private void ComputePCA(VotingRules.VotingSituation situation)
{
var channels = new double[situation.PartyCount][];
for (int i = 0; i < situation.PartyCount; i++)
{
channels[i] = new double[situation.Electorates.Count];
}
for (int i = 0; i < situation.Electorates.Count; i++)
{
var electorate = situation.Electorates[i];
int[] voteCounts = new int[situation.PartyCount]; // Number of votes for each party.
foreach (var index in electorate.VoteCounts)
{
var preferenceOrder = situation.GetPreferenceOrderByIndex(index);
voteCounts[preferenceOrder[0]] += electorate.VoteCounts[index];
}
for (int j = 0; j < situation.PartyCount; j++)
{
channels[j][i] = voteCounts[j];
}
}
var m = PrincipalComponentAnalysis.CalculateMatrix(channels, situation.Electorates.Count);
VarExplainedByComponentOfFirstPrefScores = m.VarianceExplainedByComponent;
}
public override List <int> CalculateResults(VotingSituation situation)
{
var baseRule = new ProportionalByDistrictVotingRule()
{
Apportionment = Apportionment
};
var newSituation = new VotingSituation();
newSituation.PartyCount = situation.PartyCount;
newSituation.Electorates.AddRange(situation.Electorates);
int LargeDistrictSize = TotalSeats - situation.Electorates.Count;
if (LargeDistrictSize > 0)
{
var newElectorate = new ElectorateVotes();
newElectorate.Magnitude = LargeDistrictSize;
newElectorate.VoteCounts = new HashMultiset <Int64>();
foreach (var smallDistrict in situation.Electorates)
{
foreach (var prefOrder in smallDistrict.VoteCounts)
{
newElectorate.VoteCounts[prefOrder] += smallDistrict.VoteCounts[prefOrder];
}
}
newSituation.Electorates.Add(newElectorate);
}
return(baseRule.CalculateResults(newSituation));
}
public static SimulationResults ComputeSimulation(VotingRules.VotingSituation situation, VotingRules.VotingRule rule)
{
var seatResults = rule.CalculateResults(situation);
// Calculate number of votes for each party.
int[] voteCounts = new int[seatResults.Count]; // Number of votes for each party.
return(ComputeSimulationScores(seatResults, situation.GetTotalVotesByParty().ToArray(), true, false, situation));
}
public List <int> CalculateResults(int partyCount, Multiset <Int64> votingSituation, List <List <int> > preferenceOrders)
{
// For legacy purposes.
var situation = new VotingSituation();
situation.PartyCount = partyCount;
situation.LegacyPreferenceOrders = preferenceOrders;
situation.Electorates.Add(new ElectorateVotes()
{
VoteCounts = votingSituation, Magnitude = 1
});
return(CalculateResults(situation));
}
public static VotingSituation FromInfo(IEnumerable <HashMultiset <Int64> > districts, int partyCount, int districtMagnitude)
{
var electorates = new List <ElectorateVotes>();
foreach (var d in districts)
{
var ev = new ElectorateVotes();
ev.Magnitude = districtMagnitude;
ev.VoteCounts = d;
electorates.Add(ev);
}
var result = new VotingSituation();
result.Electorates = electorates;
result.PartyCount = partyCount;
return(result);
}
public override List <int> CalculateResults(VotingSituation situation)
{
List <int> results = new int[situation.PartyCount].ToList();
foreach (var electorate in situation.Electorates)
{
if (electorate.Magnitude != 1)
{
throw new NotSupportedException();
}
int[] voteCounts = new int[situation.PartyCount]; // Number of votes for each party.
