Israeli Parliamentary Coalitions

IsraeliParliamentaryCoalitions.csx

// https://ayende.com/blog/190275-C/giving-a-job-candidate-a-hard-problem

static var parliment = new Dictionary<string, (int Seats, int Index)>
{
    ["Likud"] = (36, 0),
    ["KahulLaval"] = (33, 1),
    ["JointList"] = (15, 2),
    ["Shas"] = (9, 3),
    ["YahadutHatora"] = (7, 4),
    ["IsrealBeitenu"] = (7, 5),
    ["AvodaGesherMeretz"] = (7, 6),
    ["Yemina"] = (6, 7)
};

static var likes = new[,]
{
    // likud,     kahul,    joint,     shas,    yahdut,    beitenu, avoda,    yemina
    {   1.0,    -0.5,   -1.0,   0.95,   0.95,   -0.2,   -0.8,   0.95}, // likud
    {  -0.9,     1.0,   -0.6,   -0.5,   -0.5,    0.5,    0.8,   -0.2}, // kahul
    {  -0.9,    -0.3,    1.0,   -0.6,   -0.6,   -1.0,   -0.2,   -1.0}, // joint
    {  0.96,    -0.7,   -0.6,    1.0,    0.9,   -1.0,   -0.7,    0.8}, // shas
    {  0.97,    -0.6,   -0.6,   0.92,    1.0,   -1.0,   -0.6,    0.7}, // yahadut
    {  -0.4,    -0.1,   -1.0,  -0.99,  -0.99,    1.0,   -0.6,    0.1}, // beitenu
    { -0.95,    0.98,    0.3,  -0.89,  -0.89,   -0.01,   1.0,  -0.75}, // avoda
    { 0.999,   -0.92,   -1.0,   0.86,   0.85,   -0.3,   -0.4,    1.0}, // yemina
};

static var target = Math.Ceiling((parliment.Sum(party => party.Value.Seats) + 1) / 2.0); // 61

Coalition.GetAllCoalitions()
    .Where(coalition => coalition.IsSufficient && coalition.IsLikely)
    .OrderByDescending(coalition => coalition.Likelyhood)
    .Select(coalition => coalition.ToString())
    .Dump();

public class Coalition
{
    public Coalition(IReadOnlyCollection<KeyValuePair<string, (int Seats, int Index)>> members)
    {
        this.Members = members ?? throw new ArgumentNullException(nameof(members));
        
        if (this.Members.Count == 0)
        {
            throw new ArgumentOutOfRangeException(nameof(members), "There must be at least 1 member of a coalition.");
        }
    }

    private IReadOnlyCollection<KeyValuePair<string, (int Seats, int Index)>> Members { get; }
    
    public IReadOnlyCollection<string> MemberNames => this.Members.Select(party => party.Key).ToArray();
    
    public int Seats => this.Members.Sum(party => party.Value.Seats);
    
    public bool IsSufficient => Seats >= target;
    
    private double DenormalizedLikelyhood => this.Members.SelectMany(party1 => this.Members.Select(party2 => new {party1, party2}))
        .Sum(relationship => likes[relationship.party1.Value.Index, relationship.party2.Value.Index]);
        
    public double Likelyhood => this.Members.Count == 1
        ? DenormalizedLikelyhood
        : 2 * (DenormalizedLikelyhood - this.Members.Count) / (this.Members.Count * (this.Members.Count - 1));
        
    public bool IsLikely => this.Likelyhood > 0.0;

    public override string ToString()
    {
        return string.Format("Seats: {0}  Likelyhood: {1:0.0000}  Members: {2}", this.Seats, this.Likelyhood, string.Join(", ", this.MemberNames));
    }
      
    public static IEnumerable<Coalition> GetAllCoalitions()
    {
        var combo = new bool[parliment.Count];
        
        // Ignore all false...
        
        while (GetNextCombo(ref combo, combo.Length - 1))
        {
            yield return new Coalition(parliment.Where(party => combo[party.Value.Index]).ToArray());
        }
    }
    
    private static bool GetNextCombo(ref bool[] combo, int index)
    {
        if (index < 0) return false;
    
        if (!combo[index])
        {
            return combo[index] = true;
        }
        
        combo[index] = false;
        return GetNextCombo(ref combo, index - 1);
    }
}

/*
Seats: 65  Likelyhood: 0.6029  Members: Likud, Shas, YahadutHatora, IsrealBeitenu, Yemina
Seats: 91  Likelyhood: 0.5989  Members: Likud, KahulLaval, Shas, YahadutHatora, Yemina
Seats: 65  Likelyhood: 0.4829  Members: Likud, Shas, YahadutHatora, AvodaGesherMeretz, Yemina
Seats: 73  Likelyhood: 0.4509  Members: Likud, JointList, Shas, YahadutHatora, Yemina
Seats: 85  Likelyhood: 0.3250  Members: Likud, KahulLaval, Shas, YahadutHatora
Seats: 82  Likelyhood: 0.2998  Members: Likud, KahulLaval, YahadutHatora, Yemina
Seats: 84  Likelyhood: 0.2998  Members: Likud, KahulLaval, Shas, Yemina
Seats: 67  Likelyhood: 0.2250  Members: Likud, JointList, Shas, YahadutHatora
Seats: 98  Likelyhood: 0.1193  Members: Likud, KahulLaval, Shas, YahadutHatora, AvodaGesherMeretz, Yemina
Seats: 98  Likelyhood: 0.1073  Members: Likud, KahulLaval, Shas, YahadutHatora, IsrealBeitenu, Yemina
Seats: 66  Likelyhood: 0.0698  Members: Likud, JointList, Shas, Yemina
Seats: 64  Likelyhood: 0.0532  Members: Likud, JointList, YahadutHatora, Yemina
*/