ElectoralMethods.scala

import scala.collection.SortedSet

trait Method {
	// options to choose from
	type Option
	// a choice made on the ballot
	type Choice
  	// a completed ballot
	type Ballot
	// the voting rule (algorithm)
	type Rule <: Seq[RuleIn] => RuleOut
	// the election result
	type Result	

	type ConverterIn <: Ballot => RuleIn	
	type RuleIn
	type RuleOut		
	type ConverterOut <: RuleOut => Result
	type Id[X] = X => X
}

trait Rules { self: Method =>
	type Plurality = Seq[Set[Choice]] => SortedSet[Option]
	type Stv = Seq[SortedSet[Choice]] => Set[Option]
	type Irv = Seq[SortedSet[Choice]] => Option
	type Borda = Seq[SortedSet[Choice]] => SortedSet[Option]
	type PairwiseBeta = Seq[Set[Choice]] => SortedSet[Option]
	type Score = Seq[Set[Choice]] => SortedSet[Option]
	type Copeland = Seq[SortedSet[Choice]] => SortedSet[Option]
}

trait SingleWinner extends Method with Rules {
	type RuleOut =  SortedSet[Option]
	type ConverterOut = SortedSet[Option] => Option
	type Result = Option
}

trait SingleWinnerId extends Method with Rules {
	type RuleOut =  Option
	type ConverterOut = Id[Option]
	type Result = Option
}

trait MultipleWinner extends Method with Rules {
	type RuleOut = SortedSet[Option]
	type ConverterOut = SortedSet[Option] => Set[Option]
	type Result = Set[Option]
}

trait MultipleWinnerId extends Method with Rules {
	type RuleOut = Set[Option]
	type ConverterOut = Id[Set[Option]]
	type Result = Set[Option]
}

trait FirstPastThePost extends SingleWinner {
	type Choice = Option
	type Ballot = Choice
	type Rule = Plurality	

	type ConverterIn = Choice => Set[Choice]	
	type RuleIn = Set[Choice]
}

trait Approval extends SingleWinner {
	type Choice = Option
	type Ballot = Set[Choice]
	type Rule = Plurality	
	
	type ConverterIn = Id[Set[Choice]]
	type RuleIn = Set[Choice]
}

trait IRV extends SingleWinnerId {
	type Choice = Option
	type Ballot = SortedSet[Choice]
	type Rule = Irv
	
	type ConverterIn = Id[SortedSet[Choice]]
	type RuleIn = SortedSet[Choice]
}

trait PluralityAtLarge extends MultipleWinner {
	type Choice = Option
	type Ballot = Set[Choice]
	type Rule = Plurality	
	
	type ConverterIn = Id[Set[Choice]]
	type RuleIn = Set[Choice]
}

trait SNTV extends MultipleWinner {
	type Choice = Option
	type Ballot = Choice
	type Rule = Plurality	

	type ConverterIn = Choice => Set[Choice]	
	type RuleIn = Set[Choice]
}

trait STV extends MultipleWinnerId {
	type Choice = Option
	type Ballot = SortedSet[Choice]
	type Rule = Stv
	
	type ConverterIn = Id[SortedSet[Choice]]
	type RuleIn = SortedSet[Choice]
}

trait Pairwise extends MultipleWinner {
	type Choice = (Option, Option)
	type Ballot = Set[Choice]
	type Rule = PairwiseBeta
	
	type ConverterIn = Id[Set[Choice]]
	type RuleIn = Set[Choice]
}

trait BordaCount extends SingleWinner {
	type Choice = Option
	type Ballot = SortedSet[Choice]
	type Rule = Borda
	
	type ConverterIn = Id[SortedSet[Choice]]
	type RuleIn = SortedSet[Choice]
}

trait Range extends MultipleWinner {
	type Choice = (Option, Int)
	type Ballot = Set[Choice]
	type Rule = Score
	
	type ConverterIn = Id[Set[Choice]]
	type RuleIn = Set[Choice]
}

trait Cumulative extends MultipleWinner {
	type Choice = (Option, Int)
	type Ballot = Set[Choice]
	type Rule = Score
	
	type ConverterIn = Id[Set[Choice]]
	type RuleIn = Set[Choice]
}

trait CondorcetCopeland extends SingleWinner {
	type Choice = Option
	type Ballot = SortedSet[Choice]
	type Rule = Copeland
	
	type ConverterIn = Id[SortedSet[Choice]]
	type RuleIn = SortedSet[Choice]
}