Majority.Value

Type MajorityValue

newtype MajorityValue grade

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.

Constructors

MajorityValue

Fields

• unMajorityValue :: [Middle grade]

Instances

Eq grade => Eq (MajorityValue grade)

Defined in Majority.Value

Methods

(==) :: MajorityValue grade -> MajorityValue grade -> Bool

(/=) :: MajorityValue grade -> MajorityValue grade -> Bool

Ord grade => Ord (MajorityValue grade)

Defined in Majority.Value

Methods

compare :: MajorityValue grade -> MajorityValue grade -> Ordering

(<) :: MajorityValue grade -> MajorityValue grade -> Bool

(<=) :: MajorityValue grade -> MajorityValue grade -> Bool

(>) :: MajorityValue grade -> MajorityValue grade -> Bool

(>=) :: MajorityValue grade -> MajorityValue grade -> Bool

max :: MajorityValue grade -> MajorityValue grade -> MajorityValue grade

min :: MajorityValue grade -> MajorityValue grade -> MajorityValue grade

Show grade => Show (MajorityValue grade)

Defined in Majority.Value

Methods

showsPrec :: Int -> MajorityValue grade -> ShowS

show :: MajorityValue grade -> String

showList :: [MajorityValue grade] -> ShowS

Type Middle

data Middle grade

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.

Constructors

Middle

Fields

• middleShare :: Share

  the same Share of lowGrade and highGrade.

• lowGrade :: grade
• highGrade :: grade

Instances

Eq grade => Eq (Middle grade)

Defined in Majority.Value

Methods

(==) :: Middle grade -> Middle grade -> Bool

(/=) :: Middle grade -> Middle grade -> Bool

Ord grade => Ord (Middle grade)

Defined in Majority.Value

Methods

compare :: Middle grade -> Middle grade -> Ordering

(<) :: Middle grade -> Middle grade -> Bool

(<=) :: Middle grade -> Middle grade -> Bool

(>) :: Middle grade -> Middle grade -> Bool

(>=) :: Middle grade -> Middle grade -> Bool

max :: Middle grade -> Middle grade -> Middle grade

min :: Middle grade -> Middle grade -> Middle grade

Show grade => Show (Middle grade)

Defined in Majority.Value

Methods

showsPrec :: Int -> Middle grade -> ShowS

show :: Middle grade -> String

showList :: [Middle grade] -> ShowS

majorityValue :: Ord grade => Merit grade -> MajorityValue grade

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

majorityGrade :: Show grade => Ord grade => Merit grade -> Maybe grade

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.

Type MajorityRanking

type MajorityRanking choice grade = [(choice, MajorityValue grade)]

majorityValueByChoice :: Show grade => Ord grade => MeritByChoice choice grade -> HashMap choice (MajorityValue grade)

majorityRanking :: Show grade => Ord grade => MeritByChoice choice grade -> MajorityRanking choice grade

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.

Orphan instances

(Show grade, Ord grade) => Ord (Merit grade)

Methods

compare :: Merit grade -> Merit grade -> Ordering

(<) :: Merit grade -> Merit grade -> Bool

(<=) :: Merit grade -> Merit grade -> Bool

(>) :: Merit grade -> Merit grade -> Bool

(>=) :: Merit grade -> Merit grade -> Bool

max :: Merit grade -> Merit grade -> Merit grade

min :: Merit grade -> Merit grade -> Merit grade