The net affect-measure preserves much of the original information even after aggregation
(in particular, the strength of positive and negative emotions), but suffers from the
disadvantage any cardinal measure possesses: it is unclear what the scale of measurement
really refers to and whether different people interpret the scale in the same way. These issues
are addressed by the U-index (for “unpleasant” or “undesirable”) that does not require a
cardinal conception of individuals’ feelings. Kahneman and Krueger (2006) define the U-
index as the proportion of time in which the highest-rated feeling was a negative one. The U-
index can be computed for each individual, i.e. the fraction of a person’s waking time that is
spent in an unpleasant state, or for each activity, i.e. the fraction of the time people spend on a
specific activity that is experienced as unpleasant (Krueger et al. 2009). The U-index for
person i engaged in activity j is defined by
1 if max{NAi1,...,NAik,...,NAiK} >max{PAi1,...,PAil,...,PAiL}
(3)
ijijijijijij
0 otherwise
The U-index for individual i is calculated by weighting the U-index for each activity, Uij, by
the fraction of time the individual was engaged in that activity, hjj :
Ui=∑hijUij. (4)
j
The U-index for activity j is then given by
Uj=∑ ⅛√∑ hj. (5)
ii
According to Kahneman and Krueger (2006), the U-index has the favorable property that it
relies only on an ordinal ranking of feelings. In particular, the U-index is independent of scale
effects. If one person uses only values between 2 and 4 to characterize his feelings, while
another person uses the full scale from 0 to 6 but ranks his feelings in the same order, both
people will have the same U-index (whereas the same does not necessarily hold for net
affect).
Other authors have questioned the validity of the U-index as an ordinal measure. Layard
(2009) claims that if the assessment of feelings is truly ordinal, the U-index does not
overcome the problem that the reported strength of feelings cannot be aggregated in a
meaningful way. Suppose, for example, that two people have the same “true”, but
unobservable strengths of feelings. Both people use the 11-point-scale in different ways.