foreach (var index in electorate.VoteCounts)
{
var preferenceOrder = situation.GetPreferenceOrderByIndex(index);
voteCounts[preferenceOrder[0]] += electorate.VoteCounts[index];
}
int maxScore = 0;
int maxIndex = 0;
for (int i = 0; i < situation.PartyCount; i++)
{
if (voteCounts[i] > maxScore)
{
maxScore = voteCounts[i];
maxIndex = i;
}
}
results[maxIndex]++;
}
return(results);
}
public abstract List <int> CalculateResults(VotingSituation situation);
public override List <int> CalculateResults(VotingSituation situation)
{
List <int> results = new int[situation.PartyCount].ToList();
foreach (var electorate in situation.Electorates)
{
int electedRepresentitives = 0;
bool[] isExcluded = new bool[situation.PartyCount];
double quota = ((double)electorate.VoteCounts.Weight) / (1.0 + (double)electorate.Magnitude);
double[] preferenceWeights = new double[situation.PreferenceOrdersCount];
for (int i = 0; i < preferenceWeights.Length; i++)
{
preferenceWeights[i] = 1.0;
}
List <List <int> > preferenceOrders = new List <List <int> >();
foreach (var index in electorate.VoteCounts)
{
var preferenceOrder = situation.GetPreferenceOrderByIndex(index);
preferenceOrders.Add(preferenceOrder);
}
for (int round = 0; round < situation.PartyCount; round++)
{
int winnersThisRound = 0;
double[] votesByParty = new double[situation.PartyCount];
//int[] votedForIndex = new int[situation.PreferenceOrdersCount];
//Dictionary<Int64, int> votesForIndexLookup = new Dictionary<long, int>(situation.PreferenceOrdersCount);
List <int> votesForIndex = new List <int>();
//for (int i = 0; i < votedForIndex.Length; i++)
//{
// votedForIndex[i] = -1;
//}
int index2 = 0;
foreach (var index in electorate.VoteCounts)
{
var preferenceOrder = preferenceOrders[index2];
var firstNonExcludedPreference = (from x in preferenceOrder where !isExcluded[x] select x).First();
votesByParty[firstNonExcludedPreference] += preferenceWeights[index] * (double)electorate.VoteCounts[index];
//votedForIndex[index] = firstNonExcludedPreference;
//votesForIndexLookup.Add(index, firstNonExcludedPreference);
votesForIndex.Add(firstNonExcludedPreference);
index2++;
}
for (int i = 0; i < situation.PartyCount; i++)
{
if ((!isExcluded[i]) && votesByParty[i] > quota)
{
double multiplier = (votesByParty[i] - quota) / votesByParty[i];
double removedVotes = 0.0;
int prefOrderIndex = 0;
foreach (var prefOrder in electorate.VoteCounts)
{
if (votesForIndex[prefOrderIndex] == i)
{
removedVotes += preferenceWeights[prefOrder] * (double)electorate.VoteCounts[prefOrder];
preferenceWeights[prefOrder] *= multiplier;
}
prefOrderIndex++;
}
var removedVotes2 = removedVotes * (1.0 - multiplier);
//foreach (var x in votesForIndexLookup)
//{
// if (x.Value == i)
// {
// preferenceWeights[x.Key] *= multiplier;
// }
//}
//for (int j = 0; j < votedForIndex.Length; j++)
//{
// if (votedForIndex[j] == i)
// {
// preferenceWeights[i] *= multiplier;
// }
//}
// By commenting out this line, we allow for multiple seats per party per district.
//isExcluded[i] = true;
results[i]++;
winnersThisRound++;
electedRepresentitives++;
if (electedRepresentitives >= electorate.Magnitude)
{
goto endElectorate;
}
}
}
if (winnersThisRound == 0)
{
if ((from x in isExcluded where x == false select x).Count() + electedRepresentitives == electorate.Magnitude)
{
// The number of remaining candidates
// is equal to the number we want to elect
// we shouldn't ever get here
// but it seems like there is a problem with
// floating point math...
// TODO: Look into this.
throw new Exception();
for (int i = 0; i < results.Count; i++)
{
if (!isExcluded[i])
{
results[i]++;
}
}
goto endElectorate;
}
int lowestIndex = 0;
double lowestVotes = double.MaxValue;
for (int i = 0; i < situation.PartyCount; i++)
{
if (!isExcluded[i])
{
if (votesByParty[i] < lowestVotes)
{
lowestVotes = votesByParty[i];
lowestIndex = i;
}
}
}
isExcluded[lowestIndex] = true;
}
}
endElectorate:
continue;
}
return(results);
}
public override List <int> CalculateResults(VotingSituation situation)
{
List <int> results = new int[situation.PartyCount].ToList();
foreach (var electorate in situation.Electorates)
{
int[] voteCounts = new int[situation.PartyCount]; // Number of votes for each party.
