Confirmation Bias

Confirmation Bias

Confirmation bias is the systematic tendency to over-weight prior beliefs when updating from new evidence — the parametric mirror image of base-rate neglect. In the Rabin (1998) template
$\frac{\pi (A\mid S)}{\pi (B\mid S)}={\left(\frac{p(S\mid A)}{p(S\mid B)}\right)}^c{\left(\frac{p(A)}{p(B)}\right)}^d,$
confirmation bias is the case $d>1$ — the prior odds enter the posterior with more than full Bayesian weight. Bayes’ rule is $c=d=1$. Operationally, the confirmation-biased investor updates more on signals that agree with her existing view than on signals that disagree with it, even when the two signals carry equal Bayesian information content. The bias produces belief polarization: two agents with opposite priors who observe the same body of evidence become more confident in their original opposing positions, not less.

A close relative is motivated reasoning: updating more on news that is personally favorable than on news that is personally unfavorable, even when the two carry equal Bayesian information content. Confirmation bias is about the prior view; motivated reasoning is about the self-interest. The two often coincide because people’s prior views and their self-interests are usually aligned, but they are conceptually distinct. Both push beliefs further from the data than Bayes’ rule allows.

Intuition

Bayes’ rule is symmetric: a signal that disconfirms the prior should move beliefs by the same magnitude (in log-odds space) as a signal that confirms it, provided both have the same likelihood ratio. Confirmation bias breaks this symmetry by asymmetrically weighting confirming versus disconfirming evidence. The behavioral mechanism is that agents subject confirming evidence to lighter scrutiny — accepting it at face value — and subject disconfirming evidence to heavier scrutiny — looking for methodological flaws, alternative interpretations, or reasons to discount it. The net effect is that prior beliefs receive disproportionate weight in the final posterior, which is exactly what $d>1$ encodes.

The most striking empirical demonstration is the belief polarization result of Lord, Ross & Lepper ($1979$). Two groups of subjects — one initially supportive of capital punishment, one initially opposed — read the same packet of mixed empirical studies on the deterrent effect of executions. Bayesian updating predicts the two groups should converge: both observe the same evidence, both should move toward a common posterior. The actual result was the opposite: each group reported being more confident in its original position after reading the mixed evidence, with the gap between the two groups widening rather than narrowing. The mechanism is that each side accepted the studies that confirmed its view and discounted the studies that disconfirmed it.

Properties

(Parametric Form) Confirmation bias is $d>1$ in the Rabin template.

In the Rabin (1998) deviation from Bayes’ rule, $d$ governs the weight on the prior odds. Bayes is $d=1$. Confirmation bias is $d>1$, with empirically estimated values typically between $1.2$ and $2.5$ depending on the domain and the strength of the prior commitment. The parameter $c$ on the signal is left at $1$, meaning the confirmation-biased investor still uses the new evidence correctly in the symmetric sense — she just over-weights the prior relative to the signal. This makes confirmation bias a strict mirror of base-rate neglect along the prior-weight axis.

(Belief Polarization) Same evidence, opposite movements.

Confirmation bias predicts that two agents with opposite priors who observe the same mixed evidence will end up further apart, not closer. Lord, Ross & Lepper ($1979$) document exactly this in the capital-punishment study: pro-death-penalty subjects became more pro after reading mixed studies, and anti subjects became more anti. The finding has been replicated across many domains — vaccine attitudes, climate change, political endorsements, candidate evaluations. The implication for finance is that two analysts with opposite priors about a stock can observe the same earnings release and move their target prices in opposite directions, both citing the same data.

(Asymmetric Information Processing) Confirming signals get full weight; disconfirming get discounted.

Operationally, confirmation bias arises because subjects evaluate confirming and disconfirming evidence by different standards. Confirming evidence is accepted at face value: “this study supports my view, so its methodology is sound.” Disconfirming evidence is subjected to scrutiny: “this study contradicts my view, so I’ll look for the flaw.” The differential scrutiny is what produces the asymmetric weighting captured by $d>1$. When the experiment removes the opportunity to scrutinize differentially — by forcing subjects to write down their evaluation of each piece of evidence in real time — the polarization shrinks but does not disappear (Munro & Ditto, $1997$).

(Motivated Reasoning Distinguished) Self-interest is a separate driver.

Motivated reasoning is the closely related tendency to update more on news that is personally favorable than on news that is personally unfavorable. Eil & Rao ($2011$) and Möbius, Niederle, Niehaus & Rosenblat ($2022$) document the pattern in laboratory experiments where subjects receive feedback about their own performance on intelligence or attractiveness tests: positive feedback updates beliefs about own ability much more than equally informative negative feedback. The conceptual difference from confirmation bias is that the asymmetry runs along the self-interest axis rather than the prior-belief axis. In practice the two coincide, because people’s priors about themselves and their self-interest are usually aligned, but the distinction matters for asset pricing: an analyst with a buy rating exhibits both biases simultaneously when she discounts a negative earnings surprise.

