Interjacency
It is well known that social choice rules have at least one profile at which they are manipulable. In this short note, the author reports some constructions that lead to interjacency conjectures of the following type: for a certain class of rules, determine m, the minimum number such that there is a rule \(f_ 1\) in the class with exactly m profiles at which \(f_ 1\) is manipulable, and determine M, the maximum number such that there is a rule \(f_ 2\) in the class with exactly M profiles at which \(f_ 2\) is manipulable. Then, for every integer n between m and M, there is a rule in the class with exactly n profiles at which it is manipulable. Such an interjacency conjecture seems to be of much interest and is worthy of further investigation.
scientific article; zbMATH DE number 4167785