The agent-neutral values are now denoted by variables instead of numbers. The worst case is represented by z , where the agent neither enjoys the beneﬁts of PAP, nor those of RXR. y represents the value yielded by the choice of PAP whereasx corresponds to the value yielded by the choice of RXR. The best case arises if the agent chooses PAP while RXR is not necessary, since then the agent-neutral value incorporates the beneﬁts of PAP and RXR, amounting to w. Therefore, clearly the following relation holds:

w>x>y>z

From there, the equivalence under question follows.

I guess I don’t understand why w > x > y > z implies w—y = x—y iff w—x = y—z. Sorry if this is a standard result I’ve forgotten, but at first glance it’s not totally obvious to me.

Maybe it gets clearer if you compare the relative values of the 4 variables.w−y corresponds to the benfits of RXR, x−z also corresponds to the benefits of RXR. But maybe I was not precise enough: The equivalence does not follow only from w>x>y>z, we also need to take into account the definitions of the 4 variables. Do you see what I mean?

The reasoning is the following:

The agent-neutral values are now denoted by variables instead of numbers.

w>x>y>zThe worst case is represented by z , where the agent neither enjoys the beneﬁts

of PAP, nor those of RXR. y represents the value yielded by the choice of

PAP whereasx corresponds to the value yielded by the choice of RXR. The

best case arises if the agent chooses PAP while RXR is not necessary, since

then the agent-neutral value incorporates the beneﬁts of PAP and RXR,

amounting to w. Therefore, clearly the following relation holds:

From there, the equivalence under question follows.

Do you agree?

I guess I don’t understand why w > x > y > z implies w—y = x—y iff w—x = y—z. Sorry if this is a standard result I’ve forgotten, but at first glance it’s not totally obvious to me.

Maybe it gets clearer if you compare the relative values of the 4 variables.w−y corresponds to the benfits of RXR, x−z also corresponds to the benefits of RXR. But maybe I was not precise enough: The equivalence does not follow only from w>x>y>z, we also need to take into account the definitions of the 4 variables.

Do you see what I mean?