Abstract
Two volumes, published roughly 50 years apart and both dealing with the probabilistic analysis of collective decision-making, are reviewed with the aim of tracing the developments in the field that stands somewhat outside the mainstream social choice and voting theory. It turns out that the core topics have remained the same, but with the passage of time the issues addressed have become more nuanced and the analysis techniques more advanced and variegated. Some topics dealt with in the earlier volume have been left behind and replaced by others in the later one. Originated largely in the U.S., the probabilistic tradition has now gained a firm foothold in several European research centers with many important topics analyzed by cross-Atlantic teams. At the same time, new approaches stemming from computer science, geometry, and other parts of mathematics have opened new vistas to the analysis of voting procedures.
The author thanks Benoît Le Maux for constructive comments on an earlier version of this paper.
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Notes
- 1.
Of course, this very brief exposition is not intended as a listing of Manfred’s scholarly contributions, not even the most influential ones, but as a background to the following pages.
- 2.
While not an author in the Diss and Merlin volume, Peter C. Fishburn—one of the contributors to the Niemi and Weisberg book—certainly had an important role as the supervisor and mentor of William V. Gehrlein, a contributor to and one of the two honorees of Diss and Merlin (2021).
- 3.
This approach differs from (in fact, reverses) the one where the effects of voting rules on “closeness” of results are sometimes analyzed.
- 4.
This paradox is also known as the violation of the Chernoff or heritage property.
- 5.
The profile is a minor simplification of the one presented in (Felsenthal and Nurmi, 2018, p. 34).
- 6.
This is not the proper place to address the age-old topic of what constitutes a science sensu stricto. No doubt voices have occasionally been raised to argue that ‘science’ should denote natural sciences and should not be applied to the study of such ‘soft’ entities as politics—or economics for that matter.
- 7.
This expression is not intended to play down the significance of findings regarding paradoxes or incompatibilities between performance criteria. Such findings may be exceedingly difficult to make.
- 8.
See, however, the pioneering work of Farquharson (1956) where the idea of sophisticated voting as a form of successful preference misrepresentation and the concept of straightforward voting rule as a rule immune to successful misrepresentation was introduced. These ideas were further developed in Farquharson (1969). See also Dummett and Farquharson (1961).
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Nurmi, H. (2023). Probabilistic Study of Voting Rules: A Tale of Two Volumes. In: Leroch, M.A., Rupp, F. (eds) Power and Responsibility. Springer, Cham. https://doi.org/10.1007/978-3-031-23015-8_11
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