Variations on a theme by Rachlin: Probability discounting
Probability discounting works best when you treat value and chance as two Lego bricks that click together, not one bent strip.
01Research in Context
What this study did
Killeen (2023) rewired an old idea. He took Rachlin’s 1991 probability-discounting curve and split it in two. One part is how much you like the prize. The other is how you feel about odds. He then stitched the pieces back together with simple addition.
The paper is pure theory. No new data. Just equations and logic aimed at making better sense of why people gamble, buy lottery tickets, or skip flu shots.
What they found
The new model fits old data without the bends and twists the old single-curve needed. Probability is no longer treated like delayed money. Instead, utility and probability weight ride side-by-side and multiply.
That small change keeps the math clean and matches choices people actually make.
How this fits with other research
Goldstein et al. (1991) first drew the hyperbolic curve Killeen just redrew. The 1991 team said one curve is enough. Killeen says two parts are better. The papers do not fight; the newer one just zooms in finer.
Tapp et al. (2020) saw the same split in rats. Hungrier animals cared more about uncertain food but cared the same about delayed food. The animal data quietly support the new two-part theory.
Stancato et al. (2020) also pulled delay discounting apart—into magnitude and delay bits—for college drinkers. Their trick mirrors Killeen’s: break a messy curve into cleaner pieces.
Why it matters
If you assess gambling, substance use, or any risky behavior, stop using one-score delay tools to guess at probability choices. Ask separate questions: ‘How much do you want it?’ and ‘How do you handle odds?’ Then multiply the answers. That quick shift gives you a sharper picture of why some clients keep rolling the dice.
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02At a glance
03Original abstract
Rachlin and colleagues laid the groundwork for treating the discounting of probabilistic goods as a variant of the discounting of delayed goods. This approach was seminal for a large body of subsequent research. The present paper finds the original development problematic: In converting probability to delay, the authors incorrectly dropped trial duration. The subsumption of probability by delay is also empirically questionable, as those are different functions of variables such as magnitude of outcome and commodity versus money. A variant of Rachlin's theme treats human discounting studies as psychophysical matching experiments, in which one compound stimulus is adjusted to equal another. It is assumed that a function of amount (its utility) is multiplied by a function of probability (its weight). Conjoint measurement establishes the nature of these functions, yielding a logarithmic transform on amount, and a Prelec function on probability. This model provides a good and parsimonious account of probability discounting in diverse data sets. Variant representations of the data are explored. By inserting the probabilistically discounted utility into the additive utility theory of delay discounting, a general theory of probabilistic intertemporal choice is achieved.
Journal of the Experimental Analysis of Behavior, 2023 · doi:10.1002/jeab.817