A general stability analysis on regional and national voting schemes against noise-why is an electoral college more stable than a direct popular election?

By discarding the previous restrictive weak average distribution assumption on region sizes, we have developed a new general probabilistic model on the regional voting (known as “direct popular voting” in political science) and the national voting (typically, the electoral college), where we regard the percentage of a candidate's supporters in the nation as the probability of a voter voting for the candidate. Our analysis demonstrates that the regional voting is always more stable than the national voting, and that the stability margin of the regional voting always increases as the size of such partitioned regions decreases down to a certain critical value of region size, beyond which the stability margin starts to decrease, asymptoting to a national voting level where the size of the partitioned regions approaches the unit of voting cell so that the improved stability of the regional voting by localizing the effects of noise into a restricted number of smaller effective areas will not be effective. Our stability analysis remains valid over the entire range in size of the partitioned regions for regional voting. We show that the regional voting asymptotes to the national voting in two extreme limiting cases, when the region size decreases to a voting cell size and when the region size increases to the size of the nation.