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 undermore realistic models
present research challenges in modeling and computation
