Limitations of spatial models of voting: Difference between revisions

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With these mathematical results, it is possible to infer the minimum dimensions of any real life ranked election or ballot scenario, and maybe even infer whether enough candidate diversity was present. For <math>n</math> candidates and <math>d</math> dimensions, the following table shows the absolute maximum number of ballots that ''any'' distribution of voters and candidates could possibly generate if voters are using those <math>d</math> dimensions to classify the candidates.
With these mathematical results, it is possible to infer the minimum dimensions of any real life ranked election or ballot scenario, and maybe even infer whether enough candidate diversity was present. For <math>n</math> candidates and <math>d</math> dimensions, the following table shows the absolute maximum number of ballots that ''any'' distribution of voters and candidates could possibly generate if voters are using those <math>d</math> dimensions to classify the candidates.


The rows of the table end at the dimension that exactly allows for all possible <math>n!</math> ballots to occur (the minimum dimension for [[Unrestricted_domain]] to apply).
The rows of the table end at the dimension that exactly allows for all possible <math>n!</math> ballots to occur (the minimum dimension for [[unrestricted domain]] to apply).


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