Weber’s Law: why $5 is easy to wave off
In 1834, German physiologist Ernst Heinrich Weber published De Subtilitate Tactus, a study on the sense of touch that would reshape our understanding of perception. Weber discovered that humans don’t perceive changes in absolute terms — they perceive them as proportions of the original stimulus.
His finding, now called Weber’s Law, states that the smallest detectable difference in a stimulus is a constant ratio of the original. Round numbers show the idea: if you needed 10 additional grams to notice a difference on a 300-gram weight, you’d need 20 on a 600-gram weight.
ΔI / I = kWeber’s fraction: the just-noticeable difference is a constant proportion of the original stimulus, not a fixed amount. This means $5 on a $40 bill (12.5%) feels different from $5 on a $200 bill (2.5%).
Applied to money: a $5 difference on a $40 dinner tab represents 12.5% — noticeable, maybe worth mentioning. But a $5 difference on a $200 group dinner with eight people? That’s 2.5%. A far smaller share, and far easier to wave off.
Weber measured weights, not prices, and no reliable source turned up that sets a fixed percentage below which a restaurant overcharge goes unnoticed. The arithmetic does the work anyway. Your group dinner bill is designed — by sheer arithmetic of group size — to make each individual overcharge a small share of the total.
This is why minimizing works. The minimizer isn’t just saying “$5 is small.” They’re leaning on how we judge amounts in proportion. In the context of a $200 check, a $5 discrepancy looks like nothing.
The effect scales with group size. At a dinner for four, a $5 overcharge on a $120 bill is 4.2%. At a dinner for eight, the same $5 on a $300 bill is 1.7%. The bigger the group, the more the minimizer benefits, because the same $5 shrinks as a share of the bill.
And here’s what makes it insidious: the frequency doesn’t help. Kahneman and Tversky’s prospect theory, published in Econometrica in 1979, demonstrated that people evaluate gains and losses relative to a reference point rather than in terms of total wealth. Thaler’s reading of that finding is that “transactions are often evaluated one at a time.” So each $5 overcharge gets assessed by itself. Your brain rarely asks “how much have I overpaid across all dinners this year?” It only asks “is this $5 worth fighting about right now?”
The answer, predictably, is always no.
Sources: Weber, De Subtilitate Tactus, 1834; Kahneman & Tversky, Econometrica, 1979; Thaler, Journal of Behavioral Decision Making, 1999