foreach (var index in electorate.VoteCounts)
{
var preferenceOrder = situation.GetPreferenceOrderByIndex(index);
voteCounts[preferenceOrder[0]] += electorate.VoteCounts[index];
}
List <int> localResults = new int[situation.PartyCount].ToList();
var indicies = Enumerable.Range(0, situation.PartyCount).ToArray();
double[] voteCounts2 = (from x in voteCounts select Math.Abs((double)x + ((Rand.NextDouble() - 0.5) / (double)voteCounts.Sum()))).ToArray();
double standardDivisor = (double)voteCounts2.Sum() / (double)electorate.Magnitude;
var standardQuota = (from x in voteCounts2 select(double) x / standardDivisor).ToArray();
var lowerQuota = (from x in standardQuota select Math.Floor(x)).ToList();
var upperQuota = (from x in standardQuota select Math.Ceiling(x)).ToList();
var fractionalQuota = (from x in indicies select standardQuota[x] - lowerQuota[x]).ToList();
double MD = standardDivisor;
switch (Apportionment)
{
case ApportionmentMethod.StLague:
for (int i = 0; i < electorate.Magnitude; i++)
{
double maxQuot = 0.0;
int maxIndex = 0;
for (int j = 0; j < situation.PartyCount; j++)
{
var quot = ((double)voteCounts[j]) / (2.0 * ((double)localResults[j]) + 1.0);
if (quot > maxQuot)
{
maxQuot = quot;
maxIndex = j;
}
}
localResults[maxIndex]++;
}
break;
case ApportionmentMethod.Hill:
//while (true)
//{
// var candidateQuota = (from x in voteCounts2 select (double)x / MD).ToArray();
// var candidateQuotaLo = (from x in candidateQuota select (int)Math.Floor(x)).ToArray();
// var candidateQuotaHi = (from x in candidateQuota select (int)Math.Ceiling(x)).ToArray();
// var candidateQuotaGeo = (from i in indicies select Math.Sqrt((double)candidateQuotaLo[i] * (double)candidateQuotaHi[i])).ToArray();
// //var candidate = (from i in indicies select candidateQuota[i] > candidateQuotaGeo[i] ? (int)upperQuota[i] : (int)lowerQuota[i]).ToArray();
// var candidate = (from i in indicies select standardQuota[i] > candidateQuotaGeo[i] ? (int)upperQuota[i] : (int)lowerQuota[i]).ToArray();
// if (candidate.Sum() == electorate.Magnitude)
// {
// for (int i = 0; i < situation.PartyCount; i++)
// {
// localResults[i] += candidate[i];
// }
// }
// if (localResults.Sum() > 0)
// {
// break;
// }
// MD = standardDivisor * Rand.NextDouble();
//}
for (int i = 0; i < electorate.Magnitude; i++)
{
double maxQuot = 0.0;
int maxIndex = 0;
for (int j = 0; j < situation.PartyCount; j++)
{
var geoMean = Math.Sqrt(Math.Pow((double)localResults[j], 2.0) + Math.Pow((double)(localResults[j] + 1), 2.0));
var quot = ((double)voteCounts[j]) / geoMean;
if (quot > maxQuot)
{
maxQuot = quot;
maxIndex = j;
}
}
localResults[maxIndex]++;
}
break;
case ApportionmentMethod.Jefferson:
//while (localResults.Sum() == 0)
//{
// var candidateQuota = (from x in voteCounts2 select (int)Math.Floor((double)x / MD)).ToArray();
// if (candidateQuota.Sum() == electorate.Magnitude)
// {
// for (int i = 0; i < situation.PartyCount; i++)
// {
// localResults[i] += candidateQuota[i];
// }
// }
// MD = standardDivisor * Rand.NextDouble();
//}
var matrix = new double[situation.PartyCount, electorate.Magnitude];
List <double> mValues = new List <double>();
for (int i = 0; i < situation.PartyCount; i++)
{
var pcVotes = voteCounts2[i];
for (int j = 0; j < electorate.Magnitude; j++)
{
var value = ((double)pcVotes) / ((double)(j + 1));
matrix[i, j] = value;
mValues.Add(value);
}
}
//List<int> localResults2 = new List<int>();
var cutoff = (from x in mValues orderby x descending select x).Take(electorate.Magnitude).Min();
var cCount = (from x in mValues where x >= cutoff select x).Count();
for (int i = 0; i < situation.PartyCount; i++)
{
int seatCount = 0;
for (int j = 0; j < electorate.Magnitude; j++)
{
if (matrix[i, j] >= cutoff)
{
seatCount++;
}
}
localResults[i] = (seatCount);
}
break;
case ApportionmentMethod.Hamilton:
for (int i = 0; i < situation.PartyCount; i++)
{
localResults[i] = (int)lowerQuota[i];
}
foreach (var i in (from x in indicies orderby fractionalQuota[x] descending select x))
{
if (electorate.Magnitude > localResults.Sum())
{
localResults[i]++;
}
else
{
break;
}
}
break;
default:
throw new Exception();
}
// Copy district results to global results.
