# Statistics

Statistics is the study of data. It often appears in voting theory when deciding how to simulate and measure the performance of a voting method under various circumstances and using different metrics.

One example of a statistic would be the voter distribution, which is how the voters are distributed in the way that they are related to each other politically. This is then further used in a spatial model of voting, which is used to map out voter preferences; it is common to aim for voting methods that elect a winner who best approximates the centroid (center) of the voter distribution.

Another example of a statistic is voting method criteria. For example, all Condorcet methods will elect the Condorcet winner 100% of the time in any circumstances. This measure is known as Condorcet efficiency.

###### Measures[edit | edit source]

The Smith efficiency of a voting method measures how Smith-efficient it is i.e. how often it elects someone in the Smith set. One consequence of this measure is that it indirectly measures the mutual majority efficiency and majority criterion efficiency of a voting method, since the Smith set is a subset of the mutual majority set when there is a mutual majority set, and so every time a voting method elects from the Smith set, it must also have elected from the mutual majority-preferred set of candidates, if one existed.