In a number of jurisdictions there is increasing interest in incorporating concerns for fairness in models for economic evaluation of health interventions. Cost–value analysis is a name for evaluations with such a broader aim. The most widely held concern for fairness is a concern for the worse off, i.e. the idea that severity of illness should count in determining priorities. In economic evaluations of improvements in health-related quality of life this concern may be taken into account by replacing conventional health state utilities with societal values for health states that are characterised by strong upper end compression and decreasing marginal value of utility gains. We review evidence on the strength of concerns for the worse off--measured at the cardinal level--in 15 articles published in peer-reviewed journals in the time period 1978–2010, with reports from altogether 20 individual studies in nine different countries. We report 116 individual observations of paired comparisons of utility improvements with different start levels. Concerns for severity show up quite strongly across countries, sample types and question framings. By means of regression analyses we fit a societal value function to the data that has the property of decreasing marginal value of utility gains. Using the central tendency in the data we present two plausible transformations of EQ-5D utilities into societal values that reflect concerns for the worse off.