Scalar human brain responses to vectorial economic choice options: a concept-driven approach

Rewarding choice options typically contain multiple components, but neural signals vary in one dimension (up or down). We used rigorous concepts of Revealed Preference Theory to investigate how scalar neural responses represent vectorial rewards. Each reward constituted a bundle containing the same two milkshakes with independently set amounts. Using psychophysics, we estimated stochastic choice indifference curves (IC) that reflected the orderly integration of the bundle components. All bundles on same ICs were equally revealed preferred (choice indifference); bundles on higher ICs were preferred to bundles on lower ICs. Functional magnetic resonance imaging (fMRI) demonstrated brain responses in reward-related brain structures, including striatum, midbrain and medial orbitofrontal cortex. These responses followed the characteristic revealed preference pattern: similar responses along ICs, but monotonic change across ICs. Thus, the striatum, midbrain and medial orbitofrontal cortex integrate multiple reward components into a scalar reward signal beyond known subjective value coding.

Introduction 6 component choice options should vary between any bundle on a higher IC and any bundle on a 211 lower IC. To reflect the proper integration of the two bundle components irrespective of specific 212 physical properties, the neural signal should follow the IC rank even when one component 213 milkshake of the higher-IC bundle is lower than in the lower-IC bundle (partial physical non-214 dominance). To identify such differences, we used the GLM2. With pairwise comparisons, GLM2 215 should identify higher responses to revealed preferred bundles with partial physical non-dominance. 216 Thus, GLM2 compared all bundle pairs that fit the following condition within each participant: 217 bundle 1 was located on higher IC but had a lower amount of one component milkshake compared 218 to bundle 2 that was located on a lower IC (Fig. 3A). 219 The GLM2 analysis demonstrated significant activations in similar regions as with GLM1. 220 Striatum (peak at [12,4,0], z-score=4.17; with extension to the thalamus [-6, -26, 0], z-score = 221 4.31) and OFC (peak at [22, 26, -28], z-score = 4.74) showed whole-brain corrected significant 222 activations (p < 0.001) (Fig. 3B). We found small volume-corrected (6 mm radius sphere) 223 significant activation in the midbrain (Fig. 3C;peak at [8,, z-score = 3.21, cluster-level 224 FWE corrected p = 0.033). Also, we found significant activities in other regions, including insula, 225 superior frontal gyrus and cingulate, as shown in Table 2. 226 We also performed ROI analyses (coordinates identified by GLM2 with leave-one-out 227 procedure) that calculated betas of partial physical non-dominance (higher revealed preference) and 228 partial physical dominance bundles (lower revealed preference) as described in Methods. For each 229 ROI, we computed three models, which compared bundles pairwise, with low vs. middle, middle 230 vs. high, and low vs. high revealed preference, respectively. Neural beta regression coefficients 231 were extracted at 6 s after the onset of the bundle stimulus, which corresponded to the canonical 232 hemodynamic response. In regard to high vs. low revealed preference level, we found significance 233 in the striatum (p = 0.0239) and OFC (p = 0.0140) when comparing bundles in high IC vs. low IC 234 (Fig. 3C). We also found significant differences in the OFC (p = 0.0157) when comparing high vs. 235 middle IC bundles. In the midbrain, we found no significance (p > 0.05) in the three comparisons 236 between bundles on low, middle and high ICs (although such a tendency existed in two out of the 237 three comparisons). Becker-DeGroot-Marschak (BDM) control of revealed preference 244 To validate the order of revealed preferences represented by the ICs with an independent estimation 245 mechanism, we used a monetary Becker-DeGroot-Marschak (BDM) bidding task that estimated 246 each participant's utility for each bundle. In 50% of trials during fMRI scanning, each participant 247 made a monetary BDM bid (UK pence) for one of the 15 bundles, out of a fresh endowment of 20 248 UK pence in each trial (BDM bidding phase; Fig. 1E). The 15 bundles constituted the indifference 249 points of the ICs that were estimated during the binary choice task with each participant (Fig. S1).

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The BDM bids followed the order of revealed preference levels across ICs, as evidenced by 251 the bidding phase. As described above, we found significant, small-volume corrected activation in 263 OFC in GLM1 that indicated its involvement in encoding IC levels during the bundle-on phase.

