The theoretical results don’t depend on the scale being 3-point. Their argument deals directly with the assumed underlying normal distributions and transforms them into log-normal distributions with the order of the expected values reversed, so it doesn’t matter how you’ve estimated the parameters of the normal distributions or if you’ve even done it at all.
In the case of life satisfaction scales, is there any empirical evidence we could use to decide the form of the underlying continuous distribution?
They do suggest that you could “use objective measures to calibrate cardinalizations of happiness”, e.g. with incidence of mental illness, or frequencies of moods, as the authors have done something similar here https://www.nber.org/papers/w19243.
Well, I confess I don’t fully understand the paper and a further social scientist I’ve since spoken to had a different take on what the paper said altogether. I’ll try to bring this up with a few more people.
The theoretical results don’t depend on the scale being 3-point. Their argument deals directly with the assumed underlying normal distributions and transforms them into log-normal distributions with the order of the expected values reversed, so it doesn’t matter how you’ve estimated the parameters of the normal distributions or if you’ve even done it at all.
In the case of life satisfaction scales, is there any empirical evidence we could use to decide the form of the underlying continuous distribution?
They do suggest that you could “use objective measures to calibrate cardinalizations of happiness”, e.g. with incidence of mental illness, or frequencies of moods, as the authors have done something similar here https://www.nber.org/papers/w19243.
Well, I confess I don’t fully understand the paper and a further social scientist I’ve since spoken to had a different take on what the paper said altogether. I’ll try to bring this up with a few more people.