Modeling the effect of reward amount on probability discounting.
Bigger hypothetical rewards make college students gamble more, so size your reinforcers carefully when chance is involved.
01Research in Context
What this study did
Myerson et al. (2011) asked college students to pick between a sure small amount of money and a chance at a bigger amount. The team made the bigger prize grow across trials while the odds of winning it stayed the same.
They wrote a math rule that lets reward size change how steeply people discount odds. Then they checked if the rule fit each student's choices better than older rules that ignore amount.
What they found
The new rule with an amount-dependent exponent tracked the data well. When the hypothetical jackpot got larger, students became more willing to gamble even when the true odds were poor.
The pattern looked different from delay discounting, where bigger rewards usually make people more patient. Here, bigger rewards made people more risk-prone, not less.
How this fits with other research
Kazdin (1977) showed that rats divide time between wheel running and sucrose drinking in line with matching-law equations. Joel's team builds on that quantitative spirit by adding reward size as a variable inside the equation itself.
Fields (1978) found that payoff size in pigeons shifts response bias without changing how well they can tell stimuli apart. The human data echo this: amount does not just scale preference; it bends the whole probability curve.
HENDRY et al. (1964) saw that rats on fixed-ratio schedules slowed down when each press delivered more food, a seeming contradiction to the high-rate world of ratio schedules. Likewise, Joel et al. show that larger rewards can push organisms toward riskier, not safer, choices — another case where bigger payoffs produce unexpected response patterns.
Why it matters
If you run probability-based reinforcement games or token economies, do not assume a single discount curve fits all prize sizes. A $10 jackpot may inflate risk-taking more than a $1 jackpot, so adjust the odds or teaching steps accordingly. When fading from sure tokens to chance-based tokens, start with smaller amounts to keep behavior stable, then raise the prize only after the skill is solid.
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Cut the size of the 'grand prize' in half and see if clients still pick the risky option at the same odds.
02At a glance
03Original abstract
The present study with college students examined the effect of amount on the discounting of probabilistic monetary rewards. A hyperboloid function accurately described the discounting of hypothetical rewards ranging in amount from $20 to $10,000,000. The degree of discounting increased continuously with amount of probabilistic reward. This effect of amount was not due to changes in the rate parameter of the discounting function, but rather was due to increases in the exponent. These results stand in contrast to those observed with the discounting of delayed monetary rewards, in which the degree of discounting decreases with reward amount due to amount-dependent decreases in the rate parameter. Taken together, this pattern of results suggests that delay and probability discounting reflect different underlying mechanisms. That is, the fact that the exponent in the delay discounting function is independent of amount is consistent with a psychophysical scaling interpretation, whereas the finding that the exponent of the probability-discounting function is amount-dependent is inconsistent with such an interpretation. Instead, the present results are consistent with the idea that the probability-discounting function is itself the product of a value function and a weighting function. This idea was first suggested by Kahneman and Tversky (1979), although their prospect theory does not predict amount effects like those observed. The effect of amount on probability discounting was parsimoniously incorporated into our hyperboloid discounting function by assuming that the exponent was proportional to the amount raised to a power. The amount-dependent exponent of the probability-discounting function may be viewed as reflecting the effect of amount on the weighting of the probability with which the reward will be received.
Journal of the experimental analysis of behavior, 2011 · doi:10.1901/jeab.2011.95-175