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This result was confirmed by an additional ROI analysis that showed significant rank correlation 265 between OFC activation and IC levels at around 6 s after bundle onset (Fig. 4B top; bundle-on 266 phase; p < 0.05; Spearman's Rho), consistent with the expected haemodynamic response function.

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By contrast, we found no significant correlation between OFC activation and BDM bids at 5 -7 s 268 after BDM cue onset (Fig. 4B bottom; bidding phase; p > 0.05). Thus, OFC activation covaried with 269 IC levels but not with BDM bids (which correlated with revealed preference levels).

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Analysis with GLM3 demonstrated activation in vmPFC that encoded BDM bids during the 271 bidding phase (Fig. 4C top;peak at [4,32,6], z-score = 3.24, small-volume corrected significance 272 with cluster-level FWE corrected p = 0.021), together with other brain regions (Table 3) prerequisite for testing the underlying neural mechanisms. In fMRI scans with GLM and post-hoc 289 ROI analyses, we identified brain regions whose activations correlated with levels of revealed 290 preference. The GLM1 and post-hoc Spearman rank analysis demonstrated activations in the 291 striatum, midbrain and OFC that reflected revealed preference levels across ICs but failed to vary 292 along equal-preference ICs. The GLM2 specifically dissociated revealed preference from physical 293 dominance and showed consistent results with those from GLM1. A mechanism-independent 294 control with a Becker-DeGroot-Marschak (BDM) bidding task confirmed the validity of ICs for 295 representing revealed preference levels. Interestingly, however, BDM bidding was associated with 296 activations in vmPFC rather than the previously identified reward structures following IC levels.

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Together, these data demonstrate systematic, single-dimensional neural activations in the striatum, 298 midbrain and OFC that reflect vectorial multi-component choice options.

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In our binary choice task, we elicited revealed preferences with repeated, psychophysically  Economic choice experiments often involve substantial but imaginary sizes or amounts of 307 consumer items and money, or use random singular payouts (Simonson, 1989;Tversky & Simonson 308 1993;Rieskamp el al., 2006). By contrast, we tailored our payout schedule to fit the requirements of 309 neuroimaging studies and made our participants choose tangible and consumable rewards over 310 hundreds of trials, while also controlling for satiety effects. These behavioral choices resembled 311 small daily activities, such as consumptions of drinks and snacks. In this way, we obtained three The copyright holder for this preprint (which was not peer-reviewed) is the . https://doi.org/10.1101/2020.04.06.028001 doi: bioRxiv preprint revealed preferences for multi-component bundles, without involving imagined items or monetary 314 reward (Pastor-Bernier et al. 2019b). 315 We used the BDM task as an authoritative, mechanism-independent control for eliciting 316 subjective values, thereby providing an additional validating mechanism for the revealed 317 preferences elicited in our binary choice test. The value estimating mechanism for BDM bids differs 318 substantially from the one for revealed preference ICs. The truthful revelations (incentive 319 compatibility) of BDM makes this mechanism an essential tool in experimental economics that is 320 becoming more popular in human decision research (Plassmann et al., 2007;Medic et al., 2014;321 Zangemeister et al., 2016). Our obtained BDM bids correlated well with the revealed preference 322 levels and thereby validated our empirically estimated IPs used in our fMRI task. Our participants 323 performed the BDM task during fMRI scanning. Previous neuroimaging studies showed activations 324 in the prefrontal cortex that correlated with BDM bids (Chib et al., 2009;McNamee et al., 2013). 325 Here, we used an experimental design that dissociated the value elicitation period (bundle-on phase) The copyright holder for this preprint (which was not peer-reviewed) is the . https://doi.org/10.1101/2020.04.06.028001 doi: bioRxiv preprint current study, we used a concept-driven design and found that neural responses in the striatum, 366 midbrain and OFC integrated multiple bundle components in a way that followed the ICs scheme 367 (changing across ICs but being similar along equal-preference ICs). Moreover, we demonstrate the studies, we also found significant activation in these regions. As shown in Table 1 and Table 2, the 377 BOLD signals identified by GLM1 and GLM2 showed that these regions also encode bundle values 378 during the bundle-on phase, together with the striatum, midbrain, and mid-OFC. Our results are 379 consistent with these previous studies, suggesting that a considerable number of brain regions also 380 play a role in multi-component decision making.

