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The Generic Existence of a Core for q-Rules


  • Donald G. Saari



A q-rule is where a winning coalition has q or more of the n voters. An important issue is to understand when, generically, core points exist; that is, to determine when the core exists in other than highly contrived settings. As known, the answer depends upon the dimension of issue space. McKelvey and Schoeld found bounds on these dimensions, but Banks found a subtle, critical error in their proofs. The sharp dimensional values along with results about the structure of the core are derived. These values can be identied with the number of issues needed to lure previously supporting voters into a new coalition.

Suggested Citation

  • Donald G. Saari, 1995. "The Generic Existence of a Core for q-Rules," Public Economics 9506001, EconWPA.
  • Handle: RePEc:wpa:wuwppe:9506001
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    References listed on IDEAS

    1. Banks, Jeffrey S., 1995. "Singularity theory and core existence in the spatial model," Journal of Mathematical Economics, Elsevier, vol. 24(6), pages 523-536.
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    More about this item


    core; spatial voting; q-rules;

    JEL classification:

    • D6 - Microeconomics - - Welfare Economics
    • D7 - Microeconomics - - Analysis of Collective Decision-Making
    • H - Public Economics


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