective decisions are made using voting and, in scenarios such as committee or board elections, employing voting rules that return multiple winners. In multi-winner approval voting (AV), an agent submits a ballot consisting of approvals for as many candidates as they wish, and winners are chosen by tallying up the votes and choosing the top-k candidates receiving the most approvals. In many scenarios, an agent may manipulate the ballot they submit in order to achieve a better outcome by voting in a way that does not reflect their true preferences. In complex and uncertain situations, agents may use heuristics instead of incurring the additional effort required to compute the manipulation which most favors them. In this paper, we examine voting behavior in single-winner and multi-winner approval voting scenarios with varying degrees of uncertainty using behavioral data obtained from Mechanical Turk. We find that people generally manipulate their vote to obtain a better outcome, but often do not identify the optimal manipulation. There are a number of predictive models of agent behavior in the social choice and psychology literature that are based on cognitively plausible heuristic strategies. We show that the existing approaches do not adequately model our real-world data. We propose a novel model that takes into account the size of the winning set and human cognitive constraints; and demonstrate that this model is more effective at capturing real-world behaviors in multi-winner approval voting scenarios.more » « less
-
The study of fairness in multiwinner elections focuses on settings where candidates have attributes. However, voters may also be divided into predefined populations under one or more attributes. The models that focus on candidate attributes alone may systematically under-represent smaller voter populations. Hence, we develop a model, DiRe Committee Winner Determination (DRCWD), which delineates candidate and voter attributes to select a committee by specifying diversity and representation constraints and a voting rule. We analyze its computational complexity and develop a heuristic algorithm, which finds the winning DiRe committee in under two minutes on 63% of the instances of synthetic datasets and on 100% of instances of real-world datasets. We also present an empirical analysis of feasibility and utility traded-off. Moreover, even when the attributes of candidates and voters coincide, it is important to treat them separately as diversity does not imply representation and vice versa. This is to say that having a female candidate on the committee, for example, is different from having a candidate on the committee who is preferred by the female voters, and who themselves may or may not be female.more » « less
-
With each successive election since at least 1994, congressional elections in the United States have transitioned toward nationalized two-party government. Fewer voters split their tickets for different parties between President and Congress. Regional blocs and incumbency voting --- a key feature of U.S. elections in the latter 20th century --- appear to have given way to strong party discipline among candidates and nationalized partisanship among voters. Observers of modern American politics are therefore tempted to write off the importance of the swing voter, defined here as voters who are indifferent between the two parties and thus likely to split their ticket or switch their party support. By assembling data from historical elections (1950 -- 2020), surveys (2008 -- 2018), and cast vote record data (2010 -- 2018), and through developing statistical methods to analyze such data, I argue that although they comprise a smaller portion of the electorate, each swing voter is disproportionately decisive in modern American politics, a phenomenon I call the swing voter paradox. Historical comparisons across Congressional, state executive, and state legislative elections confirm the decline in aggregate measures of ticket splitting suggested in past work. But the same indicator has not declined nearly as much in county legislative or county sheriff elections (Chapter 1). Ticket splitters and party switchers tend to be voters with low news interest and ideological moderate. Consistent with a spatial voting model with valence, voters also become ticket splitters when incumbents run (Chapter 2). I then provide one of the first direct measures of ticket splitting instate and local office using cast vote records. I find that ticket splitting is more prevalent in state and local elections (Chapter 3). This is surprising given the conventional wisdom that party labels serve as heuristics and down-ballot elections are low information environments. A major barrier for existing studies of the swing voter lies in the measurement from incomplete electoral data. Traditional methods struggle to extract information about subgroups from large surveys or cast vote records, because of small subgroup samples, multi-dimensional data, and systematic missingness. I therefore develop a procedure for reweighting surveys to small areas through expanding poststratification targets (Chapter 4), and a clustering algorithm for survey or ballot data with multiple offices to extract interpretable voting blocs (Chapter 5). I provide open-source software to implement both methods. These findings challenge a common characterization of modern American politics as one dominated by rigidly polarized parties and partisans. The picture that emerges instead is one where swing voters are rare but can dramatically decide the party in power, and where no single demographic group is a swing voter. Instead of entrenching elections into red states and blue states, nationalization may heighten the role of the persuadable voter.more » « less
-
Integrity of elections is vital to democratic systems, but it is frequently threatened by malicious actors.The study of algorithmic complexity of the problem of manipulating election outcomes by changing its structural features is known as election control Rothe [2016].One means of election control that has been proposed, pertinent to the spatial voting model, is to select a subset of issues that determine voter preferences over candidates.We study a variation of this model in which voters have judgments about relative importance of issues, and a malicious actor can manipulate these judgments.We show that computing effective manipulations in this model is NP-hard even with two candidates or binary issues.However, we demonstrate that the problem becomes tractable with a constant number of voters or issues.Additionally, while it remains intractable when voters can vote stochastically, we exhibit an important special case in which stochastic voting behavior enables tractable manipulation.more » « less
