Generic Instability of Majority Rule
证明，在光滑政策空间上，当空间维度达到某个阈值时，多数决投票的核几乎总是空的，且存在稠密的偏好循环，对理解投票制度的稳定性有重要理论意义。
Majority rule voting with smooth preferences on a smooth policy space W is examined. It is shown that there is an integer w(n), which is 2 when the size of the society n is odd and 3 when n is even such that when the dimension of W is at least w(n) then, for almost preference profiles on W, the core of the voting game is empty when the dimension of W exceeds w(n) then for almost all preference profiles on W, there exist dense preference cycles in W. Moreover in dimension w(n) + 1 the policy space can be partitioned into a finite number of path connected components, such that any two points in one of the components can be connected by a majority voting trajectory. In dimension greater than w(n) + 1 there exists only one such component.