Therre’s something a bit odd about the formulation U = U1 + aV = U1 + aV1 + abU1 = … The term abU1 amplifies your “autologous” utility U1 by adding the value you place on the value the other gets from knowing that you are getting U1. And there will be additional terms ababU1, abababU1, etc. like a series of reflections in a pair of mirrors. If ab is close to 1 then both of your autologous utilities get hugely amplified. (BTW, this is where dependence on b shows up: the larger b is, the greater the utility you get over U1 + aV1, by a factor of 1/(1-ab).)
Would U = U1 + aV1, V = V1 + bU1 be more realistic? You’re still trying to maximise U1+aV1, but without the echo chamber of multiple orders of vicarious utility.
Or you could carry it on one term further, allowing two orders of vicarious utility: U = U1 + aV1 + abU1 = (1+ab)U1 + aV1, and V = (1+ab)V1 + bU1.
I am not sure there is a principled way to decide among these.
Therre’s something a bit odd about the formulation U = U1 + aV = U1 + aV1 + abU1 = … The term abU1 amplifies your “autologous” utility U1 by adding the value you place on the value the other gets from knowing that you are getting U1. And there will be additional terms ababU1, abababU1, etc. like a series of reflections in a pair of mirrors. If ab is close to 1 then both of your autologous utilities get hugely amplified. (BTW, this is where dependence on b shows up: the larger b is, the greater the utility you get over U1 + aV1, by a factor of 1/(1-ab).)
Would U = U1 + aV1, V = V1 + bU1 be more realistic? You’re still trying to maximise U1+aV1, but without the echo chamber of multiple orders of vicarious utility.
Or you could carry it on one term further, allowing two orders of vicarious utility: U = U1 + aV1 + abU1 = (1+ab)U1 + aV1, and V = (1+ab)V1 + bU1.
I am not sure there is a principled way to decide among these.