Private, subjective beliefs about uncertainty have been found to have idiosyncratic computational and neural substrates yet, humans share such beliefs seamlessly and cooperate successfully. Bringing together decision making under uncertainty and interpersonal alignment in communication, in a discovery plus pre-registered replication design, we examined the neurocomputational basis of the relationship between privately held and socially shared uncertainty. Examining confidence-speed-accuracy trade-off in uncertainty-ridden perceptual decisions under social vs isolated context, we found that shared (i.e. reported confidence) and subjective (inferred from pupillometry) uncertainty dynamically followed social information. An attractor neural network model incorporating social information as top-down additive input captured the observed behavior and demonstrated the emergence of social alignment in virtual dyadic simulations. Electroencephalography showed that social exchange of confidence modulated the neural signature of perceptual evidence accumulation in the central parietal cortex. Our findings offer a neural population model for interpersonal alignment of shared beliefs.