If you can turn a bunch of “A is worse than B” statements into a cardinal ordering, then why do you need the population equivalence questions at all? Why not just include “perfect health” and “death” among your disabilities? Then we can eventually say “the difference between perfect health and A is X% of the difference between perfect health and death.”
I guess part of my confusion is I don’t really see how you can get this cardinal ordering from the data. So let’s say we find that condition A is universally considered worse than all other conditions. Perhaps it’s “death”, perhaps it’s just clearly the worst of the conditions we’re looking at. How can statistics give us a ratio by which it’s worse? If somehow it were twice as bad we would still see it be considered as “worst” in all it’s comparisons.
You are correct. You can’t really turn the ordinal stuff into a cardinal ordering, just into a kind of proxy ordering that has some cardinal structure, but it might not correspond to the cardinal structure we care about. For example if ‘perfect health’ was added and 100% of people ranked this above the other choice, then it would end up very far (possibly infinitely far) from the nearest option on the cardinal scale. What it is really measuring is the amount of disagreement about things at this part of the ordering, which is a proxy for closeness of the health levels, but there are cases like ‘perfect health’ vs slightly worse than that where they are close but there is no disagreement.
If you can turn a bunch of “A is worse than B” statements into a cardinal ordering, then why do you need the population equivalence questions at all? Why not just include “perfect health” and “death” among your disabilities? Then we can eventually say “the difference between perfect health and A is X% of the difference between perfect health and death.”
I guess part of my confusion is I don’t really see how you can get this cardinal ordering from the data. So let’s say we find that condition A is universally considered worse than all other conditions. Perhaps it’s “death”, perhaps it’s just clearly the worst of the conditions we’re looking at. How can statistics give us a ratio by which it’s worse? If somehow it were twice as bad we would still see it be considered as “worst” in all it’s comparisons.
You are correct. You can’t really turn the ordinal stuff into a cardinal ordering, just into a kind of proxy ordering that has some cardinal structure, but it might not correspond to the cardinal structure we care about. For example if ‘perfect health’ was added and 100% of people ranked this above the other choice, then it would end up very far (possibly infinitely far) from the nearest option on the cardinal scale. What it is really measuring is the amount of disagreement about things at this part of the ordering, which is a proxy for closeness of the health levels, but there are cases like ‘perfect health’ vs slightly worse than that where they are close but there is no disagreement.