Figure 3. Decision accuracy across the decision space.

Accuracy (light-yellow indicates high accuracy, dark-red indicates low accuracy) is plotted across the decision space defined by decision difficulty (HV-LV) and relative distractor value (D–HV) from (a) Experiment 1 fMRI2014, (c) Experiment 2 Gluth4, (e) Experiment 3 Hong Kong. In the case of each experiment, GLM analysis indicates that similar factors influence accuracy. The difference in value between the better and worse choosable option (HV-LV) is a major influence on accurately choosing the better option HV. However, accurate choice of HV is also more likely when the distractor is high in value (D-HV is high) and this effect is more apparent when the decision is difficult (negative interaction of (HV-LV)(D–HV)) in the data from (b) Experiment 1 fMRI2014, (d) Experiment 2 Gluth4, (f) Experiment 3 Hong Kong. (g) A model comparison shows that participants’ behaviour in Experiments 1 to 3 is best described by the dual route model, as opposed to the null, mutual inhibition, or divisive normalisation models. (h) Posterior probability of each model in accounting for the behaviour of individual participants. Null: null model; Mutual: mutual inhibition model; DivNorm: divisive normalisation model; Dual: dual route model. *p<0.05, **p<0.01, ***p<0.001. (a–f) Error bars indicate standard error. (g–h) Error bars indicate standard deviation.

Figure 3—figure supplement 1. A similar (HV-LV)(D–HV) effect was observed when the HV+LV term was added to GLM1a which was done in GLM1b.

A negative (HV-LV)(D–HV) interaction effect was found in (a) Experiment 1, (b) Experiment two and (c) Experiment 3. *p<0.05, **p<0.01, ***p<0.001. Error bars indicate standard error.

Figure 3—figure supplement 2. The dual route model is better than the mutual inhibition, divisive normalisation and null models in predicting participants’ accuracy and reaction time.

(a) A plot showing the choice accuracy of participants of Experiments 1–3 as a function of HV-LV and D-HV. In other words, it shows the averaged data of Figure 3a,c,e. (b) The fitted parameters were applied back to the corresponding models to predict choices in the exact same trials that the participants performed. The predictions were repeated for 1000 iterations and the absolute deviation of the predictions from the empirical data was calculated (i.e. absolute difference between models’ and participants’ accuracy). The results show that overall the dual route model (top-left) is better than (darker colors) the mutual inhibition (top-right), divisive normalisation (bottom-left) and null (bottom-right) models in predicting participants’ accuracy. The same procedure was then repeated to test the models’ prediction of reaction time (RT). (c) Participants’ reaction times were slower (yellow colors) on trials that were harder (bottom rows) and with larger distractor values (right columns). (d) As in (b), the absolute deviation in RT between models’ predictions and participants’ behaviour is plotted. The dual route model (top-left) is better than (darker colors) the mutual inhibition (top-right), divisive normalisation (bottom-left) and null (bottom-right) models in predicting participants’ RT.

Figure 3—figure supplement 3. The dual route model provides the best account of participants’ behaviour regardless of the parameterisation of non-decision time Tnd and inhibition level f.

(a) Replica of Figure 3g and h. In this set of models, Tnd is fixed at 0.3 s and f is fixed at 0.5. (b) In this set of models, Tnd is fixed at 0.3 s and f is a free parameter with a prior at 0.5. In the dual route model, the f of each route is fitted independently. (c) In this set of models, Tnd is a free parameter with a prior at 0.3 s and f is also a free parameter with a prior at 0.3. In all three versions of model set, the dual route model provide the best fit of participants’ behaviour. (d) All twelve models in a–c) are compared in a single analysis. The dual route model with fixed Tnd and f provides the best account of participant behaviour (Ef = 0.413, Xp = 1.000). Null: null model; Mutual: mutual inhibition model; DivNorm: divisive normalisation model; Dual: dual route model. Error bars indicate standard deviation.