The likelihood of single-peaked preferences under classic and new probability distribution assumptions

The paper offers new results about the probabilities of single-peaked preference profiles according to the impartial culture, impartial anonymous culture, impartial anonymous neutral culture, uniform culture, dual culture, and maximal culture assumptions. Two new probabilistic assumptions are studied. The uniform plurality culture assumption developed in the paper preserves uniformly distributed plurality votes, and it is easier than other culture assumptions. The case of abstention of voters is discussed.