Impartial culture: Difference between revisions

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This model is not particularly realistic, but it's mathematically easy to work with.

As the number of candidates ~~approach~~ infinity, the election becomes increasingly close to a perfect tie. Effects that depend on elections being tie-like in some way (like the lack of a Condorcet winner) will thus become increasingly frequent in many candidates under impartial culture. Tsetlin et al. found that impartial culture is the model that maximizes the chance of there being no Condorcet winner, consistent with this observation.<ref name="Tsetlin Regenwetter Grofman 2003 pp. 387–398">{{cite journal | last=Tsetlin | first=Ilia | last2=Regenwetter | first2=Michel | last3=Grofman | first3=Bernard | title=The impartial culture maximizes the probability of majority cycles | journal=Social Choice and Welfare | publisher=Springer | volume=21 | issue=3 | year=2003 | jstor=41106568 | pages=387–398 | url=https://www.researchgate.net/profile/Bernard-Grofman/publication/24064463_The_impartial_culture_maximizes_the_probability_of_majority_cycles/links/0fcfd51266f8e241fa000000/The-impartial-culture-maximizes-the-probability-of-majority-cycles.pdf | access-date=2022-03-26}}</ref>

As the number of candidates approaches infinity, the election becomes increasingly close to a perfect tie. Effects that depend on elections being tie-like in some way (like the lack of a Condorcet winner) will thus become increasingly frequent in many candidates under impartial culture. Tsetlin et al. found that impartial culture is the model that maximizes the chance of there being no Condorcet winner, consistent with this observation.<ref name="Tsetlin Regenwetter Grofman 2003 pp. 387–398">{{cite journal | last=Tsetlin | first=Ilia | last2=Regenwetter | first2=Michel | last3=Grofman | first3=Bernard | title=The impartial culture maximizes the probability of majority cycles | journal=Social Choice and Welfare | publisher=Springer | volume=21 | issue=3 | year=2003 | jstor=41106568 | pages=387–398 | url=https://www.researchgate.net/profile/Bernard-Grofman/publication/24064463_The_impartial_culture_maximizes_the_probability_of_majority_cycles/links/0fcfd51266f8e241fa000000/The-impartial-culture-maximizes-the-probability-of-majority-cycles.pdf | access-date=2022-03-26}}</ref>