A preference ordering on lotteries over outcomes is called geometrically rational if there exists some probability distribution P over interval valued utility functions on outcomes such that L⪯M if and only if GU∼PEO∼LU(O)≤GU∼PEO∼MU(O).
How does this work with Kelly betting? There, aren’t the relevant utility functions going to be either linear or logarithmic in wealth?
Yeah, I think this definition is more centrally talking about Nash bargaining than Kelly betting. Kelly betting can be expressed as maximizing a utility function that is logarithmic in wealth, and so can be seen as VNM rational
How does this work with Kelly betting? There, aren’t the relevant utility functions going to be either linear or logarithmic in wealth?
Yeah, I think this definition is more centrally talking about Nash bargaining than Kelly betting. Kelly betting can be expressed as maximizing a utility function that is logarithmic in wealth, and so can be seen as VNM rational