Theory and method in the quantitative analysis of ”impulsive choice” behaviour: implications for psychopharmacology

Abstract

Impulsive choice refers to the selection of small immediate gains in preference to larger delayed gains, or the selection of large delayed penalties in preference to smaller immediate penalties. Current theoretical interpretations of impulsive choice are reviewed, and a synthesis of these ideas, the "multiplicative hyperbolic model of choice", is presented. The model assumes that the value of a positive reinforcer increases as a hyperbolic function of its size, and decreases as a hyperbolic function of its delay and the odds against its occurrence. Each hyperbolic function contains a single discounting parameter which quantifies the organism's sensitivity to the variable in question. The hyperbolic discounting functions combine multiplicatively to determine the overall value of the reinforcer. Equivalent functions are postulated to govern the (negative) value of aversive events, the net value of an outcome reflecting the algebraic sum of the positive and negative values. The model gives rise to a quantitative methodology for studying impulsive choice, based on a family of linear indifference (null) equations, which describe performance under conditions of indifference, when the values of the reinforcers are assumed to be equal. This methodology may be used to identify individual differences in sensitivity to the magnitude, delay and probability of reinforcement. The methodology is also suitable for the quantitative evaluation of the effects of some pharmacological interventions on discounting parameters. Recent psychopharmacological studies of impulsive choice are reviewed, and the utility of indifference equations for extending this work, and developing a quantitative psychopharmacology of impulsive choice is discussed.

Effects of quinolinic acid-induced lesions of the nucleus accumbens core on inter-temporal choice: a quantitative analysis

“…As in previous experiments (Kheramin et al 2002(Kheramin et al , 2003(Kheramin et al , 2004 (Ho et al 1999), allows formal separation of the parameters that represent the rate of delay discounting and sensitivity to reinforcer magnitude (see below).…”

“…Models of inter-temporal choice that are based on the computation of hypothetical 'values' of reinforcers generally predict extreme preference for the more highly valued of two mutually exclusive reinforcers (see Herrnstein 1981;Ho et al 1999). This suggests that the ideal preference function should be a step function, %B falling precipitously from near 100% to near 0% around the point at which V A =V B .…”

“…Moreover, simple null equations may be derived which allow changes in the delay-and size-discounting parameters to be distinguished. For example, expansion of the indifference relation, V A =V B using equation 1, and solving for d B(50) (the value of d B at the point of indifference) yields the following linear relation between d B(50) and d A : [2] The slope of the function, which defines the ratio of the instantaneous values of the two reinforcers, is influenced by Q, but not by K. The intercept, on the other hand, is jointly determined by Q and K. It follows, therefore, that an intervention which selectively alters the delay discounting parameter K, should alter the intercept of the indifference function (see Ho et al 1999). …”

Effects of clomipramine on self-control choice in Lewis and Fischer 344 rats

“…Thus, any observed differences in choice between Lewis and Fischer 344 rats may be due differential sensitivities to reinforcer delay and/or magnitude. Future studies and quantitative analyses may elucidate some of the mechanisms that underlie choice deemed "impulsive" and allow for a teasing apart of factors that influence such choice, e.g., sensitivity to reinforcer magnitude and delay (see Ho et al, 1999 andPitts andFebbo, 2004 for further discussions of quantitative analyses). Certainly, there are many operational definitions and paradigms to study impulsivity (cf.…”

Risk-Taking Behavior in a Gambling Task Associated with Variations in the Tryptophan Hydroxylase 2 Gene: Relevance to Psychiatric Disorders

“…To assess an individual's overall tendency to take a safer vs more risky choice, we plotted yB against yA and calculated a global area under the curve measure (AUCy) using the trapezoid method requiring all four indifference points; a smaller value indicating safer choice. Using AUCy gives weight to choices, in which wins are unlikely and is sensitive to how much the individual is willing to take a risk for a greater reward under conditions where both outcomes are uncertain (Ho et al, 1999).…”