I’m still not perfectly convinced: there still seems to be a symmetric formulation. You describe it in terms of pushing instead of pulling. But what about the symmetry between expressions “an existing individual in X pushes the situation from X to Y”, versus “an existing individual in Y pulls the situation from X to Y”? Why would there be no money pump in pulling cases if there could be a money pump in a pushing case?
In the pushing case, if you make one choice, you’re sometimes compelled to change your mind: if you’ve chosen X, the individuals in X can push you towards Y. In the pulling case, the reasons to change your mind don’t apply in the option you’ve chosen: if you’ve chosen X, the individuals in Y can’t pull you towards Y, because those claims don’t come from X. The claims in Y for Y over X only make a difference if there are also claims in Y for X (or something else) over Y that they defeat, which is captured by “in Y, a stronger overall interest in Y than in X” or “in Y, a stronger overall interest in X than in Y” (or equality).
I’ll break it down into cases to illustrate:
Suppose “an existing individual in X pushes the situation from X to Y”. Then:
1. If you choose X, an individual who exists in X has a claim to Y over X, so you have reason to change your mind to Y, and this reason only applies in X, which you’ve chosen. That’s a reason to change your mind to Y, although it may ultimately be outweighed if there are other claims (but first by other claims in X, and then if there’s an overall claim in X to Y over X, i.e. in the same direction, also by claims in Y). If there are no other reasons to be concerned with, then this is not a stable solution, since you have an overall reason in X to change your mind to Y, and no other reasons in any other outcome to change your mind.
2. If you choose Y, we don’t have enough information to say anything (we don’t know if the individuals in Y have claims to anything else). The claim in X to Y over X does not apply here, since you didn’t choose X, although there could be other claims. If there are no other reasons to be concerned with, then this is a stable solution, since you have no reason in Y to change your mind.
Now, instead suppose “an existing individual in Y pulls the situation from X to Y”. Then:
1. If you choose Y, an individual who exists in Y has a claim to Y over X, so you have a reason to not change your mind to X, but this reason only applies in Y, which you’ve chosen. That’s a reason to not change your mind to X, although it may ultimately be outweighed if there are other claims (but first by other claims in Y, and then if there’s an overall claim in Y to X over Y, i.e. in the opposite direction, also by claims in X). If there are no other reasons to be concerned with, then this is a stable solution, since you have no reason in Y to change your mind.
2. If you choose X, we don’t have enough information to say anything (we don’t know if the individuals in Y have claims to anything else). The claim in Y to Y over X does not apply here, since you didn’t choose Y, although there could be other claims. If there are no other reasons to be concerned with, then this is a stable solution, since you have no reason in X to change your mind.
In the pushing case, if you make one choice, you’re sometimes compelled to change your mind: if you’ve chosen X, the individuals in X can push you towards Y. In the pulling case, the reasons to change your mind don’t apply in the option you’ve chosen: if you’ve chosen X, the individuals in Y can’t pull you towards Y, because those claims don’t come from X. The claims in Y for Y over X only make a difference if there are also claims in Y for X (or something else) over Y that they defeat, which is captured by “in Y, a stronger overall interest in Y than in X” or “in Y, a stronger overall interest in X than in Y” (or equality).
I’ll break it down into cases to illustrate:
Suppose “an existing individual in X pushes the situation from X to Y”. Then:
1. If you choose X, an individual who exists in X has a claim to Y over X, so you have reason to change your mind to Y, and this reason only applies in X, which you’ve chosen. That’s a reason to change your mind to Y, although it may ultimately be outweighed if there are other claims (but first by other claims in X, and then if there’s an overall claim in X to Y over X, i.e. in the same direction, also by claims in Y). If there are no other reasons to be concerned with, then this is not a stable solution, since you have an overall reason in X to change your mind to Y, and no other reasons in any other outcome to change your mind.
2. If you choose Y, we don’t have enough information to say anything (we don’t know if the individuals in Y have claims to anything else). The claim in X to Y over X does not apply here, since you didn’t choose X, although there could be other claims. If there are no other reasons to be concerned with, then this is a stable solution, since you have no reason in Y to change your mind.
Now, instead suppose “an existing individual in Y pulls the situation from X to Y”. Then:
1. If you choose Y, an individual who exists in Y has a claim to Y over X, so you have a reason to not change your mind to X, but this reason only applies in Y, which you’ve chosen. That’s a reason to not change your mind to X, although it may ultimately be outweighed if there are other claims (but first by other claims in Y, and then if there’s an overall claim in Y to X over Y, i.e. in the opposite direction, also by claims in X). If there are no other reasons to be concerned with, then this is a stable solution, since you have no reason in Y to change your mind.
2. If you choose X, we don’t have enough information to say anything (we don’t know if the individuals in Y have claims to anything else). The claim in Y to Y over X does not apply here, since you didn’t choose Y, although there could be other claims. If there are no other reasons to be concerned with, then this is a stable solution, since you have no reason in X to change your mind.
got it! :-)