log_score_vox.py

# https://www.vox.com/future-perfect/2020/1/7/21051910/predictions-trump-brexit-recession-2019-2020

from math import log2 as lg

predictions = [
    # summary, probability, outcome
    ("Trump in office", 0.9, True),
    ("No Dem frontrunner", 0.6, False),
    ("No US recession", 0.8, True),
    ("No border wall", 0.95, True),
    ("US murders decline", 0.8, True),
    ("Brexit on schedule", 0.8, False),
    ("Modi Indian PM", 0.6, True),
    ("India and China no recession", 0.7, True),
    ("Malaria decline", 0.8, True),
    ("No new UBI countries", 0.9, True),
    ("More meat", 0.6, True),
    ("National fake meat", 0.95, False),
    ("No autotaxis", 0.9, True),
    ("New DeepMind app", 0.5, True),
    ("Warming", 0.6, True),
    ("More carbon", 0.8, True),
]

def score_prediction(probability, outcome):
    if outcome:
        return lg(probability)
    else:
        return lg(1 - probability)

logarithmic_score = sum(
    score_prediction(probability, outcome)
    for _, probability, outcome in predictions
)

# Trump in office -0.15200309344504997
# No Dem frontrunner -1.3219280948873622
# No US recession -0.3219280948873623
# No border wall -0.07400058144377693
# US murders decline -0.3219280948873623
# Brexit on schedule -2.3219280948873626
# Modi Indian PM -0.7369655941662062
# India and China no recession -0.5145731728297583
# Malaria decline -0.3219280948873623
# No new UBI countries -0.15200309344504997
# More meat -0.7369655941662062
# National fake meat -4.321928094887361
# No autotaxis -0.15200309344504997
# New DeepMind app -1.0
# Warming -0.7369655941662062
# More carbon -0.3219280948873623
# score: -13.508976481318838 bits
# compared to chance: -16 bits