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This reduces the set of possible elections by eliminating those that are equivalent if the voter identities are unknown. For example, the two-candidate, three-voter election {A>B, A>B, B>A} is equivalent to the election where the second and third voters swap votes: {A>B, B>A, A>B},
260:
This reduces the set of possible elections further, by eliminating those that are equivalent if the candidate identities are unknown. For example, the two-candidate, three-voter election {A>B, A>B, B>A} is equivalent to the election where the two candidates are swapped: {B>A, B>A,
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It can be shown that IAC is equivalent to the assumption that the preferences of the voters are independent and identically distributed according to a multinomial distribution conditional on a prior uniform draw … This prior is a special case of a
Dirichlet
45:
The model is understood to be unrealistic, and not a good representation of real-world voting behavior, however, it is useful for mathematical comparisons of voting methods under reproducible, worst-case scenarios.
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if we use conditions that tend to exaggerate the likelihood of observing paradoxes and find that the probability is small with such calculations, the paradox is assuredly very unlikely to be observed in
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and so all variations on this set of votes are only included once. The set of all such elections is called the anonymous equivalence class (AEC), and if the strict rankings are being chosen by
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There are three variations of the model that use different subsets of the full set of possible rankings, so that different election permutations are drawn with different probabilities:
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The model assumes that each voter provides a complete strict ranking of all the candidates (with no equal rankings or blanks), which is drawn from a set of all possible rankings. For
329:
Eğecioğlu, Ömer; Giritligil, Ayça E. (October 2013). "The
Impartial, Anonymous, and Neutral Culture Model: A Probability Model for Sampling Public Preference Structures".
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125:
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709:
596:
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Tideman, T. Nicolaus; Plassmann, Florenz (2008). "The Source of
Election Results: An Empirical Analysis of Statistical Models of Voter Behavior".
423:…Using unrealistic assumptions may thus have a reasonable methodological function even if we know how to describe reality in a more realistic way…
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Tsetlin, Ilia; Regenwetter, Michel; Grofman, Bernard (1 December 2003). "The impartial culture maximizes the probability of majority cycles".
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619:"The theoretical Shapley–Shubik probability of an election inversion in a toy symmetric version of the US presidential electoral system"
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This model assumes that each voter's ranking is randomly selected from a uniform distribution. If these are chosen by
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it is widely acknowledged that the impartial culture is unrealistic … the impartial culture is the worst case scenario
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The impartial culture assumption has been criticized extensively as being implausible and empirically irrelevant
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Lehtinen, Aki; Kuorikoski, Jaakko (June 2007). "Unrealistic
Assumptions in Rational Choice Theory".
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Gehrlein, William V.; Lepelley, Dominique (2011). "Voting
Paradoxes and Their Probabilities".
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de Mouzon, Olivier; Laurent, Thibault; Le Breton, Michel; Lepelley, Dominique (March 2020).
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583:, an assumption is made that vote allocations are uniformly distributed on the simplex.
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Voting theorists generally acknowledge that they consider this model to be unrealistic
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Van Deemen, Adrian (March 2014). "On the empirical relevance of
Condorcet's paradox".
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368:[Theories of general interest and the logical problem of aggregation].
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366:"Les théories de l'intérêt général et le problème logique de l'agrégation"
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Quas, Anthony (March 2004). "Anomalous outcomes in preferential voting".
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This is also referred to as the "Dirichlet" or "simplex" model.
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597:"The Structure of the Election-Generating Universe"
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595:Tideman, T. Nicolaus; Plassmann, Florenz (2010).
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501:. Studies in Choice and Welfare. pp. 1–47.
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536:"Comparing Probabilistic Models: IC, IAC, IANC"
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161:Impartial Anonymous Culture (IAC)
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534:Veselova, Yuliya A. (2014).
343:10.1080/0022250X.2011.597012
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25:the culture of indifference
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437:Social Choice and Welfare
294:10.1007/s11127-013-0133-3
563:Stochastics and Dynamics
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150:{\displaystyle m!^{n}}
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261:A>B}.
227:−
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