not really understanding how ordinal moral theories are really meant to work
Yeah, I think this is where I’m at too. It seems inescapable that ordinal preferences have cardinal implications when combined with empirical uncertainty (e.g. if I prefer a 20% chance of A to an 80% chance of B, that implies I like A at least four times as much). The only choice we really have is whether the corresponding cardinal implications are well-formed (e.g. Dutch bookable). The best distinctions I can come up with are:
In a purely deterministic world without lotteries, there wouldn’t be an obvious mechanism forcing the cardinalization of ordinal preferences. So their overlap is only a contingent feature of the world we find ourselves in. (Though see A Theory of Experienced Utility and Utilitarianism for an alternate basis for cardinalization.)
Ordinal preferences only specify a unique cardinalization in the limit of an infinite sequence of choices. Since we aren’t likely to face an infinite sequence of choices any time soon, they’re distinct in practice.
P.S. Thanks for the Tarsney link. I have it open in a tab and should get around to reading it at some point.
Plus there’s the roadblock of me not having in-depth understanding of how the vNM utility theorem is meant to work.
Not sure if it’ll help but I have a short explanation and interactive widget trying to explain it here.
Those are two interesting distinctions. I don’t have anything to add on that, but thanks for sharing those thoughts.
Not sure if it’ll help but I have a short explanation and interactive widget trying to explain it here.
Oh, you’re the person who made this value of information widget! I stumbled upon that earlier somehow, and am likely to link to it in a later post on applying VoI ideas to moral uncertainty.
Thanks for sharing the vNM widget; I intend to look at that soon.
Yeah, I think this is where I’m at too. It seems inescapable that ordinal preferences have cardinal implications when combined with empirical uncertainty (e.g. if I prefer a 20% chance of A to an 80% chance of B, that implies I like A at least four times as much). The only choice we really have is whether the corresponding cardinal implications are well-formed (e.g. Dutch bookable). The best distinctions I can come up with are:
In a purely deterministic world without lotteries, there wouldn’t be an obvious mechanism forcing the cardinalization of ordinal preferences. So their overlap is only a contingent feature of the world we find ourselves in. (Though see A Theory of Experienced Utility and Utilitarianism for an alternate basis for cardinalization.)
Ordinal preferences only specify a unique cardinalization in the limit of an infinite sequence of choices. Since we aren’t likely to face an infinite sequence of choices any time soon, they’re distinct in practice.
P.S. Thanks for the Tarsney link. I have it open in a tab and should get around to reading it at some point.
Not sure if it’ll help but I have a short explanation and interactive widget trying to explain it here.
Those are two interesting distinctions. I don’t have anything to add on that, but thanks for sharing those thoughts.
Oh, you’re the person who made this value of information widget! I stumbled upon that earlier somehow, and am likely to link to it in a later post on applying VoI ideas to moral uncertainty.
Thanks for sharing the vNM widget; I intend to look at that soon.