Abstract
We discuss some methods aiming to reconcile Borda’s and Condorcet’s winning intuitions in the theory of voting. We begin with a brief summary of the advantages and disadvantages of binary and positional voting rules. We then review in some detail Black’s, Nanson’s and Dodgson’s rules as well as the relatively recently introduced methods based on supercovering relation over the candidate set. These are evaluated in terms of some well-known choice–theoretic criteria.
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Notes
- 1.
Pérez’s invulnerability to the positive strong no-show paradox (Pérez 2001, p. 602) refers to the same property.
- 2.
Two much simpler examples each involving only three candidates and nine voters are presented in Brandt et al. (2022) in the context of reinforcement and no-show (Sect. 4.7).
- 3.
- 4.
Brandt et al. provide simpler examples of these and other paradoxes (Brandt et al., 2022).
- 5.
Perhaps a better-known term for Baldwin’s rule is Borda elimination rule (BER)(Smaoui et al., 2016).
- 6.
Associating C. L. Dodgson (a.k.a. Lewis Carrol) with the rule described in this subsection has plausibly been called into question by, e.g., Fishburn (1977, pp. 474–475). Indeed, what is known as the Dodgson rule is just one of several proposed by him (Black, 1958). Also Tideman has doubts about the plausibility of associating Dodgson with this rule (Tideman, 1987). See Brandt (2009). Keeping these caveats in mind we shall, however, conform to the standard usage of the concept of Dodgson’s rule.
- 7.
That the use of a non-homogeneous voting rule makes the outcomes depend not only on the distribution of voters over preference rankings but also on the number of voters, obviously suggests that various participants may have different interests in the size of the voting body. This aspect relates the study of power to the institution design as pursued by the honoree of this volume and his associates.
- 8.
In a companion article, the same authors define and analyze solutions based on superdomination relation (Pérez-Fernández and De Baets, 2018b). Our focus in this paper is on the supercovering relation and the associated solutions.
- 9.
The labels of criteria in the first column are phrased so as to make ‘yes’ a preferable value to ‘no’. So, the more ‘yes’ values assigned to a rule, the better its performance in terms of this evaluation.
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Acknowledgements
The author wishes to thank Manfred J. Holler and Sascha Kurz for numerous constructive comments on an earlier draft.
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Nurmi, H. (2023). Building Bridges Over the Great Divide. In: Kurz, S., Maaser, N., Mayer, A. (eds) Advances in Collective Decision Making. Studies in Choice and Welfare. Springer, Cham. https://doi.org/10.1007/978-3-031-21696-1_2
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