Abstract
The notion of the existence of a Strict Ostrogorski Paradox presents an interesting phenomenon that could lead to some very unsettling outcomes in group decision-making situations. This phenomenon cannot be observed in two-issue situations, and when three-issue situations are considered, the probability that such an outcome will be observed never reaches a likelihood of as much as two percent for large electorates, regardless of the propensity of voters to align their preferences on issues with the standards of political parties. The probability of observing a Strict Ostrogorski Paradox in four-issue situations is nearly zero when using an assumption that exaggerates the likelihood that such a paradoxical outcome will be observed. We conclude that it is very unlikely that a Strict Ostrogorski Paradox would ever be observed in any real voting situation with a large electorate.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Brams SJ, Kilgour DM, Zwicker WS (1998) The paradox of multiple elections. Soc Choice Welfare 15:211–236
Daudt H, Rae DW (1976) The Ostrogorski paradox: a peculiarity of compound majority decision. Eur J Polit Res 4:391–398
Deb R, Kelsey D (1987) On constructing a generalized Ostrogorski paradox: necessary and sufficient conditions. Math Soc Sci 14:161–174
Gehrlein WV (1979) A representation for quadrivariate normal positive orthant probabilities. Commun Stat 8:349–358
Gehrlein WV (2006) Condorcet’s paradox. Springer, Berlin
Johnson NL, Kotz S (1972) Distributions in statistics: continuous multivariate distributions. Wiley, New York
Laffond G, Laine J (2006) Single-switch preferences and the Ostrogorski paradox. Math Soc Sci 52:49–66
List C (2005) The probability of inconsistencies in complex collective decisions. Soc Choice Welfare 24:3–32
Mbih B, Valeu A (2016) La vulnérabilité de la règle de la majorité aux paradoxes d’Anscombe et d’Ostrogorski: une analyse comparative. Revue Internationale des Économistes de Langue Française 1:171–191
Merlin V, Tataru M (1997) On the relation of the Condorcet winner and positional voting rules. Math Soc Sci 34:81–90
Merlin V, Tataru M, Valognes F (2000) On the probability that all decision rules select the same winner. J Math Econ 33:183–207
Merlin V, Tataru M, Valognes F (2002) On the likelihood of Condorcet’s profiles. Soc Choice Welfare 19:193–206
Nurmi H (1999) Voting paradoxes and how to deal with them. Springer, Berlin
Ostrogorski M (1902) La démocratie et l’organisation des partis politiques. Calmann-Levy, Paris
Saari DG, Tataru MM (1999) The likelihood of dubious election outcomes. Econ Theor 13:345–363
Saari DG, Sieberg KK (2001) The sum of the parts can violate the whole. Am Polit Sci Rev 95:415–433
Slepian D (1962) The one-sided barrier problem for Gaussian noise. Bell Syst Tech J 41:463–501
Acknowledgements
The authors are grateful for comments from two extremely helpful reviewers of an earlier version of this chapter.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Gehrlein, W.V., Merlin, V. (2021). On the Probability of the Ostrogorski Paradox. In: Diss, M., Merlin, V. (eds) Evaluating Voting Systems with Probability Models. Studies in Choice and Welfare. Springer, Cham. https://doi.org/10.1007/978-3-030-48598-6_6
Download citation
DOI: https://doi.org/10.1007/978-3-030-48598-6_6
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-48597-9
Online ISBN: 978-3-030-48598-6
eBook Packages: Economics and FinanceEconomics and Finance (R0)