For a given subjective well-being (SWB) scale, say life satisfaction, is going from 7 to 8 for one person equivalent to another person going from 2 to 3? This is the question of whether the scales exhibit interpersonal cardinality. Let’s unpack this concern in stages.
Are SWB scales cardinal or ordinal?
The first question to ask is: does the underlying phenomena of interest - the thing the SWB scales are trying to measure - have a cardinal structure, or is it merely ordinal? That is, it represents something that can be quantified - like length, height, weight, etc. - or does it merely represent an ordering - like ‘A is taller than B’? (1st, 2nd, 3rd … are the ordinal numbers, 1, 2, 3, … are the cardinal numbers).
It is intuitively obvious that happiness is cardinal, as revealed by our linguistic use. It is entirely sensible to say “X hurt twice as much as Y” or “I feel 10 times better than I did yesterday”. If happiness were ordinal, the most we could say would be “X hurts worse than Y” and “I feel better today than I did yesterday”.
If life satisfaction scales capture a psychological state of satisfaction, then this would be cardinal; as above, intuitively, one can feel twice as satisfied about X vs Y.
Are SWB scales linear or logarithmic?
Given the underlying phenomena of interest has a cardinal structure, the next question is whether individuals’ reporting on the scale is equal-interval (another term for this is linear), i.e. going from 5/10 to 6/10 is an equivalent improvement as going from 7/10 to 8/10. One worry is that individuals interpret SWB scales as logarithmic, like the Richter scale, where the magnitude of going from 6/10 to 7/10 is 10 times that of going from 5/10 to 6/10, rather than as linear/equal-interval.
While possible, non-linear reporting seem unlikely. Experimental evidence from Van Praag (1993) suggests that when presented with a number of (non SWB-related) points, respondents automatically treat the difference between points as roughly equal-interval. Further, it is intuitively much harder for ordinary people (i.e. non-mathematicians) to report how happy/satisfied they feel on a logarithmic scale than a linear one. If I ask myself “how happy am I right now in a 0-10 logarithmic scale?” to try to answer this question I first have to think “how happy am I on a linear, 0-10 scale?” I then try to remember how logarithms work and convert from there. This is so much harder to do that I assume scale use must be equal-interval.
Given the scales have intrapersonal cardinality, the final question is whether they have interpersonal cardinality: is one person’s reported one point increase on a 0 to 10 scale equivalent to a one point increase for someone else?
There are two different concerns here. First, individuals could correctly report where they are between the minimum and maximum points of the scales, but have different capacities for SWB. There could be ‘utility monsters’ who experience 1000 times more happiness than others. Second, individuals could have the same maximum and minimum capacities, but use the scales differently. Suppose almost everyone reports a given sensation as 6/10, but a few people report the same feeling as an 8/10; keeping the same terminology, this latter group are ‘language monsters’.
We can make the same reply to both concerns. So long as these differences are randomly distributed in the surveyed population, they will wash out as ‘noise’ across large numbers of people: there will be as many people with a greater capacity for SWB as those with less, and as many who use the scale too conservatively as use it too generously.
Specifically, in response to utility monsters, it seems unlikely, given our shared biology, that the utility capacities of humans will, in practice, vary by very much.
Regarding the language worry, I observe we do tend to, in general, regulate one another’s language use. For instance, if I say “I’m having a terrible day: I stubbed my toe” you are likely to say “Hold on. That’s not a terrible day. That’s a mildly bad day”. A hypothesis, which could conceivably be tested, is that this language regulation pushes us towards using SWB scales in a similar way. If language did not have a shared meaning, it would be of no use at all.
We might object to the this last point that, even if groups regulate their members’ language use, different groups could still use scales differently. As an empirical test on this, a study by Helliwell et al. (2016) of immigrants moving from over 100 different countries to Canada found that, regardless of country of origin, the average levels and distributions of life satisfaction among immigrants mimic those of Canadians, suggesting LS reports are primarily driven by life circumstances. If there really was substantial cultural difference in LS scale use, this result would not occur.
Therefore, it seems reasonable to interpret SWB data as interpersonally cardinal. However, as this point seems important, more work here would be welcome.
 A doubt here is whether, given the diversity of experiences, there is any one property that all happy (and unhappy) experiences have, such that we can quantify them on a single scale. Following Crisp (2006) I think there is: the property of pleasantness, or ‘hedonic tone’. Even though headaches and heartbreaks feel different, I find nothing confusing in saying one can feel as bad as another. For dissent, see, e.g. Nussbaum (2012)
 An alternative motivation for measuring life satisfaction is that it captures a cognitive judgement of the extent to which someone’s preferences are satisfied - i.e. the world is going the way they want it to - rather than a feeling. If unclear if preferences can be cardinal. As Hausmann (1995) argues at length, while we can order preferences (preferences are about how entire worlds go), there is in principle no conceptual unit of distance between our ranked preferences to generate cardinality. This is too much of a diversion to discuss further here. Given we are ultimately interested in happiness here, and evaluations are relevant only as proxies for, it seems convenient to side-step the problem say evaluations capture a felt strength of satisfaction.
 The worry individuals may self-report in this way has been raised with me separately by Toby Ord and James Snowden.
 If it turned out reported SWB was a function of log(actual SWB) that wouldn’t make it impossible to make interpersonal cardinal comparisons: we simply need to convert individuals’ scores onto a linear scale.
 We might reasonably worry this assumption does not hold if we wished to compare current humans to either (a) non-human animals or (b) some hypothetical future humans that are genetically modified to be happier. These are not issues that need trouble us here.