Abstract
It has long been recognized that Instant Runoff Voting (IRV) suffers from a defect known as nonmonotonicity, wherein increasing support for a candidate among a subset of voters may adversely affect that candidate’s election outcome. The expected frequency of this type of behavior, however, remains an open and important question, and limited access to detailed election data makes it difficult to resolve empirically. In this paper, we develop a spatial model of voting behavior to approach the question theoretically. We conclude that monotonicity failures in three-candidate IRV elections may be much more prevalent than widely presumed (results suggest a lower bound estimate of 15 % for competitive elections). In light of these results, those seeking to implement a fairer multi-candidate election system should be wary of adopting IRV.
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Notes
Our analysis here closely parallels work by Lepelley et al. (1996) and Miller (2012), but differs in its construction of condition (1). In our analysis of the spatial model (Sect. 4), we ignore cases where two candidates tie for fewest first-place votes, so we include a stronger version of condition (1) than in these previous papers.
For convenience, we define c=c 1+c 2.
The qualitative results presented in this paper are robust to alternate specifications of utility, including city block distance and squared Euclidean distance.
In the polarized case, we ensure that there is at least one candidate in each “camp”, and two in the larger camp.
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Acknowledgements
The authors thank Ross A. Hammond and the anonymous reviewers for insightful comments and suggestions. Any errors remain the responsibility of the authors.
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Ornstein, J.T., Norman, R.Z. Frequency of monotonicity failure under Instant Runoff Voting: estimates based on a spatial model of elections. Public Choice 161, 1–9 (2014). https://doi.org/10.1007/s11127-013-0118-2
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DOI: https://doi.org/10.1007/s11127-013-0118-2