# 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

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.

## Models of voter behavior

Discussions around modeling voter behavior often involve arguments over whether voters follow the Expressive model of voter behavior (i.e. they tend to vote honestly, without much consideration for the outcome) or the Pivotal model (they tend to vote strategically, trying to maximize their own satisfaction with the outcome; this is also known as the rational voter model). Note that maximizing one's own satisfaction with the outcome need not be for selfish reasons; an altruistic Pivotal/strategic voter may prefer to vote in a way that brings about what they'd consider a more consensus-oriented or better outcome for society.