We highlight a new paradox for the social evaluation of risk that bears on the evaluation of individual well-being rather than social welfare, but has serious implications for social evaluation. The paradox consists in a tension between rationality, respect for individual preferences, and a principle of informational parsimony that excludes individual risk attitudes from the assessment of riskless situations. No evaluation criterion can satisfy these three principles. This impossibility result has implications for the evaluation of social welfare under risk, especially when the preferences of some individuals are not known. It generalizes existing impossibility results, while relying on very weak principles of social rationality and respect for individual preferences. We explore the possibilities opened by weakening each of our three principles and discuss the advantages and drawbacks of these different routes.