 A second way to argue that the above theoretical observations are robust is to find supporting empirical evidence. For instance, is there evidence that majority cycles have occurred in actual elections? While Riker (1982) offers a number of intriguing examples, the most comprehensive analysis of the empirical evidence for majority cycles is provided by Mackie (2003, especially Chapters 14 and 15). The conclusion is that, in striking contrast to the probabilistic analysis referenced above, majority cycles typically have not occurred in actual elections. However, this literature has not reached a consensus about this issue (cf. Riker 1982): The problem is that the available data typically does not include voters’ opinions about all pairwise comparison of candidates, which is needed to determine if there is a majority cycle. So, this information must be inferred (for example, by using statistical methods) from the given data. 