THE GENERIC EXISTENCE OF A CORE FOR Q-RULES

A q-rule is where a winning coalition has q or more of the a voters. I t is important to understand when, generically, core points exist; tha t is, when does the core exist in other than highly contrived settings ? As known, the answer depends upon the dimension of issue space. McKe lvey and Schofield 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 here. I t is interesting how these dimensional values correspond to the number of issues that are needed to lure previously supporting voters into a new coalition.