I don’t trust the transitivity axiom of VNM utility. Thought I should mention this to make it clear that the “most of us” in your post is not a rhetorical device and there really are actual people who don’t buy into the VNM hegemony.
Answering for myself, my unreflective preferences are nontransitive on problems like dust specks vs torture. I prefer N years of torture for X people to N years minus 1 second of torture for 1000X people, and any time of torture for X people over the same time of very slightly less painful torture for 1000X people, and yet I prefer a very slight momentary pain for any number of people, however large, to 50 years of torture for one person.
If I ever reverse the latter preference, it will be because I will have been convinced by theoretical/abstract considerations that non transitive preferences are bad (and because I trust the other preferences in the cycle more), but I don’t think I will ever introspect it as a direct preference by itself.
If I ever reverse the latter preference, it will be because I will have been convinced by theoretical/abstract considerations that non transitive preferences are bad (and because I trust the other preferences in the cycle more), but I don’t think I will ever introspect it as a direct preference by itself.
So suppose we use the dust specks vs. torture situation to construct a cycle of options A1, A2, …, An, in which you prefer A1 to A2, A2 to A3, and so on, and prefer An to A1. (For example, say that A1 is 50 years of torture for one person, and the other options spread things out over more people up until An is dust specks for lots of people.)
If you were asked to choose between any of the options A1 through An, which one do you pick? And why?
That might depend strongly on the filling-in details and on how the choice is framed. I can’t visualize all the options and compare them together, so I always end up comparing the nearby cases and then running through the loop. I suspect that forced to make the choice I would say An (the dust specks) but more because of it being a Schelling point than any substantial, defensible reason. And I would say it while still endorsing A(n-1) to be better than An.
I don’t trust the transitivity axiom of VNM utility. Thought I should mention this to make it clear that the “most of us” in your post is not a rhetorical device and there really are actual people who don’t buy into the VNM hegemony.
Thanks for pointing that out. I did try to make it clear that the essay was about “if you trust VNM, here’s what it means”.
I, for one, trust the transitivity axiom. It seems absurd to value going in circles, but only if you run into the right lotteries.
Maybe you could give an example of a preference cycle you think is valuable, so they rest of us could see where our intuitions diverge?
Out of curiosity, why don’t you trust the transitivity axiom?
Because when I introspect on my preferences it doesn’t seem to hold.
Examples?
Answering for myself, my unreflective preferences are nontransitive on problems like dust specks vs torture. I prefer N years of torture for X people to N years minus 1 second of torture for 1000X people, and any time of torture for X people over the same time of very slightly less painful torture for 1000X people, and yet I prefer a very slight momentary pain for any number of people, however large, to 50 years of torture for one person.
If I ever reverse the latter preference, it will be because I will have been convinced by theoretical/abstract considerations that non transitive preferences are bad (and because I trust the other preferences in the cycle more), but I don’t think I will ever introspect it as a direct preference by itself.
Nicely put.
So suppose we use the dust specks vs. torture situation to construct a cycle of options A1, A2, …, An, in which you prefer A1 to A2, A2 to A3, and so on, and prefer An to A1. (For example, say that A1 is 50 years of torture for one person, and the other options spread things out over more people up until An is dust specks for lots of people.)
If you were asked to choose between any of the options A1 through An, which one do you pick? And why?
That might depend strongly on the filling-in details and on how the choice is framed. I can’t visualize all the options and compare them together, so I always end up comparing the nearby cases and then running through the loop. I suspect that forced to make the choice I would say An (the dust specks) but more because of it being a Schelling point than any substantial, defensible reason. And I would say it while still endorsing A(n-1) to be better than An.
Can you give an example? I am having a hard time imagining preferences contradicting that axiom (which is a failure on my part).