Keltham: And so long as that gets transcripted and sent out soon enough, hopefully nobody from Chelish Governance gives me a completely baffled look if I say that my baseline fair share of an increase in Chelish production ought to be around roughly the amount that Chelish production would’ve increased by adding me in the alternate world where the country had randomly half of its current people, or gets confused and worried if I say that a proposed contract clause would be annoying enough in a final offer to make me visibly generate a random number between 0 and 999 and walk out on Cheliax if the number is 0.
(time passes)
Lrilatha: Ah, Keltham. We understand that you expect to get about half the shares in Project Lawful based on a fair division of spoils, calculated as your marginal value as added to all possible subsets of actors.
Keltham: If the word ‘spoils’ is translating at all correctly, it has odd connotations for a scientific project. But that’s exactly right. I will reject lesser splits with a probability corresponding to how disproportionately they reserve the gains for you.
Lrilatha: There’s no need for that. We accept your terms. Here is a contract to that effect between you, Cheliax, and other parties.
Keltham: Oh. I was expecting more … what was the word again … “haggling”.
Lrilatha: Asmodeus is a god of both negotiations and contracts. Today we offer the second.
Lrilatha: I do not expect any of the terms of this contract to have any unexpected unpleasant consequences for yourself, relative to the fair division of spoils, calculated as discussed. You should be aware, if you are not, that there are some devils with veto rights over projects of this form, which affects that division.
Keltham: Asmodia why don’t you chart this out for us and anyone reading the transcripts to show how this affects the fair division? It will be a good opportunity to refresh their understanding.
Asmodia: certainly. Let’s assume that there is one devil with veto power, so the actors are Keltham, Cheliax, and the Veto Devil. Then the marginal value of each actor is:
Keltham only: minimal
Cheliax only: current Chelish production
Veto Devil only: minimal
Keltham + Cheliax: current Chelish production, because the Veto Devil vetoes the project.
Cheliax + Veto Devil: current Chelish production
Veto Devil + Keltham: minimal
Keltham + Cheliax + Veto Devil: current Chelish production plus the gains from Project Lawful, whatever they are...
Carissa: Let’s say a million resurrection diamonds.
Asmodeus: So as you can see from this diagram, the fair division is that Keltham, Cheliax, and the Veto Devil all get three hundred and thirty three thousand, three hundred and thirty three resurrection diamonds, plus an equal share of the final diamond. Cheliax retains its rights to current Chelish production.
Keltham: That’s right. But why would a devil get to veto an agreement between me and Cheliax?
Lrilatha: The veto provisions are part of an old contract between Hell and Cheliax, in exchange for Hell’s assistance in certain matters. Both parties expected it not to come up, since mortals in Golarian do not attempt to bargain using the fair division of spoils as you calculate it, and prefer to “haggle”. But here we are.
Asmodeus is the God of Trickery, so Lrilatha is glossing over the fact that there are a very large number of devils on the Committee for Considering Shapley Value Agreements with Lawful Clueless Outsiders, all of whom get a veto. Not an infinite amount of course, unlike the Abyss, Hell is reassuringly finite, plus it is helpful to be able to sign contracts in a finite time. But certainly all of the Contract Devils are on it, because why wouldn’t they?
I don’t know how the story ends. Seems like a fair division should resist problems with group entities that structure themselves so as to maximize their joint share of a future fair division. Perhaps Keltham spontaneously invents it. But I don’t know what it is (other than “lol, no I’m not giving almost all the gains to the Veto Committee, go to Hell”).
Hopefully this is the place for planecrash-inspired fanfic based on understanding Shapley values with Venn diagrams.
Keltham: And so long as that gets transcripted and sent out soon enough, hopefully nobody from Chelish Governance gives me a completely baffled look if I say that my baseline fair share of an increase in Chelish production ought to be around roughly the amount that Chelish production would’ve increased by adding me in the alternate world where the country had randomly half of its current people, or gets confused and worried if I say that a proposed contract clause would be annoying enough in a final offer to make me visibly generate a random number between 0 and 999 and walk out on Cheliax if the number is 0.
(time passes)
Lrilatha: Ah, Keltham. We understand that you expect to get about half the shares in Project Lawful based on a fair division of spoils, calculated as your marginal value as added to all possible subsets of actors.
Keltham: If the word ‘spoils’ is translating at all correctly, it has odd connotations for a scientific project. But that’s exactly right. I will reject lesser splits with a probability corresponding to how disproportionately they reserve the gains for you.
Lrilatha: There’s no need for that. We accept your terms. Here is a contract to that effect between you, Cheliax, and other parties.
Keltham: Oh. I was expecting more … what was the word again … “haggling”.
Lrilatha: Asmodeus is a god of both negotiations and contracts. Today we offer the second.
Keltham: Please assure me that there are meant to be no unexpected unpleasant consequences for myself, as seen from my individual perspective. I mean, I probably didn’t have to say that, but why trust what you can verify?.
Lrilatha: I do not expect any of the terms of this contract to have any unexpected unpleasant consequences for yourself, relative to the fair division of spoils, calculated as discussed. You should be aware, if you are not, that there are some devils with veto rights over projects of this form, which affects that division.
Keltham: Asmodia why don’t you chart this out for us and anyone reading the transcripts to show how this affects the fair division? It will be a good opportunity to refresh their understanding.
Asmodia: certainly. Let’s assume that there is one devil with veto power, so the actors are Keltham, Cheliax, and the Veto Devil. Then the marginal value of each actor is:
Keltham only: minimal
Cheliax only: current Chelish production
Veto Devil only: minimal
Keltham + Cheliax: current Chelish production, because the Veto Devil vetoes the project.
Cheliax + Veto Devil: current Chelish production
Veto Devil + Keltham: minimal
Keltham + Cheliax + Veto Devil: current Chelish production plus the gains from Project Lawful, whatever they are...
Carissa: Let’s say a million resurrection diamonds.
Asmodeus: So as you can see from this diagram, the fair division is that Keltham, Cheliax, and the Veto Devil all get three hundred and thirty three thousand, three hundred and thirty three resurrection diamonds, plus an equal share of the final diamond. Cheliax retains its rights to current Chelish production.
Keltham: That’s right. But why would a devil get to veto an agreement between me and Cheliax?
Lrilatha: The veto provisions are part of an old contract between Hell and Cheliax, in exchange for Hell’s assistance in certain matters. Both parties expected it not to come up, since mortals in Golarian do not attempt to bargain using the fair division of spoils as you calculate it, and prefer to “haggle”. But here we are.
Asmodeus is the God of Trickery, so Lrilatha is glossing over the fact that there are a very large number of devils on the Committee for Considering Shapley Value Agreements with Lawful Clueless Outsiders, all of whom get a veto. Not an infinite amount of course, unlike the Abyss, Hell is reassuringly finite, plus it is helpful to be able to sign contracts in a finite time. But certainly all of the Contract Devils are on it, because why wouldn’t they?
I don’t know how the story ends. Seems like a fair division should resist problems with group entities that structure themselves so as to maximize their joint share of a future fair division. Perhaps Keltham spontaneously invents it. But I don’t know what it is (other than “lol, no I’m not giving almost all the gains to the Veto Committee, go to Hell”).