talent_vs_luck.py

"""
Implementation of https://arxiv.org/pdf/1802.07068.pdf by Aur Saraf
"""

import random

def histogram(items):
    counts = {}
    for item in items:
        if item not in counts:
            counts[item] = 0
        counts[item] += 1
    return counts
def by_key(hist):
    if None in hist:
        hist[0] = hist[None]
        del hist[None]
    total = sum(hist.values())
    for key in sorted(hist):
        print(f'{key} {hist[key]} {hist[key] / total:.0%}')

event_likelihood = 2 * 500 / (100 * 100) # they say 500 on 201 by 201, but also event diameter 2, and there are 2 kinds
p_l = .5
good_likelihood = event_likelihood * p_l
bad_likelihood = event_likelihood * (1 - p_l)
iterations = 80
for P in [.6, .7, .2, .9]:
    N = 1000
    wealth = [10] * N
    talent = [random.gauss(P, .1) for _ in wealth]
    good_luck = [0] * N
    bad_luck = [0] * N
    for i in range(iterations):
        for j in range(N):
            if good_likelihood >= random.random():
                if random.random() <= talent[j]:
                    wealth[j] *= 2
                good_luck[j] += 1
            if bad_likelihood >= random.random():
                wealth[j] /= 2
                bad_luck[j] += 1

    print('***', P)
    #by_key(histogram(wealth))
    sorted_wealth = list(wealth)
    sorted_wealth.sort()
    total = sum(sorted_wealth)
    rich = sum(sorted_wealth[800:])
    print(rich, total, f'{rich / total:.0%}')

    import numpy as np
    from sklearn.linear_model import LinearRegression
    from sklearn.preprocessing import normalize
    params = np.array([talent, good_luck, bad_luck])
    params = normalize(params, axis=1, norm='l2')
    params = params.transpose()
    reg = LinearRegression().fit(params, wealth)
    print(reg.coef_, reg.intercept_, reg.score(params, wealth))