Talk:Space of possible elections: Difference between revisions
→Some remarks
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One thing I'd like to highlight, given this analysis, is that the impartial culture model of simply drawing ballots at random does not seem to be good enough to sample the space of possible elections uniformly.
The exchange symmetry between voters and the fact most possible partitions of voters into identical-ballot groups is highly non-uniform means the typical impartial culture model will sample a region of this space which is exceptionally void of interesting structure. If you have ''n'' voters, the vast majority of partitions will divide voters into 0.2n - 0.4n distinct groups
The interesting structure is in the lower end of the partitions. So, for 100 voters, if voter partitions are drawn at random most elections will divide the voters into 20-40 unique ballot groups. In contrast, the typical impartial culture model would create as many groups as possible and all with roughly equal number of voters, focusing on the higher end of this distribution of number of groups.
A sampling model which takes the distribution of partitions into account would more adequately sample this space, and biasing towards smaller partition sizes (due to voter and candidate correlations) would be more likely to reproduce results useful for estimating real-life elections. [[User:lucasvb|lucasvb]] ([[User_talk:lucasvb|talk]]} 21:26, 24 July 2020 (UTC)
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