(Asset-Pricing Implications) Slow downgrades, sticky theses, momentum amplification.

In financial markets, confirmation bias predicts that analysts who have publicly committed to a thesis will be slow to revise it in light of disconfirming evidence — analysts who issued buy ratings should downgrade more slowly than the data warrant after a negative earnings surprise. Empirical evidence broadly supports this pattern: McNichols & O’Brien ($1997$) document that analysts who issue sell ratings are far more likely to drop coverage than to revise to buy, suggesting that the cost of admitting they were wrong is asymmetric. The bias also amplifies momentum by causing investors to stick with winning trades past the point where the evidence supports them, and contributes to overconfidence by allowing investors to selectively remember the evidence that confirmed their successful calls.

(Tension with Conservatism) Both can coexist within one agent.

Confirmation bias makes the prior sticky; conservatism makes new evidence absorbed too slowly. The two biases are not contradictory — both produce sticky beliefs but through different parametric channels ($d>1$ versus $c<1$). An investor exhibiting both biases simultaneously will under-react to new evidence and especially under-react when that evidence runs against her prior. The combined effect is much stronger sluggishness than either bias produces alone, and is consistent with the slow incorporation of bad news into stock prices documented in the post-earnings-announcement-drift literature.

Examples

Belief polarization in the Lord-Ross-Lepper (1979) capital punishment study

Subjects were sorted into “proponents” and “opponents” of capital punishment based on a pre-test. Both groups then read the same packet containing two studies: one that found capital punishment had a deterrent effect on murder rates, and one that found it had no such effect. After reading both studies, subjects rated their attitudes again. Bayesian updating predicts both groups should weaken their initial views — the evidence is mixed, so the posterior should be moderated. The actual result: proponents reported being more convinced of capital punishment’s deterrent effect, and opponents reported being more convinced of its lack of effect. The gap between the two groups widened by approximately one full point on a seven-point scale. Free-response data showed subjects accepted the study that supported their view at face value and aggressively criticized the methodology of the study that contradicted it.

Numerical update under $d=2$

An investor starts with prior odds $3:1$ that a firm is in a “high earnings” state versus a “low earnings” state — she believes the firm is probably high-earnings. She observes a single positive earnings surprise with likelihood ratio $\frac{p(S\mid \text{high})}{p(S\mid \text{low})}=2$. The Bayesian posterior odds are $3\cdot 2=6:1$, so $\mathrm{Pr}(\text{high}\mid S)\approx 0.86$. The confirmation-biased investor with $d=2$ computes posterior odds $2\cdot 3^2=18:1$, so $\mathrm{Pr}(\text{high}\mid S)\approx 0.95$. Now imagine the surprise had been negative, with likelihood ratio $\frac{p(S\mid \text{high})}{p(S\mid \text{low})}=0.5$. Bayesian posterior: $3\cdot 0.5=1.5:1$, $\mathrm{Pr}(\text{high})\approx 0.60$. Confirmation-biased posterior: $0.5\cdot 9=4.5:1$, $\mathrm{Pr}(\text{high})\approx 0.82$. The Bayesian moves $26$ points; the confirmation-biased investor moves only $13$. Disconfirming evidence is absorbed at half the speed.

The intelligence-test feedback experiment (Eil & Rao, 2011)

Subjects take an IQ test and a beauty-rating test, then receive noisy but informative feedback about their relative performance. Eil & Rao decompose the updating into two components: how much subjects move their posterior toward the good end after positive feedback, and how much they move it toward the bad end after negative feedback. The Bayesian benchmark predicts these two should be symmetric in log-odds space. The actual finding is that subjects update roughly $50\%$ more on positive feedback than on negative feedback of the same Bayesian magnitude. The asymmetry is sharpest for the dimensions subjects care about most (subjects who report caring about beauty show stronger asymmetry on the beauty test than the IQ test, and vice versa). This is motivated reasoning — the asymmetry is driven by self-interest, not by a pre-existing prior.

See Also

• 8.6. Belief-Based Biases — parent hub.
• 8.6.3. Base-Rate Neglect — sibling: the parametric mirror image ($d<1$ instead of $d>1$).
• 8.6.1. Conservatism — sibling: makes new signals sticky; combined with confirmation bias produces especially slow updating to disconfirming evidence.
• 8.6.2. Overreaction — the parametric mirror image on the signal axis ($c>1$).
• 8.7.4. Overconfidence and Trading Volume — closely related: confirmation bias contributes to overconfidence by selective recall of confirming successes.
• 8.8. Momentum — confirmation bias amplifies momentum by causing investors to stick with winning trades past the point evidence supports.