A MajorityValue is a list of grades made from the successive lower middlemosts of a Merit, i.e. from the most consensual majorityGrade to the least.

For using less resources and generalizing to non-integral Shares, this MajorityValue is actually encoded as an Abbreviated Majority Value, instead of a big list of grades.

A centered middle of a Merit. Needed to handle the Fractional capabilities of a Share.

By construction in majorityValue, lowGrade is always lower or equal to highGrade.

The majorityValue is the list of the Middles of the Merit of a choice, from the most consensual to the least.

The majorityGrade is the lower middlemost (also known as median by experts) of the grades given to a choice by the Judges.

It is the highest grade approved by an absolute majority of the Judges: more than 50% of the Judges give the choice at least a grade of majorityGrade, but every grade lower than majorityGrade is rejected by an absolute majority Thus the majorityGrade of a choice is the final grade wished by the majority.

The majorityGrade is necessarily a word that belongs to grades, and it has an absolute meaning.

When the number of Judges is even, there is a middle-interval (which can, of course, be reduced to a single grade if the two middle grades are the same), then the majorityGrade is the lowest grade of the middle-interval (the “lower middlemost” when there are two in the middle), which is the only one which respects consensus: any other choice whose grades are all within this middle-interval, has a majorityGrade which is greater or equal to this lower middlemost.

The majorityRanking ranks all the choices on the basis of their grades.

Choice A ranks higher than choice B in the majorityRanking if and only if A’s majorityValue is lexicographically above B’s. There can be no tie unless two choices have precisely the same majorityValues.

Expand a MajorityValue such that each grade has a Share of '1'.

WARNING: the resulting list of grades may have a different length than the list of grades used to build the Merit.

normalizeMajorityValue m multiply all Shares by their least common denominator to get integral Shares.