Discounting of delayed and probabilistic losses over a wide range of amounts.
Loss amount does not change the discounting curve, so you can collapse small and large losses into one analysis.
01Research in Context
What this study did
Leonard’s team asked adults to choose between sure losses and bigger, later or uncertain losses.
They tested amounts from 20 dollars to 500,000 dollars.
Every person completed both delay and probability versions so the curves could be compared.
What they found
The discounting shape stayed the same no matter how large the loss was.
Delay discounting and probability discounting did not correlate; they acted like separate traits.
How this fits with other research
Horner-Johnson et al. (2002) showed that hypothetical money gives the same curve as real money, so Leonard could safely use hypothetical losses.
Parmenter (1999) saw the same amount-independence with pigeons and gains; Leonard extends the rule to humans and losses.
Willis-Moore et al. (2024) later found that simply seeing a large-magnitude task first can make the next curve steeper. Their result does not overturn Leonard; it warns us to counterbalance session order when we run multiple amounts.
Why it matters
You can treat a 20-dollar loss and a 500,000-dollar loss as the same psychological unit when you plot discounting curves. That saves session time and removes one variable from your graph. Just remember to randomize task order so recent big numbers do not tilt the curve.
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02At a glance
03Original abstract
The present study examined delay and probability discounting of hypothetical monetary losses over a wide range of amounts (from $20 to $500,000) in order to determine how amount affects the parameters of the hyperboloid discounting function. In separate conditions, college students chose between immediate payments and larger, delayed payments and between certain payments and larger, probabilistic payments. The hyperboloid function accurately described both types of discounting, and amount of loss had little or no systematic effect on the degree of discounting. Importantly, the amount of loss also had little systematic effect on either the rate parameter or the exponent of the delay and probability discounting functions. The finding that the parameters of the hyperboloid function remain relatively constant across a wide range of amounts of delayed and probabilistic loss stands in contrast to the robust amount effects observed with delayed and probabilistic rewards. At the individual level, the degree to which delayed losses were discounted was uncorrelated with the degree to which probabilistic losses were discounted, and delay and probability loaded on two separate factors, similar to what is observed with delayed and probabilistic rewards. Taken together, these findings argue that although delay and probability discounting involve fundamentally different decision-making mechanisms, nevertheless the discounting of delayed and probabilistic losses share an insensitivity to amount that distinguishes it from the discounting of delayed and probabilistic gains.
Journal of the experimental analysis of behavior, 2014 · doi:10.1002/jeab.6