Effort task. (a,b) Effectiveness of precommitment: proportion of achieved effort-requiring LRs was higher in precommitment trials (black) than in standard trials (grey; a) and declined with increasing effort requirements (b; triangles, predicted probability; circles, observed data). (c,d) Choice behaviour: opt outs of an initial LR choice during the waiting period were rare (c) and proportion of LR choices (without or with previous precommitment) showed a similar pattern to LR achievement. (e–g) Comparison of the MM and WP precommitment models. (e) Average value of precommitment to the LR option at each waiting requirement level as determined by the MM and WP model. (f) The average obtained θ value reflecting sensitivity of participants’ precommitment decisions to the model-predicted value of precommitment was numerically higher for the MM model than for the WP model, and this difference became statistically significant (p < 0.5) when subjects with unreliable parameter estimation were excluded (see main text for details). (g) Observed precommitment rates (black circles) closely aligned with the predicted probabilities of precommitment by the MM precommitment model (grey diamonds), but showed the opposite pattern than that predicted by the WP precommitment model (white diamonds). Error bars represent s.e.m.; *** denotes a significant effect with p ≤ 0.001.