Many societal decision problems lie in high-dimensional continuous spaces not amenable to the voting techniques common for their discrete or single-dimensional counterparts. These problems are typically discretized before running an election or decided upon through negotiation by representatives. We propose a algorithm called Iterative Local Voting for collective decision-making in this setting. In this algorithm, voters are sequentially sampled and asked to modify a candidate solution within some local neighborhood of its current value, as defined by a ball in some chosen norm, with the size of the ball shrinking at a specified rate. We first prove the convergence of this algorithm under appropriate choices of neighborhoods to Pareto optimal solutions with desirable fairness properties in certain natural settings: when the voters' utilities can be expressed in terms of some form of distance from their ideal solution, and when these utilities are additively decomposable across dimensions. In many of these cases, we obtain convergence to the societal welfare maximizing solution.We then describe an experiment in which we test our algorithm for the decision of the U.S. Federal Budget on Mechanical Turk with over 2,000 workers, employing neighborhoods defined by various L-Norm balls. We make several observations that inform future implementations of such a procedure.
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Collaborative Optimization for Collective Decision-making in Continuous Spaces
Many societal decision problems lie in high-dimensional continuous spaces not amenable to the voting techniques common for their discrete or single-dimensional counterparts. These problems are typically discretized before running an election or decided upon through negotiation by representatives. We propose a meta-algorithm called Iterative Local Voting for collective decision-making in this setting, in which voters are sequentially sampled and asked to modify a candidate solution within some local neighborhood of its current value, as defined by a ball in some chosen norm. In general, such schemes do not converge, or, when they do, the resulting solution does not have a natural description.
We first prove the convergence of this algorithm under appropriate choices of neighborhoods to plausible solutions in certain natural settings: when the voters' utilities can be expressed in terms of some form of distance from their ideal solution, and when these utilities are additively decomposable across dimensions. In many of these cases, we obtain convergence to the societal welfare maximizing solution.
We then describe an experiment in which we test our algorithm for the decision of the U.S. Federal Budget on Mechanical Turk with over 4,000 workers, employing neighborhoods defined by §L1, §L2 and §L∞ balls. We make several observations that inform future implementations of such a procedure.
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- Award ID(s):
- 1637397
- NSF-PAR ID:
- 10026405
- Date Published:
- Journal Name:
- WWW '17 Proceedings of the 26th International Conference on World Wide Web
- Page Range / eLocation ID:
- 617 to 626
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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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. To this end, we investigate a natural model, where voters' preferences between two alternatives depend on a discrete state variable that is not directly observable. Each voter receives a private signal that is correlated with the state variable. We reveal a surprising equilibrium between a strategy profile being a strong equilibrium and leading to the decision favored by the majority of agents conditioned on them knowing the ground truth (referred to as the informed majority decision): as the size of the vote goes to infinity, every ε-strong Bayes Nash Equilibrium with ε converging to 0 formed by strategic agents leads to the informed majority decision with probability converging to 1. On the other hand, we show that informative voting leads to the informed majority decision only under unbiased instances, and sincere voting leads to the informed majority decision only when it also forms an equilibrium.more » « less
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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
- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1145/3038912.3052690
