Incomplete Preferences, Well-Being Measurement, and the Identification of the Worst-Off

When individual preferences are incomplete, the information available for well-being measurement is interval-valued rather than point-identified. We show that in this case, well-being measurement involves an unavoidable normative choice: any procedure that delivers policy-relevant complete rankings must resolve incomparability in a substantive way. We axiomatically characterize wellbeing measures under incomplete preferences and show that any measure satisfying four natural axioms must aggregate the bounds using a Hurwicz criterion indexed by a parameter that governs the weight placed on the upper bound. We then use survey data from 2,050 Dutch adults to document that incomplete preferences over income, health, and social relations are empirically prevalent. Different resolutions of incompleteness have first-order distributive consequences. In particular, evaluating individuals at the lower bound systematically prioritizes those with the most incomplete preferences rather than those with the lowest outcomes: only 42 percent of individuals in the bottom decile under the lower-bound approach remain there under the upper-bound approach, and measured inequality varies by up to five Gini points. Measuring well-being under incomplete preferences therefore requires explicit normative choices about how interval-valued information is aggregated.