for (int i = 0; i < situation.PartyCount; i++)
{
results[i] += localResults[i];
}
}
return(results);
}
public static SimulationResults ComputeSimulationScores(List <int> results, int[] voteCounts, bool computeShapleyShubikPowerIndex, bool computeBanzhafPowerIndex, VotingRules.VotingSituation situation)
{
// Number of parties = results.Count
var simResult = new SimulationResults();
simResult.SeatResults = results;
simResult.Result = results;
// Index calculation
simResult.GallagherIndex = 0.0;
//simResult.EntropyIndex = 0.0;
//simResult.MaxDisprop = 0.0;
simResult.RaesIndex = 0.0;
simResult.LijphartIndex = 0.0;
simResult.LoosemoreHanbyIndex = 0.0;
simResult.EffectiveNumberOfParties = 0.0;
List <double> seatsProp = new List <double>();
List <double> proportionFirst = new List <double>();
List <double> deltas = new List <double>();
for (int i = 0; i < results.Count; i++)
{
double proportionSeats = (double)simResult.Result[i] / (double)simResult.Result.Sum();
double proportionFirstVotes = (double)voteCounts[i] / (double)voteCounts.Sum();
double delta = proportionSeats - proportionFirstVotes;
deltas.Add(delta);
proportionFirst.Add(proportionFirstVotes);
seatsProp.Add(proportionSeats);
simResult.GallagherIndex += Math.Pow(delta, 2.0);
var logDelta = Math.Log(delta);
if (double.IsNaN(logDelta))
{
logDelta = 0.0;
}
//simResult.EntropyIndex += delta * logDelta;
//simResult.MaxDisprop = Math.Max(simResult.MaxDisprop, delta);
simResult.RaesIndex += Math.Abs(delta);
simResult.LoosemoreHanbyIndex += Math.Abs(delta);
simResult.TrueDispropIndex += Math.Abs(delta);
simResult.LijphartIndex = Math.Max(simResult.LijphartIndex, delta);
simResult.EffectiveNumberOfParties += Math.Pow(proportionSeats, 2.0);
}
simResult.TrueDispropIndex = simResult.TrueDispropIndex / (double)simResult.Result.Sum();
simResult.GallagherIndex = Math.Sqrt(simResult.GallagherIndex / 2.0);
simResult.RaesIndex /= (double)results.Count;
simResult.LoosemoreHanbyIndex /= 2;
simResult.EffectiveNumberOfParties = 1.0 / simResult.EffectiveNumberOfParties;
// For debugging.
var seatsPropSum = seatsProp.Sum();
var propFirstSum = proportionFirst.Sum();
var deltaSum = deltas.Sum();
// Shapley Shubik power index
if (computeShapleyShubikPowerIndex)
{
simResult.ShapleyShubikPowerIndex = new double[results.Count];
// Naive method of computing Shapley Shubik.
