Electoral College and Direct Popular Vote for Multi-Candidate Election

We introduce a stability analysis model for multi-candidate regional and national voting schemes (aka Electoral College and Direct Popular Vote, respectively), which can be expressed as the a posteriori probability that a winning candidate will continue to be chosen after the system is subjected to noise. The model shows, in most situations, that regional voting is more stable than national voting; that the stability of regional voting increases as the size of the subdivided regions decreases, up to a certain level, and then the stability starts to decrease approaching the stability of national voting as the region size approaches the original unit cell size; and that the stability of regional voting approaches that of national voting in the two extremities as the regional size increases to the original national voting size or decreases to the unit cell size. It also shows, for the special situation of homogeneous noise dominance with negligibly small amount of inhomogeneous noise, that national voting is surprisingly more stable than regional voting. The theory is evaluated by face recognition experiments on FERET and Yale Face datasets where exceptional improvements have been achieved.