Abstract
The yolk, an important concept of spatial majority voting theory, is assumed to be unique when the number of individuals is odd. We prove that this claim is true in \( {\mathbb {R}} ^{2}\) but false in \( {\mathbb {R}} ^{3}\), and discuss the differing implications of non-uniqueness from the normative and predictive perspectives.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Notes
For a simple and very clear presentation, see Miller (2015).
If n is odd then, \(S\subseteq N\) is a minimal blocking coalition if and only if S is a minimal winning coalition.
For a discussion on the limiting median lines, see Stone and Tovey (1992). In this example, there is no Tovey “anomaly”.
See Owen (1990) for a presentation of these concepts and their links to solutions of side-payment games.
Indeed, they were careful to describe the yolk as “a minimal sphere which intersects with every median hyperplane” (page 59, emphasis added), whereas they define a different ball as “the smallest closed ball containing all ideal points” (page 58, emphasis added). It is easy to see that the latter is unique.
References
Eban G, Stephen WS (1990) Predicting committee behavior in majority rule voting experiments. RAND J Econ 21:293–313
Ferejohn JA, McKelvey R, Packel E (1984) Limiting distributions for continuous state Markov models. Soc Choice Welf 1:45–67
Grofman B, Scott LF, Miller NR (1988) Centripetal forces in spatial voting: on the size of the Yolk. Public Choice 59:37–50
McKelvey RD (1986) Covering, dominance, and institution free properties of social choice. Am J Political Sci 30:283–314
Miller NR (1980) A new solution set for tournaments and majority voting. Am J Political Sci 24:68–96
Miller NR (1983) The covering relation in tournaments: two corrections. Am J Political Sci 27:382–385
Miller NR (2007) In search of the uncovered set. Political Anal 15(1):21–45
Miller NR (2015) The spatial model of social choice and voting. In: Heckelman JC, Miller NR (eds) Handbook of social choice and voting chapter10. Edward Elagar, Cheltenham, pp 163–181
Owen G (1990) Stable outcomes in spatial voting games. Math Soc Sci 19:269–279
Owen G, Shapley L (1989) Optimal location of candidates in idealogical space. Int J Game Theory 18:339–356
Plott C (1967) A notion of equilibrium and its possibility under majority rule. Am Econ Rev 57:787–806
Rubinstein A (1979) A note about the ‘nowhere denseness’ of societies having an equilibrium under majority rule. Econometrica 47:511–514
Schofield NJ (1983) Generic instability of majority rule. Rev Econ Stud 50:696–705
Scott LF, Grofman B, Hartley R, Kilgour MO, Miller NR, Noviello N (1987) The uncovered set in spatial voting games. Theory Decis 23:129–156
Stone RE, Tovey CA (1992) Limiting median lines do not suffice to determine the Yolk. Soc Choice Welf 9:33–35
Tovey CA (1992) A polynomial algorithm to compute the Yolk in fixed dimension. Mathematical Programming 57:259–277. Presented at SIAM Symposium on Complexity Issues in Numerical Optimization, March 1991. Ithaca, NY
Tovey CA (2010) A finite exact algorithm for epsilon-core membership in two dimensions. Math Soc Sci 60(3):178–180
Tovey CA (2010) The probability of majority rule instability in two dimensions with an even number of voters. Soc Choice Welf 35(4):705–708
Tovey CA (2011) The Finagle point and the epsilon-core: a comment on Bräuninger’s proof. J Theor Politics 23(1):135–139
Tovey CA (2010) The instability of instability of centered distributions. Math Soc Sci 59:53–73 previously released as technical report NPSOR-91-15, Naval Postgraduate School, May 1991
Wuffle A, Scott LF, Owen G, Grofman B (1989) Finagle’s law and the Finagle point: a new solution concept for two-candidate competition in spatial voting games without a core. Am J Political Sci 33:348–375
Author information
Authors and Affiliations
Corresponding author
Additional information
We would like to thank Prof. Nicholas R. Miller and the reviewers for their important helpful comments.
Mathieu Martin: This research has been developed within the center of excellence MME-DII (ANR-11-LBX-0023-01).
Craig A. Tovey: Research supported by National Science Foundation Grant #1335301.
Rights and permissions
About this article
Cite this article
Martin, M., Nganmeni, Z. & Tovey, C.A. On the uniqueness of the yolk. Soc Choice Welf 47, 511–518 (2016). https://doi.org/10.1007/s00355-016-0979-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00355-016-0979-7