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ratio_bias
Ratio bias (denominator neglect) is the tendency to focus on absolute numbers rather than proportions or rates when evaluating probabilities. People are more impressed by '10 out of 100' than '1 out of 10,' even though both represent the same 10% rate. This bias can lead to preferring the larger-denominator option even when the probability is actually lower, because the absolute number of 'successes' is larger.
Participants in a study are offered a choice between two bowls for a lottery. Bowl A has 1 red marble among 10 total (10% chance). Bowl B has 8 red marbles among 100 total (8% chance). Many people choose Bowl B because '8 chances' feels better than '1 chance,' even though Bowl A offers better odds.
A hospital safety report states that Hospital A had 3 surgical errors last year, while Hospital B had 22. Patients overwhelmingly prefer Hospital A, ignoring that Hospital A performed 30 surgeries (10% error rate) while Hospital B performed 1,100 surgeries (2% error rate).
An anti-drug campaign poster warns that '1,200 young people were hospitalized due to this substance last year,' prompting widespread alarm. Few readers seek out the denominator — 4 million annual users — which would reveal a hospitalization rate of 0.03%, lower than many common medications.
Binary (yes/no) questions an LLM must answer to identify this aspect:
Are absolute numbers being presented without the appropriate base rate or denominator?
Type: binaryWould presenting the same data as a rate or percentage change the impression?
Type: binaryIs the audience likely to misjudge risk because the denominator is missing?
Type: binaryAre comparisons being made between groups of different sizes using raw counts?
Type: binaryRatio bias (denominator neglect) is the tendency to focus on absolute numbers rather than proportions or rates when evaluating probabilities. People are more impressed by '10 out of 100' than '1 out of 10,' even though both represent the same 10% rate. This bias can lead to preferring the larger-denominator option even when the probability is actually lower, because the absolute number of 'successes' is larger.
The brain processes absolute frequencies more easily than proportions. 'Eight red marbles' is more vivid and tangible than an abstract 8% probability. This reflects a deeper tendency to think in terms of counts rather than rates.
Always convert comparisons to the same denominator or express them as percentages side by side. Ask 'What is the rate?' rather than 'How many?'
Ratio bias affects medical decision-making (patients react more to '200 out of 10,000 will die' than '2%'), product marketing ('9 out of 10 dentists' sounds better than '90%'), and risk communication.
Use these tools to detect, analyze, or train this aspect.