Absolute qualified majoritarianism: How does the threshold matter?

We study absolute qualified majority rules in a setting with more than two alternatives. We show that given two qualified majority rules, if transitivity is desired for the societal outcome and if the thresholds of one of these rules are at least as high as the other’s for any pair of alternatives, then at each preference profile the rule with higher thresholds results in a coarser social ranking. Hence all absolute qualified majority rules can be expressed as specific coarsenings of the simple majority rule.