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Participants 385 A total of 24 participants (19-36 years old with mean age 25.4 years; 11 males, 13 females) 386 performed a binary choice task that was followed, in 50% of trials, by a Becker-DeGroot-Marschak 387 (BDM) task inside the fMRI scanner using sugary and fatty milkshakes. All participants had known 388 milkshake appetite, and none had diabetes or lactose intolerance. All participants provided written right on the two-dimensional IC (Fig. 1B). We are aware that testing with unidirectional progression 475 may cause particular variations in IP estimations than testing in a random sequence or in opposite 476 directions (Knetsch, 1989). However, our primary interest in this study was to investigate basic 477 neural processes in close relation to unequivocally estimated IPs and ICs rather than addressing the 478 more advanced features of irreversibility or hysteris in ICs. 479 We used three different fixed amounts of component B for the Reference Bundle (2 ml, 5 ml, We graphically displayed the fitted ICs (Fig. 1B, C)  levels (low, medium, high) farther away from the origin (Fig. 1B, C). The indifference map that 539 resulted from the 3 x 5 IPs was unique for each of the 24 participants ( Fig. 1 supplement 1).

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Leave-one-out validation of ICs 542 We used a leave-one-out analysis to test the validity of the hyperbolic IC fit to the IPs. We fMRI data analysis 678 We used the Statistical Parametric Mapping package to analyze the neuroimaging data (SPM 8;

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Wellcome Trust Centre for Neuroimaging, London). We pre-processed the data by realigning the 680 functional data to include motion correction, normalizing to the standard Montreal Neurological 681 Institute (MNI) coordinate, and then smoothing using a Gaussian kernel with the full width at half 682 maximum (FWHM) of 6 mm. We then applied a high-pass temporal filter to it with a 128 s cut-off 683 period. We applied General linear models (GLMs), which assumed first-order autoregressions, to In the Spearman rank analysis, we first regressed out the motion parameters (artefact) from the 780 BOLD response with generalized linear models. Then we used the participant's residual BOLD 781 response to generate time courses of Spearman rank correlation (Rho) coefficients.

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For GLM1, we tested the correlation between BOLD response (during the bundle-on phase) 783 and revealed preference level (across-IC analysis). We then calculated group averages and standard 784 errors of the mean for each time point for all participants, yielding averaged participant effect size 785 time courses (Fig. 2C). In the along-IC analysis, we ranked the bundles along the same IC with 786 individual participant's BOLD signal (Fig. 2D). A subsequent one-sample t-test against 0 served to 787 assess the significance of the Rho coefficients across subjects.
788 For GLM3, we tested the correlation of the BOLD response (BDM bidding phase) and the 789 amount of BDM bids. Similar to GLM1, we then calculated group averages and standard errors of 790 the mean of the Rho coefficients for each time point for all participants (Fig. 4B, C). A subsequent 791 one-sample t-test against 0 served to assess coefficient significance.

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Bar chart for revealed preference level analysis 794 We used bars to illustrate how different IC levels were encoded in each region of the brain. To 795 generate an ROI bar chart, the BOLD response was first extracted using the leave-one-out The copyright holder for this preprint (which was not peer-reviewed) is the . https://doi.org/10.1101/2020.04.06.028001 doi: bioRxiv preprint height of a white bar (higher was more). Component A was a low-sugar, high-fat milkshake.        Cluster P values (P < 0.05) with family-wise error correction across the whole brain. Map threshold 1045 P < 0.005 (across ICs; high>low IC) with exclusive contrast map P > 0.005 (along ICs), extent 1046 threshold ≥ 10 voxels. *P < 0.05 with small volume correction. indifference curves (ICs) during bundle-on phase (whole-brain analysis with GLM2).

Brain region
Hemisphere MNI peak coordinates (x,y,z) peak z-score Cluster P values (P < 0.05) with family-wise error correction across the whole brain. Map threshold (whole-brain analysis with GLM3). Cluster P values (P < 0.05) with family-wise error correction across the whole brain. Map threshold 1063 P < 0.005, extent threshold ≥ 10 voxels. *P < 0.05 with small volume correction.