Abstract
The common reaction to social choice anomalies is that while these may be theoretically feasible, their role in practice is likely to be very limited since the profiles giving rise to the paradoxes are exceptional rather than common. We argue that while the significance and observation of the general no-show paradoxes and monotonicity failures may be limited, the same is not true of P-TOP and P-BOT paradoxes. These pertain to the voters’ best and worst alternatives. Hence, the occurrences associated with them are most likely to be observed and talked about. Vulnerability to these paradoxes creates bizarre incentives for voters. Failures on monotonicity, on the other hand, have more to do with the legitimacy of the voting outcomes. It is important to find out the structural properties of settings giving rise to monotonicity-related paradoxes. Thus far very little is known about these properties. We have related the paradoxes to the existence of majority cycles in the electorate. Our general finding is that the presence of a core or Condorcet winner does not, in general, make it harder to construct profiles that lead to paradoxes. Sometimes the opposite is true: the presence of cycles makes it harder, not easier, to construct paradoxical profiles. Finally, we speculate about reasons for continued use of non-monotonic rules.
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Notes
- 1.
Potthoff (2011) suggests in a recent article how to construct public opinion polls which may identify the Condorcet winner, if one exists, and thus enable some voters who would not otherwise vote (strategically) for the Condorcet winner to do so and thereby obtain an outcome they prefer.
- 2.
A display of non-monotonicity under the Alternative Vote method has actually occurred and reported recently in the March 2009 mayoral election in Burlington, Vermont. Among the three biggest vote getters, the Republican got the most first-place votes, the Democrat the fewest, and the Progressive won after the Democrat was eliminated. Yet if many of those who ranked the Republican first had ranked the Progressive first, the Republican would have been eliminated and the Progressive would have lost to the Democrat. In March 2010, Burlington replaced the Alternative Vote for electing its mayor with the Plurality with Runoff method—which is also susceptible to non-monotonicity. See the detailed report on this election in Gierzynski et al. (2009). Smith (2007) analyses the Irish 1990 presidential election which was conducted under the Alternative Vote method and concludes (p. 3) that ‘it seems clearest to regard this election as suffering from a hybrid form of non-monotonicity (type II) and no-show’ paradoxes.
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Felsenthal, D.S., Nurmi, H. (2017). Practical Significance and Open Problems. In: Monotonicity Failures Afflicting Procedures for Electing a Single Candidate. SpringerBriefs in Economics. Springer, Cham. https://doi.org/10.1007/978-3-319-51061-3_6
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