Rather than talking about reversibility, can this situation be described just by saying that the probability of certain opportunities is zero? For example, if John and David somehow know in advance that no one will ever offer them pepperoni in exchange for anchovies, then the maximum amount of probability mass that can be shifted from mushrooms to pepperoni by completing their preferences happens to be zero. This doesn’t need to be a physical law of anchovies; it could just be a characteristic of their trade partners.
But in this hypothetical, their preferences are effectively no longer strongly incomplete—or at least, their trade policy is no longer strongly incomplete. Since we’ve assumed away the edge between pepperoni and anchovies, we can (vacuously) claim that John and David will collectively accept 100% of the (non-existent) trades from anchovies to pepperoni, and it becomes possible to describe their trade policy as being a utility maximizer. (Specifically, we can say anchovies = mushrooms because they won’t trade between them, and say pepperoni > mushrooms because they will trade mushrooms for pepperoni. The original problem was that this implies that pepperoni > anchovies, which is false in their preferences, but it is now (vacuously) true in their trade policy if such opportunities have probability zero.)
It seems to me that it’s not right to assume the probability of opportunities to trade are zero?
Suppose both John and David are alive on a desert island right now (but slowly dying), and there’s a chance that a rescue boat will arrive that will save only one of them, leaving the other to die. What would they contract to? Assuming no altruistic preferences, presumably neither would agree to only the other person being rescued.
It seems more likely here that bargaining will break down, and one of them will kill off the other, resulting in an arbitrary resolution of who ends up on the rescue boat, not a “rational” resolution.
Doesn’t irreversibility imply that there is zero probability of a trade opportunity to reverse the thing? I’m not proposing a new trait that your original scenario didn’t have; I’m proposing that I identified which aspect of your scenario was load-bearing.
I don’t think I understand how your new hypothetical is meant to be related to anything discussed so far. As described, the group doesn’t have strongly incomplete preferences, just 2 mutually-exclusive objectives.
Zero probability of trade is indeed the feature which would make the argument in the OP potentially not go through, when irreversibility is present. (Though we would still get a weakened form of the argument from the OP, in which we complete the preferences by adding a preference for a trade which has zero probability, and the original system is indifferent between that completion and its original preferences.)
Rather than talking about reversibility, can this situation be described just by saying that the probability of certain opportunities is zero? For example, if John and David somehow know in advance that no one will ever offer them pepperoni in exchange for anchovies, then the maximum amount of probability mass that can be shifted from mushrooms to pepperoni by completing their preferences happens to be zero. This doesn’t need to be a physical law of anchovies; it could just be a characteristic of their trade partners.
But in this hypothetical, their preferences are effectively no longer strongly incomplete—or at least, their trade policy is no longer strongly incomplete. Since we’ve assumed away the edge between pepperoni and anchovies, we can (vacuously) claim that John and David will collectively accept 100% of the (non-existent) trades from anchovies to pepperoni, and it becomes possible to describe their trade policy as being a utility maximizer. (Specifically, we can say anchovies = mushrooms because they won’t trade between them, and say pepperoni > mushrooms because they will trade mushrooms for pepperoni. The original problem was that this implies that pepperoni > anchovies, which is false in their preferences, but it is now (vacuously) true in their trade policy if such opportunities have probability zero.)
It seems to me that it’s not right to assume the probability of opportunities to trade are zero?
Suppose both John and David are alive on a desert island right now (but slowly dying), and there’s a chance that a rescue boat will arrive that will save only one of them, leaving the other to die. What would they contract to? Assuming no altruistic preferences, presumably neither would agree to only the other person being rescued.
It seems more likely here that bargaining will break down, and one of them will kill off the other, resulting in an arbitrary resolution of who ends up on the rescue boat, not a “rational” resolution.
Doesn’t irreversibility imply that there is zero probability of a trade opportunity to reverse the thing? I’m not proposing a new trait that your original scenario didn’t have; I’m proposing that I identified which aspect of your scenario was load-bearing.
I don’t think I understand how your new hypothetical is meant to be related to anything discussed so far. As described, the group doesn’t have strongly incomplete preferences, just 2 mutually-exclusive objectives.
Zero probability of trade is indeed the feature which would make the argument in the OP potentially not go through, when irreversibility is present. (Though we would still get a weakened form of the argument from the OP, in which we complete the preferences by adding a preference for a trade which has zero probability, and the original system is indifferent between that completion and its original preferences.)