probability of encountering the Condorcet paradox is therefore which gives the value 8.77%. Some results for the case of more than three candidates have been calculated and simulated. The simulated likelihood for an impartial culture model with 25 voters increases with the number of candidates: The likelihood of a Condorcet cycle for related models approach these values for large electorates: Impartial anonymous culture (IAC): 6.25% Uniform culture (UC): 6.25% Maximal culture condition (MC): 9.17% All of these models are unrealistic, and are investigated to establish an upper bound on the likelihood of a cycle. Group coherence models When modeled with more realistic voter preferences, Condorcet paradoxes in elections with a small number of candidates and a large number of voters become very rare. Spatial model A study of three-candidate elections analyzed 12 different models of voter behavior, and found the spatial model of voting to be the most accurate to real-world ranked-ballot election data. Analyzing this spatial model, they found the likelihood of a cycle to decrease to zero as the number of voters increases, with likelihoods of 5% for 100 voters, 0.5% for 1000 voters, and 0.06% for 10,000 voters. Another spatial model found likelihoods of 2% or less in all simulations of 201 voters and 5 candidates, whether two or four-dimensional, with or without correlation between dimensions, and with two different dispersions of candidates. Empirical studies Many attempts have been made at finding empirical examples of the paradox. Empirical identification of a Condorcet paradox presupposes extensive data on the decision-makers' preferences over all alternatives—something that is only very rarely available. A summary of 37 individual studies, covering a total of 265 real-world elections, large and small, found 25 instances of a Condorcet paradox, for a total likelihood of 9.4% (and this may be a high estimate, since cases of the paradox are more likely to be reported on than cases without). An analysis of 883 three-candidate elections extracted from 84 real-world ranked-ballot elections of the Electoral Reform Society found a Condorcet cycle likelihood of 0.7%. These derived elections had between 350 and 1,957 voters. A similar analysis of data from the 1970–2004 American National Election Studies thermometer scale surveys found a Condorcet cycle likelihood of 0.4%. These derived elections had between 759 and 2,521 "voters". While examples of the paradox seem to occur occasionally in small settings (e.g., parliaments) very few examples have been found in larger groups