Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-24T19:05:58.397Z Has data issue: false hasContentIssue false
  • English
  • Français

Paradoxical oddities in two multiwinner elections from Scotland

Published online by Cambridge University Press:  12 November 2024

Adam Graham-Squire  and
David McCune
Adam Graham-Squire
Affiliation:
Department of Mathematical Sciences, High Point University, 1 University Parkway, High Point, NC, 27268 USA e-mail: [email protected]
David McCune
Affiliation:
Department of Physics and Data Science, William Jewell College, 500 College Hill, Liberty, MO, 64068-1896 e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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.

Type
Articles
Information
The Mathematical Gazette , Volume 108 , Issue 573 , November 2024 , pp. 492 - 506
Check for updates
Copyright
© The Authors, 2024 Published by Cambridge University Press on behalf of The Mathematical Association

References

McCune, D. and Graham-Squire, A., Monotonicity anomalies in Scottish local government elections, Social Choice and Welfare (2024).CrossRefGoogle Scholar
Felsenthal, D. and Tideman, N., Interacting double monotonicity failure with direction of impact under five voting methods, Mathematical Social Sciences 67 (2014) pp. 57–66.CrossRefGoogle Scholar
Ornstein, J. and Norman, R., Frequency of monotonicity failure under instant runoff voting: estimates based on a spatial model of elections. Public Choice 161:1-2 (2014) pp. 1–9.CrossRefGoogle Scholar
McCune, D. and McCune, L., The curious case of the 2021 Minneapolis Ward 2 City Council Election, The College Mathematics Journal (2023).CrossRefGoogle Scholar
Graham-Squire, A. and McCune, D., Ranked choice wackiness in Alaska, Math Horizons 31:1 (2024) pp. 24–27.CrossRefGoogle Scholar
McCune, D., Ranked choice bedlam in a 2022 Oakland School Director Election, Cornell University available at https://arxiv.org/abs/2303.05985 Google Scholar
Rules, Scottish STV, OpaVote, accessed July 2024 https://www.opavote.com/methods/scottish-stv-rules Google Scholar
Elkind, E., Faliszewski, P., Skowron, P., and Slinko, A.. Properties of multiwinner voting rules, Social Choice and Welfare 48 (2017) pp. 599–632.CrossRefGoogle ScholarPubMed
Balinski, M. and Young, H.. Fair representation: meeting the ideal of one man, one vote (2nd edn.) Brookings Institution Press (2001).Google Scholar
Teale, A.. Local Elections Archive Project, accessed July 2024. https:// www. andrewteale.me.uk/leap/results/2012/453#ward10728Google Scholar
Brams, S., Kilgour, D. M. and Sanver, M. R., A minimax procedure for electing committees, Public Choice 132 (2007) pp. 401–420.CrossRefGoogle Scholar
Ratliff, T., Selecting committees, Public Choice 126:3 (2006), pp. 343–355.CrossRefGoogle Scholar
Gehrlein, W., The Condorcet criterion and committee selection, Mathematical Social Sciences 66: 3 (1985) pp. 199–209.CrossRefGoogle Scholar
Ratliff, T., Some startling inconsistencies when electing committees. Social Choice and Welfare 21:3 (2003) pp. 433–454.CrossRefGoogle Scholar
Miller, N. R., Closeness matters: monotonicity failures in IRV elections with three candidates, Public Choice 173 (2017) pp. 91–108.CrossRefGoogle Scholar