What I don't want is a result that says "Enter into a contract with 99 other people that none of you donates $100 to puppies unless all of you do, then donate $100, so you can feel like you caused puppies to get $10000!". Somehow that seems counterproductive. Except as a one-off game for funsies, which doesn't count. :)
Actually, this isn't wrong, as long as you think about it the right way. First you are causing puppies to get $10000, but you are also causing 99 people to lose $100, so you have to account for that.
More importantly, though, frame the scenario this way: 99 people already signed the contract, and you still have to decide whether to sign it. Then, you are clearly making the entire difference and you should be willing to accept correspondingly large disutilities if they are necessary to get the deal to happen (unless they could easily find someone else, in which case both the math and the intuition agree that you are not creating as many utilions). Note that the math cannot require everyone to accept individually large disutilities, because then signing the contract would cause all of those disutilies to occur.
If, however they have not signed anything yet, either you know that they are going to and that they cannot find anyone elso to be the 100th person, in which case this is equivalent to the other scenario, or you don't know whether they are all going to sign it in which case the utility is reduced by the uncertainty and you should no longer accept as large disutilities to sign the contract.
Often we cooperate to extract surplus value from the government, hotels, the physics that makes operating cars cost money, or other sources - value that we could not extract individually. When I notice such a surplus I often wonder how the surplus should be split. What is fair? Purely cooperatively, without anyone trying to game the surplus-allocation-function, and assuming the stated coalitions are fixed rather than negotiable, how much of the surplus should be attributed to each contributing party?
Some concrete examples that have come up recently in real life*:
1. Matching donations. The company I work for will match donations to charity, dollar for dollar, up to a certain maximum. Viscerally, how should I feel about donating $100 to puppies**? More than $100, since puppies get $200, certainly. But less than $200, since my employer should feel puppy-love too, and presumably there's a conservation of visceral feeling law that should apply here. Further suppose that my employer's matching offer caused me to donate $100 instead of, say, $50. What math should be done and why?
2. Exemption splitting. An amicable divorce leaves two parents wondering who should claim their student daughter as a dependent. As a purely "what is fair?" financial question, how much of the tax savings from that exemption should be distributed to the father, mother, and daughter? Suppose the father's marginal tax rate is 25% and overall tax rate is 18%, and the mother's marginal rate is 15% and overall is 12%. What math should be done and why?
3. Refinancing. My friend has a debt at 12% and for silly reasons is obviously able to pay it off but cannot this year. I can pay it off, though, and so could several other people***. Assume there are 3 people including me who could pay it off, and our current expected returns on invested money are (say) 2%, 3.5%, and 6%, and for simplicity she will repay the loan plus any surplus due in one year. Who should pay off how much of the loan (say it's $5000)? I assume the 2% person should pay all of it. That's a 10% surplus - how much do each of the four of us get? What math should be done and why?
As in The Bedrock of Fairness, are there qualities of the solutions we have strong opinions on, even if we do not know the procedure which would generate solutions with those qualities?
*Details changed.
**I do not donate to puppies.
***Assume default risk is negligible.