Editing Random ballot (section)

===For multimember bodies===
If the random ballot is used to select the members of a multi-constituency body, it can create a kind of [[proportional representation]] on average across elections. If the winner of each race is chosen randomly, then as the number of seats in a legislature grows, the percentage representation of each party in the elected body will get closer and closer to their actual proportion of the vote across the entire electorate. At the same time, the chance of a randomly selected highly unrepresentative body diminishes.

For example, say a minority party has 1% of the vote. This party would, in a 50-person assembly, have a vanishingly small chance of winning a majority. Using the [[binomial distribution]], the probability is given by:

:<math> \sum_{k=0}^{24} {50 \choose k} \left(\frac{99}{100}\right)^k\left(\frac{1}{100}\right)^{50-k} = I_{1/100}(26, 25) \approx 10^{-38} </math>