Equivalent income versus equivalent lifetime: does the metric matter?

We examine the e¤ects of the postulated metric on the measurement of well-being, by comparing, in the (income, lifetime) space, two indexes: the equivalent income index and the equivalent lifetime index. Those in- dexes are shown to satisfy di¤erent properties concerning interpersonal well-being comparisons, which can lead to contradictory rankings. While those incompatibilities arise under distinct indi¤erence maps, we also ex- plore the e¤ects of the metric while relying on a unique indi¤erence map, and show that, even in that case, the postulated metric matters for the measurement of well-being. That point is illustrated by quantifying, by those two indexes, the (average) well-being loss due to the Syrian War. Relying on a particular metric leads, from a quantitative perspective, to di¤erent pictures of the deprivation due to the War.