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Structural instability of the core

McKelvey, Richard D. and Schofield, Norman (1986) Structural instability of the core. Journal of Mathematical Economics, 15 (3). pp. 179-198. ISSN 0304-4068. https://resolver.caltech.edu/CaltechAUTHORS:20171113-170122722

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Abstract

Let σ be a q-rule, where any coalition of size q, from the society of size n, is decisive. Let w(n,q)= 2q-n+1 and let W be a smooth ‘policy space’ of dimension w. Let U(W)N be the space of all smooth profiles on W, endowed with the Whitney topology. It is shown that there exists an ‘instability dimension’ w∗(σ) with 2≦w∗(σ)≦w(n,q) such that: 1. (i) if w≧w∗(σ), and W has no boundary, then the core of σ is empty for a dense set of profiles in U(W)N (i.e., almost always), 2. (ii) if w≧w∗(σ)+1, and W has a boundary, then the core of σ is empty, almost always, 3. (iii) if w≧w∗(σ)+1 then the cycle set is dense in W, almost always, 4. (iv) if w≧w∗(σ)+2 then the cycle set is also path connected, almost always. The method of proof is first of all to show that if a point belongs to the core, then certain generalized symmetry conditions in terms of ‘pivotal’ coalitions of size 2q−n must be satisfied. Secondly, it is shown that these symmetry conditions can almost never be satisfied when either W has empty boundary and is of dimension w(n,q) or when W has non-empty boundary and is of dimension w(n,q)+1.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1016/0304-4068(86)90009-1DOIArticle
http://www.sciencedirect.com/science/article/pii/0304406886900091PublisherArticle
http://resolver.caltech.edu/CaltechAUTHORS:20170908-145130668Related ItemWorking Paper
Additional Information:© 1986, Elsevier Science Publishers B.V. (North-Holland). Received July 1984, final version accepted June 1986. The contribution of the first author is supported, in part, by NSF grant SES-84-09654 to the California Institute of Technology, and that of the second author is based on work supported by NSF grant SES-84-18295 to the School of Social Sciences. University of California at Irvine. Presented at the Panel on Social Choice Theory, the Annual meeting of the Public Choice Society, New Orleans, February 21-23, 1985. Formerly SSWP 535.
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Funding AgencyGrant Number
NSFSES-8409654
NSFSES-8418295
Issue or Number:3
Record Number:CaltechAUTHORS:20171113-170122722
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20171113-170122722
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ID Code:83182
Collection:CaltechAUTHORS
Deposited By: Jacquelyn Bussone
Deposited On:15 Nov 2017 23:34
Last Modified:03 Oct 2019 19:03

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