Our first question is whether you intend to merge your finances.
We do, at least because I’m the only one who has income.
My next question is why the KS solution vs the Nash solution to the bargaining problem?
I’m actually not sure about this. Initially I favored KS because monotonicity seemed more natural than independence of irrelevant alternatives. But then I realized than in sequential decision making, IIA is important because it allows you to consistently optimize your policy on a certain branch of the decision tree even if you made suboptimal actions in the past. There seems to be a way of working around this violation of IIA in KS, but it makes KS look more like a hack.
But also are you sure the Shapley value doesn’t make more sense here?
Shapley value is for distributing transferable values, like money. For general utility functions there’s no easy way to convert 1 Vanessa-utilon to 1 Marcus-utilon.
Thanks so much for sharing this. It’s so sweet and nerdy and heart-warming and wonderful! And congratulations!
Ooh, this is exciting! We have real disagreements, I think!
It might all be prefaced on this: Rather than merge finances, include in your vows an agreement to, say, split all outside income 50⁄50. Or, maybe a bit more principled, explicitly pay your spouse for their contributions to the household.
One way or another, rectify whatever unfairness there is in the income disparity directly, with lump-sum payments. Then you have financial autonomy and can proceed with mechanisms and solution concepts that require transferrable utility!
Marcus has chronic illness. This means their contribution to the household can vary unpredictably, practically on any timescale. As a result, it’s hard to think of any split that’s not going to be skewed in one or other direction in some scenarios. Moreover, they are unable to hold to job, so their time doesn’t have opportunity cost in a financial sense.
Ah, super fair. Splitting any outside income 50⁄50 would still work, I think. But maybe that’s not psychologically right in y’all’s case, I don’t know. For Bee and me, the ability to do pure utility transfers feels like powerful magic!
Me to Bee while hashing out a decision auction today that almost felt contentious, due to messy bifurcating options, but then wasn’t:
I love you and care deeply about your utility function and if I want to X more than you want to Y then I vow to transfer to you U_you(Y)-U_you(X) of pure utility! [Our decision auction mechanism in fact guarantees that.]
Then we had a fun philosophical discussion about how much better this is than the hollywood concept of selfless love where you set your own utility function to all zeros in order for the other’s utility function to dominate. (This falls apart, of course, because of symmetry. Both of us do that and where does that leave us?? With no hair, an ivory comb, no watch, and a gold watchband, is where!)
PS: Of course this was also prompted by us nerding out about your and Marcus’s vows so thank you again for sharing this. I’m all heart-eyes every time I think about it!
Ah, super fair. Splitting any outside income 50⁄50 would still work, I think.
I think that a 50⁄50 splits creates the wrong incentives, but I am reluctant to discuss this in public.
PS: Of course this was also prompted by us nerding out about your and Marcus’s vows so thank you again for sharing this. I’m all heart-eyes every time I think about it!
We do, at least because I’m the only one who has income.
I’m actually not sure about this. Initially I favored KS because monotonicity seemed more natural than independence of irrelevant alternatives. But then I realized than in sequential decision making, IIA is important because it allows you to consistently optimize your policy on a certain branch of the decision tree even if you made suboptimal actions in the past. There seems to be a way of working around this violation of IIA in KS, but it makes KS look more like a hack.
Shapley value is for distributing transferable values, like money. For general utility functions there’s no easy way to convert 1 Vanessa-utilon to 1 Marcus-utilon.
Thank you <3
Ooh, this is exciting! We have real disagreements, I think!
It might all be prefaced on this: Rather than merge finances, include in your vows an agreement to, say, split all outside income 50⁄50. Or, maybe a bit more principled, explicitly pay your spouse for their contributions to the household.
One way or another, rectify whatever unfairness there is in the income disparity directly, with lump-sum payments. Then you have financial autonomy and can proceed with mechanisms and solution concepts that require transferrable utility!
Marcus has chronic illness. This means their contribution to the household can vary unpredictably, practically on any timescale. As a result, it’s hard to think of any split that’s not going to be skewed in one or other direction in some scenarios. Moreover, they are unable to hold to job, so their time doesn’t have opportunity cost in a financial sense.
Ah, super fair. Splitting any outside income 50⁄50 would still work, I think. But maybe that’s not psychologically right in y’all’s case, I don’t know. For Bee and me, the ability to do pure utility transfers feels like powerful magic!
Me to Bee while hashing out a decision auction today that almost felt contentious, due to messy bifurcating options, but then wasn’t:
I love you and care deeply about your utility function and if I want to X more than you want to Y then I vow to transfer to you U_you(Y)-U_you(X) of pure utility! [Our decision auction mechanism in fact guarantees that.]
Then we had a fun philosophical discussion about how much better this is than the hollywood concept of selfless love where you set your own utility function to all zeros in order for the other’s utility function to dominate. (This falls apart, of course, because of symmetry. Both of us do that and where does that leave us?? With no hair, an ivory comb, no watch, and a gold watchband, is where!)
PS: Of course this was also prompted by us nerding out about your and Marcus’s vows so thank you again for sharing this. I’m all heart-eyes every time I think about it!
I think that a 50⁄50 splits creates the wrong incentives, but I am reluctant to discuss this in public.
<3