Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  examine the geometrical properties of the space of expected utilities over a finite set of options, which is commonly used to model the preferences of an agent.  focus on the case where options are assumed to be symmetrical a priori. Specifically,  prove that the only Riemannian metric that respects the geometrical properties and the natural symmetries of the utility space is the round metric.
['François Durand', 'Benoît Kloeckner', 'Fabien Mathieu', 'Ludovic Noirie']
I am writing a research paper on a idea Geometry on the Utility Space
[{"from": "human", "value": "I am writing a research paper on a idea Geometry on the Utility Space"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  examine the geometrical properties of the space of expected utilities over a finite set of options, which is commonly used to model the preferences of an agent.  focus on the case where options are assumed to be symmetrical a priori. Specifically,  prove that the only Riemannian metric that respects the geometrical properties and the natural symmetries of the utility space is the round metric."}]