<p>Economists routinely measure individual welfare by (von-Neumann-Morgenstern) utility, for instance when analysing welfare intensity, social welfare, or welfare inequality. Is this welfare measure justified? Natural working hypotheses turn out to imply a different measure. It overcomes familiar problems of utility, by faithfully capturing non-ordinal information, such as welfare intensity – despite still resting on purely ordinal evidence, such as revealed preferences or self-reported welfare comparisons. Social welfare analysis changes when based on this new individual welfare measure rather than utility. For instance, Harsanyi’s ‘utilitarian theorem’ now supports prioritarianism. We compare the standard utility-based versions of utilitarianism and prioritarianism with new versions based on our welfare measure. We show that utility is a hybrid object determined by two rival influences: welfare and the attitude to intrinsic risk, i.e., to risk in welfare. A new version of Harsanyi’s theorem shows that Harsanyi makes the questionable implicit assumption that society is neutral to intrinsic risk, overruling people’s risk attitudes. We thus propose <i>risk-impartial utilitarianism</i>, which adopts people’s (average) risk attitude.</p>