Measuring What Has No Units

Governments now publish wellbeing figures drawn from asking people to rate their lives from nought to ten. The obvious objection is that the answers are subjective, but it is weaker than it looks. Reported ratings track things that can be observed independently: they fall on the day of a bereavement, they fall for the long-term unemployed, and they recover on schedules that differ predictably between the two. A number that behaves as a real quantity would behave is doing some of the work of a measurement.

[A] The serious difficulty is arithmetical rather than philosophical. A scale of this kind gives the order of the responses but not the distance between them, and every published average assumes those distances are equal. [B] Nothing guarantees that the step from six to seven matches the step from two to three, and if it does not, two populations with identical averages may be nothing alike. [C] Some economists reply that the assumption can be tested by seeing whether conclusions survive when the scale is stretched, and for many findings they do. [D] Others hold that a quantity which changes under a permitted rescaling was never a quantity, and that survival shows only robustness. The dispute is unsettled, which is worth remembering whenever a figure is quoted to one decimal place.