Market Psychology

You start 60% sure of a bullish thesis and then meet six pieces of evidence: three for it and three just as strong against. Weighed fairly they cancel, and you should end where you began: 60%. Give the contrary evidence half its weight and the same pile leaves you at 73%. Five rounds of the same balanced news later you are 97% sure — certainty built entirely from the filter, not from the evidence.

• Not every strong prior is a bias. Discounting a weak or unreliable source is correct; the bias is discounting evidence because it disagrees.
• Searching for confirming cases can be an efficient test when the hypothesis is rare (Klayman & Ha 1987); the trouble is treating the search as proof.
• Knowing about the bias does not remove it. A written “what would make me wrong” before the trade works better than good intentions.

prior = 0.60                                    # how sure you are the bullish thesis is right
lr = [1.5, 1.5, 1.5, 1 / 1.5, 1 / 1.5, 1 / 1.5]  # three pieces of evidence for it, three equally strong against

def update(p, lrs, w_against=1.0):               # Bayes in log-odds; w_against < 1 discounts contrary evidence
    logit = np.log(p / (1 - p))
    for x in lrs:
        logit += np.log(x) * (w_against if x < 1 else 1)
    return 1 / (1 + np.exp(-logit))

fair = update(prior, lr)
biased = update(prior, lr, w_against=0.5)
biased_after_5_rounds = update(prior, lr * 5, w_against=0.5)

Assumes import numpy as np and import pandas as pd. Each snippet carries its own example numbers; the comments say which are made up.