Figure 1.
A separate estimation of probability and value is necessary to guarantee rational choices in decision theory. This separation also offers more flexibility in goal oriented decisions. Indeed, the subjective values of events change with our goals but not their probabilities of occurrence which are controlled by the environment (or the response of the environment to our actions). For instance, a person is trying to estimate the probability that it will rain. On the left side of the figure, she wants to water her garden. Thus “rain” is a positive event relative to her goal. On the right side, she wants to go for a bike ride. Thus “rain” is a negative event. It can be seen that the subjective value of “rain” changes with personal goals but not the chance it will rain. Therefore, it would be adaptive for the brain to encode the probabilities and values of events separately.
Figure 2.
(a) Payoffs were determined by the colors of balls drawn from a bin. In two sampling stages, participants had the opportunity to learn probabilities by observing several drawings. Payoffs were shown in the center of the screen (stimuli). Colors were not displayed (hidden states). After each sampling stage, participants had to decide to buy the gamble or not for a certain price. In the initial sampling stage, both the composition of the bin and the color-payoff association were new. In the resampling stage, the composition of the bin remained the same (same color probabilities) but the associated payoffs were new. (b) Top insert. The color-payoff association changed in the resampling stage. Histograms. These are the true probabilities used to generate the drawings for bins with 2, 5, or 10 colors.
Table 1.
Choice models.
Figure 3.
Value and probability functions.
(a) Value function as estimated from participants' decisions (red, model M4.) Estimation obtained by Tversky and Kahneman (1992) in a study on decisions from description. (b) Probability weighting inferred from choices (red, model M5) and comparison with estimations from other studies in the gain and loss domains (Gain - Hau et al., 2008 is confounded with the linear function.) (c) Top insert. To avoid circularity, ROIs for each individual were determined based on the data of all other participants. ROI voxels common to all participants are shown in yellow. ROI voxels belonging to at least one participant are shown in red. This representation shows to which extent the ROI definitions vary in the cross-validation. Main. Increase of BOLD response with stimulus probabilities in medial prefrontal cortex and angular gyri during the learning phase. Data of the 3 ROIs has been merged. The y axis indicates the effect the presentation of new stimulus (payoff) had in the ROIs. The effect increased with the probability of the currently observed stimulus. The non-linear regression (red) includes a probability weighting function.
Figure 4.
(, uncorr.) Volume (a) and sectional (b) views of the BOLD response to stimulus probabilities in medial prefrontal cortex and bilateral angular gyrus. Activity increases with the probability of the currently observed stimulus. (c) Voxels showing increased connectivity with angular gyri and medial prefrontal cortex ROIs compared to the resting phase.
Figure 5.
(, uncorr.) (a) BOLD response in the bilateral insula to gambles combining high outcome entropy and high expected value. Outcome uncertainty increased with entropy. (b) BOLD response to choice entropy in the dorsal anterior cingulate. Participants faced a more difficult choice when the probabilities to buy and pass the gamble were close, that is when choice entropy was high. (c) Striatal activation related to the magnitude of the total payoff received at the end of the decision phase (net of the total price). Whereas activation related to outcome and choice entropy were observed before participants made a choice (anticipation), BOLD response to the net payoff was observed afterwards (feedback).
Figure 6.
(a) Voxels showing connectivity with angular gyri and medial prefrontal cortex ROIs during the resting phase. (, uncorr.) (b) Voxels showing activation (red, task-positive network) and deactivation (blue, task-negative network) during the learning and decision phases (
, uncorr.) (c) Overlap between voxels encoding stimulus probabilities (Fig. 4a+b) and the task-negative network (panel b, blue voxels).
Figure 7.
(a) During the resting phase, the spontaneous activity of the brain correlated between angular gyri, medial prefrontal cortex, and posterior cingulate cortex. This constitutes the first characteristic of the default mode network. (b) During the task (learning & decision phases), baseline activity in these regions decreased. This is the second characteristic of the default network. At the same time, activation in the occipital, superior parietal, lateral prefrontal cortex, and other regions involved in visual attention increased. (c) During the learning phase, participants only saw the payoff in the center of the bin (stimulus). Nevertheless, the brain encoded the probability of currently observed stimulus inferred from the hidden states (colors). BOLD response for frequent stimuli increased in angular gyri and medial prefrontal cortex. BOLD response for rare stimuli increased in occipital areas, superior parietal cortex, middle frontal gyri, and hippocampus (Fig. S3a in Text S1). (d) Compared to the resting phase, correlations between these regions increased during learning. (e) When participants had to decide whether to buy the gamble or not, BOLD response in the insula increased with with gamble expected value, especially for when outcome entropy was high. At the same time, the dorsal anterior cingulate cortex signaled choice entropy (Fig. 5b). (f) After six choices, a feedback was displayed. The bilateral striatum encoded the net payoff magnitude.