Majority.Rank

Convenient type aliases

type JS = Integer

Number of judges.

type GS = Integer

Number of grades.

type Rank = Integer

Rank of a MajorityValue.

Type Median

newtype Median

A median. First G (lower median) is lower or equal to the second G (higher median).

Constructors

Median (G, G)

Instances

Eq Median

Defined in Majority.Rank

Methods

(==) :: Median -> Median -> Bool

(/=) :: Median -> Median -> Bool

Show Median

Defined in Majority.Rank

Methods

showsPrec :: Int -> Median -> ShowS

show :: Median -> String

showList :: [Median] -> ShowS

median :: G -> G -> Median

Median constructor enforcing its invariant.

Ranking and unranking MajorityValues

rankOfMajorityValue :: GS -> MajorityValue (Ranked grade) -> Rank

(rankOfMajorityValue gs mv) returns the number of possible MajorityValues lower than given mv.

rankOfMajorityValue gs . majorityValueOfRank js gs
 <$> [0..lastRank js gs] == [0..lastRank js gs]

majorityValueOfRank :: JS -> GS -> Rank -> MajorityValue (Ranked ())

The inverse of rankOfMajorityValue.

majorityValueOfRank js gs . rankOfMajorityValue gs == id

positionOfMajorityValue :: GS -> MajorityValue (Ranked grade) -> Rational

Counting Merits

countMerits :: JS -> GS -> Integer

(countMerits js gs) returns the number of possible Merits of size js using grades gs. That is the number of ways to divide a segment of length js into at most gs segments whose size is between '0' and js.

The formula is: (js+gs-1)·(js+gs-2)·…·(js+1)·js / (gs-1)·(gs-2)·…·2·1 which is: (js+gs-1)nCk(gs-1)

lastRank :: JS -> GS -> Rank

(lastRank js gs) returns the rank of the MajorityValue composed of js times the highest grade of gs.

lastRank js gs == countMerits js gs - 1.

Counting Medians

countMedian :: JS -> GS -> Median -> Integer

(countMedian js gs (Median (l,h))) returns the number of possible Merits of length js using grades gs, which have (l,h) as lower and upper median grades. This is done by multiplying together the countMerits to the left of l and the countMerits to the right of h.

countMediansBefore :: JS -> GS -> G -> Median -> Integer

(countMediansBefore js gs previousHigh (Median (low,high))) returns the number of possible Merits with js judges and gs grades, whose Median (l,h) is such that ((l,h) < (low, high)) and (previousHigh <= h).

listMediansBefore :: JS -> GS -> G -> Median -> [Median]

(listMediansBefore js gs previousHigh (Median (low,high))) returns the Medians of possible Merits with js judges and gs grades with a Median strictly lower than (low,high).

probaMedian :: JS -> GS -> [Rational]

(probaMedian js gs) compute the probability of each grade to be a MajorityGrade given js judges and gs grades.

Utils

nCk :: Integral i => i -> i -> i infix 7

(nCk n k) returns the binomial coefficient of n and k, that is number of combinations of size k from a set of size n.

Computed using the formula: nCk n (k+1) == nCk n (k-1) * (n-k+1) / k