politisk-datalogi.py

"""
Suppose the better places a bet of one dollar and wins x dollars with probability p;
with probability 1-p the bookmaker keeps the one dollar.

The expected profit for the bookmaker is (1-p) - x p
= 1 - p (1 + x)

If we want the profit greater than zero, the odds x must be

1 - p (1 + x) > 0
1 > p (1 + x)
1 / p > (1 + x)
x < (1/p) - 1

The probability, given the odds x, must be

1 - p (1 + x) > 0
1 > p (1 + x)
p < 1 / (1 + x)
"""

# From https://da.wikipedia.org/wiki/Partibogstav
names = dict(
    A="Socialdemokratiet",
    B="Radikale Venstre",
    C="Det Konservative Folkeparti",
    D="Nye Borgerlige",
    E="Klaus Riskær Pedersen",
    F="Socialistisk Folkeparti",
    I="Liberal Alliance",
    K="Kristendemokraterne,",
    O="Dansk Folkeparti",
    P="Stram Kurs",
    V="Venstre",
    Ø="Enhedslisten",
    Å="Alternativet",
)

# Source: Danske Spil, retrieved 2019-05-07
# https://danskespil.dk/oddset/politik/danmark/dansk-politik/n%C3%A6ste-regering-efter-folketingsvalget-1278243.html
odds = dict(
    A=1.55,
    AF=8.00,
    AFB=13.00,
    AB=15.00,
    VC=20.00,
    VCO=22.00,
    AO=22.00,
    VO=28.00,
    VLC=28.00,
    V=28.00,
    VA=28.00,
    AFØ=40.00,
    AFØBÅ=40.00,
    VOCID=75.00,
)

result = []

for letter, name in sorted(names.items()):
    is_in = []
    is_out = []
    for combination, x in odds.items():
        if letter in combination:
            is_in.append(x)
        else:
            is_out.append(x)

    in_prob = sum(1 / (1 + x) for x in is_in)
    out_prob = sum(1 / (1 + x) for x in is_out)
    sum_of_odds = sum(is_in)
    result.append((in_prob, out_prob, letter, sum_of_odds))

result.sort(reverse=True)

for in_prob, out_prob, letter, sum_of_odds in result:
    print("%s inde: %.2f%%" % (letter, in_prob * 100))

assert result == [
    (0.7639380525799134, 0.2077034790875239, "A", 167.55),
    (0.24218623770821357, 0.7294552939592238, "V", 229.0),
    (0.23132017034456057, 0.7403213613228766, "F", 101.0),
    (0.15831881533101044, 0.8133227163364268, "B", 68.0),
    (0.13873796184614456, 0.8329035698212927, "C", 145.0),
    (0.1345971750966622, 0.8370443565707751, "O", 147.0),
    (0.04878048780487805, 0.9228610438625592, "Ø", 80.0),
    (0.024390243902439025, 0.9472512877649982, "Å", 40.0),
    (0.013157894736842105, 0.9584836369305951, "I", 75.0),
    (0.013157894736842105, 0.9584836369305951, "D", 75.0),
    (0, 0.9716415316674373, "P", 0),
    (0, 0.9716415316674373, "K", 0),
    (0, 0.9716415316674373, "E", 0),
]