Subproportionality
Cutting a probability hurts more when it starts out small.
What it means
A property of prospect theory's probability-weighting function under which a fixed ratio of probabilities produces a larger ratio of decision weights when the probabilities are small than when they are large. Concretely, the same proportional reduction in chance — say, halving it — feels far more consequential near zero than near one, which is the formal expression of people's heightened sensitivity to changes in rare-event probabilities. Together with subcertainty, subproportionality pins down the characteristic shape of the weighting function and helps generate the certainty and possibility effects as well as the common-ratio violations of expected utility seen in the Allais paradox. It captures, in a single regularity, why insurers and lotteries can both thrive and why eliminating a small risk commands a disproportionate premium. It matters as part of the precise mathematical account of how psychological probability bends away from objective chance.
Examples
Parents will pay far more to cut a vaccine's rare side effect from two in a million to one in a million than to halve their child's odds of a winter cold.
A safety upgrade halving the already tiny crash risk on a train line sells itself, while halving the far larger risk of workplace back injury barely gets a budget line.
First described in Kahneman & Tversky (1979).