The name is absent

Person A tends to use the upper part of the scale for positive feelings and the lower part for
negative feelings, while person B uses the upper part for negative feelings and the lower part
for the positive ones. The ordinal ranking of activities according to each feeling is unaffected
by this difference in the use of the scale. The U-index, however, will be much lower for
person A than for person B. Layard’s (2009) critique of the U-index is that it does not
overcome the ordinality problem, but loses a lot of information compared to other directly
cardinal measures. Loewenstein (2009) argues that the U-index depends substantially on what
emotions are included in the questionnaire. Even if people are able to assess the strength of
the various emotions they experienced, it is not clear how these emotions should be weighted
against each other. “Ecstatic” is a stronger feeling than “happy”. If the emotion “happy” on
the questionnaire were replaced by “ecstatic”, respondents’ assessment of the strength of this
emotion on the scale from 0 to 10 would certainly go down. If people simultaneously reported
some negative feelings too, more episodes would turn from positive into negative
experiences, although the “true” emotional state would remain unchanged.

Since no truly ordinal aggregation of emotions appears feasible, and any weighting of the
various emotions is arbitrary, we propose a new measure of a person’s emotional state that
assumes cardinality, but leaves the aggregation to the respondent himself. In the style of the
standard life satisfaction question, we ask respondents to answer the question “How satisfied
were you during this activity?” on a scale from 0 to 10 before we ask them about any specific
emotions. We call the respondents’ assessment episode satisfaction. By answering the
question, the respondent himself has to weight which of his emotions was most important
with regard to his overall satisfaction during some activity. The advantage of episode
satisfaction is thus that it leaves the aggregation of emotions to the respondent himself. A
person’s assessments of the satisfaction experienced during each episode is aggregated over
the entire day in the following way, where Ej denotes the episode satisfaction measure of
person i during activity j.

E_i =∑h_ijE_ij .                                         (6)

^j

Taking account of the fact that all three measures have their advantages and disadvantages, in
what follows we present results for all three measures throughout.

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