Equivalent income versus equivalent lifetime: does the metric matter?

We examine the effects 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. The conditions under which the equivalent lifetime index exists are more restrictive than the ones under which the equivalent income index exists, but it is possible to define an alternative equivalent lifetime index, based on two reference income levels, for which the non-existence problem is less acute. Those indexes are also shown to satisfy different properties concerning interpersonal well-being comparisons, which can lead to contradictory rankings. While those incompatibilities arise under distinct indifference maps, we also explore the effects of the metric while relying on a unique indifference map, and show that, even in that case, the postulated metric matters for the measurement of well-being.