I am a researcher working on topics related to subjective well-being (sometimes also called happiness).

I should preface by saying that I have relatively modest training in statistics, and the arguments put forth in this paper are quite out of my depth. For example, I have not heard of things like first order stochastic dominance before reading this paper. I hope that by being open about things that I might be somewhat ignorant, this can be a path for me to develop a deeper understanding of the concerns raised in the paper.

I think (which could well be wrong) the paper is saying that in an ordinal measure like happiness, groups and individuals differ in their 'standard' in reporting happiness (e.g., what it takes to push my happiness from 0 to 1 is different from what pushes your happiness from 0 to 1). This makes comparing 'latent' (or true level of) happiness across groups difficult, if not impossible.

Put differently, if I report a 1 and you report a 0, I cannot be certain that I am happier than you. It could be the case that my standard for reporting a 1 is lower than you. The authors showed that by changing this standard around, inferences about 'true' happiness would change.

I think this is an important point. I think happiness researchers have grappled with this to some degree (from a more abstract perspective; instead of the more statistical/mathematical perspective). E.g., A hypothesis about how people report life satisfaction is that they compare their life to an ideal life (here, the ideal life sets the standard; i.e., two people with the exact same life can have different levels of life satisfaction because they have different ideas about ideal life). Related research in social comparison could be interpreted as moving the standard for happiness higher (instead of lowering 'true' happiness). In contrast, things like gratitude may lead to higher happiness ratings because it lowers happiness standard (instead of increasing 'true' happiness). The set point hypothesis can be interpreted as 1) people fully adapting their 'true' happiness to baseline levels after experiencing major life events or 2) people create a new happiness standard after experiencing a major life event.

This paper prompts me to think harder about happiness measures. It could well be the case that the standard people set for their happiness level (a cognitive process?) may be just as important as 'true' happiness itself.