/*
* double permutationCount = Program.Factorial(partyList.Count);
*
* foreach (var x in Program.Permute(partyList))
* {
* double powerTotal = 0.0;
*
* foreach (var y in x)
* {
* int index = partyList.IndexOf(y);
*
* powerTotal += seatsProp[index];
*
* if (powerTotal > 0.5)
* {
* simResult.ShapleyShubikPowerIndex[index] += (1.0 / permutationCount);
* break;
* }
* }
* }
*/
// Shapley Shubik power index (fast method).
// http://hercules.us.es/~mbilbao/pdffiles/generat.pdf
int n = results.Count;
for (int i = 0; i < n; i++)
{
double score = 0.0;
double multiplierSum = 0.0; // Should sum to one.
// Returns whether or not the given set of parties wins.
Func <List <int>, bool> v = (List <int> set) =>
{
return((from x in set select seatsProp[x]).Sum() > 0.5);
};
var combinations = DiscreteMath.Combinations(DiscreteMath.GetIntList(results.Count)).ToList();
combinations.Add(new List <int>()); // Our combinations function does not include the empty set.
foreach (var S in combinations)
{
if (S.Contains(i))
{
// S == i
continue;
}
var unionSet = S.ToList();
unionSet.Add(i);
int s = S.Count;
double multiplier;
//multiplier = Program.Factorial(s) * Program.Factorial(n - s - 1) / Program.Factorial(n);
double a = DiscreteMath.Factorial(s);
double b = DiscreteMath.Factorial(n - (s + 1));
double c = DiscreteMath.Factorial(n);
multiplier = (a * b) / c;
multiplierSum += multiplier;
if (v(unionSet) && (!v(S)))
{
score += multiplier;
}
}
// TODO: Assert that multiplierSum = 1
simResult.ShapleyShubikPowerIndex[i] = score;
}
}
// Banzhaf power index
if (computeBanzhafPowerIndex)
{
simResult.BanzhafPowerIndex = new double[results.Count];
int winningCombinationsCount = 0;
foreach (var x in DiscreteMath.Combinations(DiscreteMath.GetIntList(results.Count)))
{
double powerTotal = 0.0;
foreach (var y in x)
{
int index = y;
powerTotal += seatsProp[index];
}
if (powerTotal > 0.5)
{
winningCombinationsCount++;
foreach (var y in x)
{
int index = y;
double thisPartyPower = seatsProp[index];
if ((powerTotal - thisPartyPower) < 0.5)
{
// This is a critical voter.
simResult.BanzhafPowerIndex[index] += 1.0;
}
}
}
}
for (int i = 0; i < results.Count; i++)
{
simResult.BanzhafPowerIndex[i] /= (double)winningCombinationsCount;
}
}
if (situation != null)
{
simResult.ComputePCA(situation);
}
return(simResult);
}
public override List <int> CalculateResults(VotingSituation situation)
{
List <int> results = new int[situation.PartyCount].ToList();
var totalVotesByParty = situation.GetTotalVotesByParty();
var totalVotes = totalVotesByParty.Sum();
var thresholdLimit = ((double)totalVotes) * Threshold;
bool[] partyNotExcluded = new bool[situation.PartyCount];
for (int i = 0; i < situation.PartyCount; i++)
{
if ((situation.MMPElectorateSeatsOverride != null) && situation.MMPElectorateSeatsOverride[i] > 0)
{
partyNotExcluded[i] = true;
}
else if (totalVotesByParty[i] > thresholdLimit)
{
partyNotExcluded[i] = true;
}
else
{
partyNotExcluded[i] = false;
}
}
int totalVotesAfterRemoval = 0;
for (int i = 0; i < situation.PartyCount; i++)
{
if (partyNotExcluded[i])
{
totalVotesAfterRemoval += totalVotesByParty[i];
}
}
var seatTotal = situation.GetSeatTotal();
for (int i = 0; i < seatTotal; i++)
{
double maxQuot = 0.0;
int maxIndex = 0;
for (int j = 0; j < situation.PartyCount; j++)
{
if (partyNotExcluded[j])
{
var quot = ((double)totalVotesByParty[j]) / (2.0 * ((double)results[j]) + 1.0);
if (quot > maxQuot)
{
maxQuot = quot;
maxIndex = j;
}
}
}
results[maxIndex]++;
}
return(results);
}
