Subjective Probability

Subjective probability is the assessment of how likely an event is to occur based on an individual’s personal judgment, experience, beliefs, or “gut feeling,” rather than on formal calculation or long-run frequency data.

How it works

It expresses a personal degree of belief in an outcome (e.g., “I think there’s a 30% chance this startup will succeed”).
It can change with new, sometimes anecdotal, information or simply with how a question is framed (e.g., choosing a single-point estimate vs. a range).
Different people often assign different subjective probabilities to the same event because they rely on different information, memories, interpretations, and biases.

How it differs from objective probability

Objective probability is derived from repeatable observations, statistical analysis, or well-defined models (e.g., a fair coin has a 50% chance of landing heads).
Subjective probability is used when historical data are limited, models are unreliable, or expert judgment is necessary.
While objective probabilities aim for reproducibility, subjective probabilities reflect individual perspective and are less consistent across observers.

Examples

Sports fandom: Before a season begins, fans might state a percentage chance their team will win a championship based on loyalty, recent performance, or roster moves—these estimates are subjective.
Coin flips: Mathematically a fair coin has a 50% chance of heads. After observing 10 tails in a row, a person might subjectively revise the chance toward tails (e.g., 75%), even though the true probability remains 50% for a fair coin.
Expert forecasts: Analysts often give probability estimates for economic or political events that combine data, models, and personal judgment.

Common biases and errors

Subjective probabilities are vulnerable to cognitive biases that can distort judgment:
– Anchoring: Relying too heavily on an initial number or piece of information.
– Availability: Overweighting recent or memorable events.
– Representativeness: Mistakenly judging probabilities by perceived similarity rather than base rates.
– Overconfidence: Underestimating uncertainty and assigning probabilities that are too extreme.
– Gambler’s fallacy: Expecting short-run outcomes to “balance” when outcomes are independent.

When to use subjective probability

When data are scarce, incomplete, or not comparable to the current situation.
For one-off decisions where no long-run frequency exists (e.g., product launches, geopolitical events).
To complement formal models with expert judgment, especially in novel or rapidly changing contexts.

How to improve subjective estimates

Calibrate: Track past forecasts and learn from errors to adjust future judgments.
Use reference classes: Compare the current case to similar, well-documented cases.
Combine methods: Blend model outputs with expert opinion rather than relying on one source.
Encourage diversity: Aggregate independent judgments from multiple experts to reduce individual biases.
Adopt structured techniques: Use pre-mortems, checklists, and scoring rules (e.g., Brier score) to make reasoning explicit and measurable.
Explicitly consider base rates and alternative hypotheses before adjusting for recent, salient information.

Key takeaways

Subjective probability captures personal belief about uncertain events and is distinct from statistically derived objective probability.
It is useful when data or models are insufficient, but it is prone to well-known cognitive biases.
Applying structured methods, calibration, and aggregation can improve the reliability of subjective probability estimates.