Sep
23
The Logic of Voting
In an election, voting power—the probability that a single vote is
decisive—is affected by the rule for aggregating votes into a single outcome.
Voting power is important for studying political representation, fairness and
strategy, and has been much discussed in political science. Although power
indexes are often considered as mathematical definitions, they ultimately
depend on statistical models of voting. Mathematical calculations of voting
power usually have been performed under the model that votes are decided
by coin flips. This simple model has interesting implications for weighted
elections, two-stage elections (such as the U.S. Electoral College) and
coalition structures. We discuss empirical failings of the coin-flip model of
voting and consider, first, the implications for voting power and, second,
ways in which votes could be modeled more realistically. Under the random
voting model, the standard deviation of the average of n votes is proportional
to 1/√n, but under more general models, this variance can have the form
cn−α or √a
− b log n. Voting power calculations under more realistic models
present research challenges in modeling and computation.
hmm I always thought the probability of your vote mattering is below 1 and that voting is done because of moral and social incentive. but it seems that may not be true.
http://www.stat.columbia.edu/~gelman/research/published/STS027.pdf
