So, I am trying to talk about the preferences of the couple, not the preferences of either individual. You might reject that the couple is capable of having preference, if so I am curious if you think Bob is capable of having preferences, but not the couple, and if so, why?
I agree if you can do arbitrary utility transfers between Alice and Bob at a given exchange rate, then they should maximize the sum of their utilities (at that exchange rate), and do a side transfer. However, I am assuming here that efficient compensation is not possible. I specifically made it a relatively big decision, so that compensation would not obviously be possible.
Whether the couple is capable of having preferences probably depends on your definition of “preferences.” The more standard terminology for preferences by a group of people is “social choice function.” The main problem we run into is that social choice functions don’t behave like preferences.
I should probably expand on this—it can make sense to have a mechanism or decision-making rule that’s inefficient or irrational for reasons of incentive compatibility, information or computational limits, or other practical constraints. That said, we should be very explicit about describing these as mechanisms, institutions, or collective decision rules and not as preferences. These are second-best tools for governance that lack basic properties you’d expect of human preferences. Actually, as Harsanyi proved back in the 1950s, the unique social choice function—up to affine transformations—which preserves individual rationality (i.e. really can be called a group’s “preferences”) is the utilitarian rule. For the same reason I’d reject calling this “geometric rationality” rather than one of the common names already used for this technique (e.g. the proportional-fair rule, Nash bargaining—or just geometric maximization for the whole family of methods).
If we’re not very clear when we describe this, it confuses the hell out of people who start to think these are alternative, contradictory formulations of rationality, and then use these arguments to reject VNM-rationality.
So, I am trying to talk about the preferences of the couple, not the preferences of either individual. You might reject that the couple is capable of having preference, if so I am curious if you think Bob is capable of having preferences, but not the couple, and if so, why?
I agree if you can do arbitrary utility transfers between Alice and Bob at a given exchange rate, then they should maximize the sum of their utilities (at that exchange rate), and do a side transfer. However, I am assuming here that efficient compensation is not possible. I specifically made it a relatively big decision, so that compensation would not obviously be possible.
Whether the couple is capable of having preferences probably depends on your definition of “preferences.” The more standard terminology for preferences by a group of people is “social choice function.” The main problem we run into is that social choice functions don’t behave like preferences.
I should probably expand on this—it can make sense to have a mechanism or decision-making rule that’s inefficient or irrational for reasons of incentive compatibility, information or computational limits, or other practical constraints. That said, we should be very explicit about describing these as mechanisms, institutions, or collective decision rules and not as preferences. These are second-best tools for governance that lack basic properties you’d expect of human preferences. Actually, as Harsanyi proved back in the 1950s, the unique social choice function—up to affine transformations—which preserves individual rationality (i.e. really can be called a group’s “preferences”) is the utilitarian rule. For the same reason I’d reject calling this “geometric rationality” rather than one of the common names already used for this technique (e.g. the proportional-fair rule, Nash bargaining—or just geometric maximization for the whole family of methods).
If we’re not very clear when we describe this, it confuses the hell out of people who start to think these are alternative, contradictory formulations of rationality, and then use these arguments to reject VNM-rationality.