Finding sharper distinctions for conditions of transitivity of the majority method Original Research Article

This paper compares some conditions of transitivity for the majority method. We use the concept of polydiversity: instead of counting the number of different possible preference rankings allowed in a profile, we compare the number of different profiles satisfying a condition. Thus, we can evaluate the compared restrictiveness of Blackʹs condition and single-peakedness, and for three alternatives, we show that the two preceding conditions are three times more restrictive than Wardʹs condition. The polydiversity equations also show how fast the probability that a random profile satisfies these conditions approaches zero.