Working Paper Series 2401 - A Happy Probability About Happiness (and Other) Scales:

The data are often treated as cardinal – that is, a difference between a 2 and a 3 for one person is the same as that of a 5 to a 6 of another. [...] This is indicative of comparability in the population they examine, but different groups may attempt different meanings to their scales.1 The state of the literature is such that is difficult to get a clear sense of what the problems are, how serious they are, and whether background theory and current evidence better support optimism or pessimism about the cardinality assumption. [...] What is the rational way for respondents to interpret subjective scales? The Grice-Schelling account Discussions about the nature of subjective scales – that is, the assumptions of linearity and comparability – tend to be quite mathematical. [...] The most famous illustration of the Schelling point is the New York question: if you are to meet a stranger in New York City, but you cannot communicate with the person, when and where will you choose to meet? Thomas Schelling, the economist after whom the term is named, asked a group of students this question, and found the most common answer was noon at the information booth at Grand Central Sta. [...] Arc-tangential relationship Why is the rational choice to use the realistic limits for the scale endpoints? If the endpoints don’t cover the full range of intensity levels, we are going to run out of room on our scales.