I have an idea for a possible utility function combination method. It basically normalizes based on how much utility is at stake in a random dictatorship. The combined utility function has these nice properties:
Pareto-optimality wrt all input utilities on all lotteries
Adding Pareto-dominated options (threats) does not change players’ utilities
Invariance to utility scaling
Invariance to cloning every utility function
Threat resistance
The combination method goes like this:
X=list of utility functions to combine
dist(U)=worlds where random utility function is argmaxed with ties broken to argmax U
Step 1: For each U in X, U=U-expect(argmax U)
Step 2: For each U in X,
U=-U/U(null universe) if (expected value of U on dist(U))==0
U=-U/(expected value of U on dist(U)) otherwise
Step 3: U(final)=sum(U in X)
I designed this to be a CEV of voting utility maximizers, but the combination has multiple discontinuities. It does not need transferrable utility like the ROSE values, but it does not have nearly have as many nice properties as the ROSE values.
I have an idea for a possible utility function combination method. It basically normalizes based on how much utility is at stake in a random dictatorship. The combined utility function has these nice properties:
Pareto-optimality wrt all input utilities on all lotteries
Adding Pareto-dominated options (threats) does not change players’ utilities
Invariance to utility scaling
Invariance to cloning every utility function
Threat resistance
The combination method goes like this:
X=list of utility functions to combine
dist(U)=worlds where random utility function is argmaxed with ties broken to argmax U
Step 1: For each U in X, U=U-expect(argmax U)
Step 2: For each U in X,
U=-U/U(null universe) if (expected value of U on dist(U))==0
U=-U/(expected value of U on dist(U)) otherwise
Step 3: U(final)=sum(U in X)
I designed this to be a CEV of voting utility maximizers, but the combination has multiple discontinuities. It does not need transferrable utility like the ROSE values, but it does not have nearly have as many nice properties as the ROSE values.