Discounting by Probabilistic Waiting

Abstract

In everyday life, many probabilistic situations may be characterized as probabilistic waiting. A gambler, for example, bets repeatedly at the racetrack, the casino, or the card table. The gambler may not win on the first try, but if a gamble is repeated enough times, a win is almost certain to occur eventually. If repeated gambles are structured as strings of losses ending in a win (probabilistic waiting) and the amount won is discounted by the delay caused by the series of losses, then strings with many losses will be discounted more than those with fewer losses, thereby causing subjective value of the series of gambles as a whole to increase. The current study used the opposite effect that amount has on the degree of delay and probability discounting as a marker to determine whether people evaluate situations involving probabilistic waiting as they evaluate situations involving delayed outcomes or as situations involving probabilistic outcomes. We find that the more likely a probabilistic waiting situation is to end in reward (e.g., a gamble is repeated indefinitely until reward is obtained), the more that situation conforms to delay discounting; the less likely a probabilistic waiting situation is to end in reward (e.g., a fixed, small number of gambles), the more that situation conforms to probability discounting. We argue that the former situation is applicable to pathological gambling, and that people with steep delay discount functions would therefore be more likely to have gambling problems.

People Wait Longer when the Alternative is Risky: The Relation Between Preferences in Risky and Inter‐temporal Choice

“…In inter‐temporal choice temporal discount rates decrease when both outcomes are multiplied by a common amount (Chapman & Weber, ; Estle, Green, Myerson, & Holt, ; Guyse & Simon, ; Kirby, ; Thaler, ; Vanderveldt, Green & Rachlin, ), leading to increased preference for the larger later outcome. In contrast, risky choice seems to show the opposite pattern, with increases in magnitude leading to either no change or a decreased preference for the larger riskier option (Chapman & Weber, ; Estle et al, ; Markowitz, ; Vanderveldt, Green & Rachlin, ; Weber & Chapman, ). These two effects have been dubbed the magnitude effect and peanuts effect , respectively.…”

The Magnitude and “Peanuts” Effects: Searching Implications

“…However, some authors [20][21][22][23] have demonstrated that in decisions with delayed rewards, the preference increases as its amount increases. This magnitude effect is based on the premise that the patience of individuals is directly related to the reward amount and that individuals are more patient for large rewards than for those of smaller amounts, leading to an increased preference for the larger later outcomes [24,25]. Following Schneider [11], the magnitude effect may be represented as follows:…”

Risk inherent in delay accounts for magnitude effects in intertemporal decision making

“…Those theories attempt to relate the delay and risk involved in decision-making and conceptualize whether one of these factors is fundamental to the discounting process. For example, it was proposed that delay discounting could be considered as a more fundamental process because choice under risk, when repeated, reflects a situation of repeated lotteries (Rachlin et al 1986(Rachlin et al , 1991Vanderveldt et al 2017). For example, when people play a lottery in which winning is highly probable, they will have to repeat it relatively few times to win, as compared to a lottery in which winning has a low probability.…”