Delay discounting and preference reversal

A hyperbolic discounter values £60 now against £100 in 30 days. Drag the extra delay to push both rewards further off together, and watch the curves cross: the preference flips from impatient to patient even though nothing but the common delay has changed. The discount rate k sets the steepness.

Discount rate k (per day)0.050
Extra delay added to both rewards (days)+0
0255075100present value (£)extra delay added to both rewards (days)£60 sooner£100 later
At an extra delay of +0 d (k = 0.050): the £60 is worth £60.0, the £100 worth £40.0 — so this chooser prefers the smaller-sooner (£60). The curves cross at +25.0 d: below it the impatient option wins, above it the patient one does. That reversal is the signature of hyperbolic discounting.

The stop-signal race

On a stop trial a go response (whose finishing times form the curve below) races a stop process that completes at SSD + SSRT. If the go process finishes first — in the shaded tail — the response escapes; otherwise it is inhibited. Lengthen the SSRT (slower brakes) or the SSD (a later signal) and the escape probability climbs. Go-RT is fixed at a mean of 490 ms, SD 90.

Stop-signal delay SSD (ms)250
Stop-signal reaction time SSRT (ms)240
200400600800go finishing time (ms)stop finishes 490 ms
Stop process finishes at 490 ms (= 250 + 240). Probability the response escapes, p(respond | signal) = 50%; inhibited on 50% of stop trials. At the defaults (SSD 250, SSRT 240) the finish lands on the mean go-RT, giving a 50/50 race — the point from which the integration method recovers an SSRT of 240 ms.

One number, many profiles

The UPPS-P model splits trait impulsivity into five facets that do not collapse into one. Set each independently: two very different people can share the same average score while differing entirely in which facet drives it. The correlate notes are illustrative of the literature, not computed from your input.

Negative urgency3/5
Positive urgency2/5
Lack of premeditation2/5
Lack of perseverance2/5
Sensation seeking3/5
NUPUPMPSSS
Naive global impulsivity score (facet mean): 2.4/5. That single number hides the shape below:
  • no single facet is elevated — this profile would look average on a global impulsivity score