Introduction: Wellbeing policy analysis is often criticized for requiring a cardinal interpretation of measurement scales, such as ranking happiness on an integer scale from 0-10. The commonly-used scales also implicitly constrain the human capacity for experience, typically that our most intense experiences can only be at most ten times more intense than our mildest experiences. This paper presents the alternative “heavy-tailed valence” (HTV) hypothesis: the notion that the accessible human capacity for emotional experiences of pleasure and pain spans a minimum (...) of two orders of magnitude. Methods: We specify five testable predictions of the HTV hypothesis. A pilot survey of adults aged 21-64 (n = 97) then tested two predictions, asking respondents to comment on the most painful and most pleasurable experiences they can recall, alongside the second most painful and pleasurable experiences. Results: The results find tentative support for the hypothesis. For instance, over half of respondents said their most intense experiences were at least twice as intense as the second most intense, implying a wide capacity overall. Simulations further demonstrate that survey responses are more consistent with underlying heavy-tailed distributions of experience than a “constrained valence” psychology. Discussion: A synthesis of these results with prior findings suggests a “kinked” scale, such that a wide range of felt experience is compressed in reports at the high end of intensity scales, even if reports at lower intensities behave more cardinally. We present a discussion of three stylized facts that support HTV and six against, lessons for a future survey, practical guidelines for existing analyses, and implications for current policy. We argue for a dramatic increase in societal ambition. Even in high average income countries, the HTV hypothesis suggests we remain far further below our wellbeing potential than a surface reading of the data might suggest. (shrink)