(In this particular example, though, the incentive is weak, as those who prefer C to A only score C 1 point above A; in a ranked Condorcet method, it's quite possible they would simply equally rank A and C because of how weak their preference is, in which case a Condorcet cycle wouldn't have formed in the first place, and A would've been the Condorcet winner). So though the cycle doesn't occur in any given set of votes, it can appear through iterated elections with strategic voters with cardinal ratings. Suppose that "x" is the fraction of voters who prefer A over B and that "y" is the fraction of voters who prefer B over C. It has been shown that the fraction "z" of voters who prefer A over C is always at least ("x + y" – 1). Since the paradox (a majority preferring C over A) requires "z"  C> B> A). We show that, for odd formula_2, formula_8 where formula_9 which makes one need to know only the joint distribution of formula_3 and formula_4. If we put formula_12, we show the relation which makes it possible to compute this distribution by recurrence: formula_13. The following results are then obtained:  The sequence seems to be tending towards a finite limit. Using the Central-Limit Theorem, we show that formula_14 tends to formula_15 where formula_16 is a variable following a Cauchy distribution, which gives formula_17 (constant ). The asymptotic probability of encountering the Condorcet paradox is therefore formula_18 which gives the value 8.77%. Some results for the case of more than three objects have been calculated. 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. Many attempts have been made at finding empirical examples of the paradox. 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).. While examples seem to occur occasionally in small settings (e.g., parliaments) very few examples have been found in larger groups, although some have been identified. When a Condorcet method is used to determine an election, the voting paradox of cyclical societal preferences implies that the election has no Condorcet winner: no candidate who can win a one-on-one election against each other candidate.