private static (List <(int candidate, ulong?preferred)> Candidates, ulong Bogeyman) GetApprovedCandidates(CoalitionBeatMatrix beatMatrix, RankedBallot ballot)
{
var candidates = new List <(int candidate, ulong?preferred)>();
var ranking = ballot.Ranking;
// Approve of the each candidate `c` which is a first choice.
foreach (var c in ranking[0])
{
candidates.Add((c, null));
}
// With fewer than three ranks, no bogeymen can chance one's preferences.
if (ranking.Count < 3)
{
return(candidates, 0ul);
}
// Then, for each candidate `b` (the "bogeyman") ranked third or below,
// compute the smallest "coalition" of candidates `c` which can beat each potential "bogeyman" `b`,
// or includes all candidates one likes better than `b`, whichever comes first.
// Approve of each member of the smallest coalition to beat all bogeymen.
var coalition = GetCoalition(ranking[0]);
var potentialBogeymen = ranking
.Skip(2)
.SelectMany(b => b)
.Where(b => beatMatrix.Beats(coalition, b) != true)
.ToList();
if (!potentialBogeymen.Any())
{
return(candidates, 0ul);
}
foreach (var tier in ranking.Skip(1).Take(ranking.Count - 2))
{
var greaterBogeymen = potentialBogeymen.Where(b => !tier.Contains(b)).ToList();
// If this tier contains all the bogeymen, the previous tier is where our approval stops.
if (!greaterBogeymen.Any())
{
break;
}
// Otherwise, enlist the help of the lesser bogeymen to beat the greater bogeymen.
foreach (var c in tier)
{
candidates.Add((c, coalition));
}
coalition |= GetCoalition(tier);
var remainingBogeymen = greaterBogeymen
.Where(b => beatMatrix.Beats(coalition, b))
.ToList();
// Huzzah! We have beaten all the bogeymen!
if (!remainingBogeymen.Any())
{
break;
}
// Otherwise, check the next teir for potential coalition-mates.
potentialBogeymen = remainingBogeymen;
}
return(candidates, GetCoalition(potentialBogeymen));
}
public override ElectionResults GetElectionResults(CandidateComparerCollection <RankedBallot> ballots)
{
var approvalCount = new int[ballots.CandidateCount];
var firstChoices = new int[ballots.CandidateCount];
var compromises = new CountedList <(int Compromise, ulong Preferred, ulong Bogeymen)>();
// First, compute "coalition" beat matrix
var beatMatrix = new CoalitionBeatMatrix(ballots);
// Then, use it to determine which candidates each ballot approves of.
foreach (var(ballot, count) in ballots.Comparers)
{
var(approvedCandidates, bogeymen) = GetApprovedCandidates(beatMatrix, ballot);
foreach (var(candidate, preferred) in approvedCandidates)
{
approvalCount[candidate] += count;
if (preferred.HasValue)
{
compromises.Add((candidate, preferred.Value, bogeymen), count);
}
else
{
firstChoices[candidate] += count;
}
}
}
var results = new ElectionResults(approvalCount.IndexRanking());
results.AddHeading("Votes");
results.AddTable(
approvalCount.IndexOrderByDescending()
.Select(c => new ElectionResults.Value[] {
(ElectionResults.Candidate)c,
approvalCount[c],
firstChoices[c],
approvalCount[c] - firstChoices[c],
}),
"Total",
"First",
"Comp.");
results.AddHeading("Compromises");
results.AddTable(
compromises.Select(c => new ElectionResults.Value[] {
(ElectionResults.Candidate)c.Item.Compromise,
c.Item.Preferred,
c.Item.Bogeymen,
c.Count
}),
"Comp.",
"Pref.",
"Bogey",
"Count"
);
beatMatrix.AddDetails(results);
return(results);
}
