Queuing theory under competitive social foraging may explain a mathematical equivalence of delay and probability in impulsive decision-making.
Intertemporal and probabilistic decision-making has been studied in psychiatry, ecology, and neuroeconomics. Because drug addicts and psycopaths often make risky decisions (e.g., drug misuse and aggression), investigation into types of impulsivity in intertemporal and probabilistic choices (delay and probability discounting) are important for psychiatric treatments. Studies in behavioral ecology proposed that delay and probability discounting are mediated by the same psychological process, because a decrease in probability of winning corresponds to an increase in delay until winning. According to this view, odds-against winning (=1/p-1) in probabilistic choice corresponds to delay in intertemporal choice. This hypothesis predicts that preference of gambling (low degree of probability discounting) may be associated with patience, rather than impulsivity or impatience, in intertemporal choice (low degree of delay discounting). However, recent empirical evidence in psychiatric research employing pathological gamblers indicates that pathological gamblers are impulsive in intertemporal choice (high degrees of delay discounting). However, a hyperbolic discounting function (usually adopted to explain intertemporal choice) with odds-against (instead of delay) explain experimental data in probabilistic choice dramatically well. Therefore, an alternative explanation is required for the hypothetical equivalence of odds-against to delay. We propose that queuing theory (often adopted for analyzing computer network traffic) under a competitive social foraging condition may explain the equivalence. Our hypothesis may help understand impulsivity of psychiatrics in social behavior (e.g., aggression and antisocial behavior) in addition to non-social impulsivity in reward-seeking (e.g., substance misuse).