A utility between 0 and 1 effectively plays the same role as “negative utilities” do under regular arithmetic expected value. So a geometric perspective can work if you map what you would ordinarily consider to be negative utilities to the interval 0 to 1, and restrict utility to R+.
But why would you? It doesn’t offer any benefit over regular artihmetic expected value calculations.
A utility between 0 and 1 effectively plays the same role as “negative utilities” do under regular arithmetic expected value. So a geometric perspective can work if you map what you would ordinarily consider to be negative utilities to the interval 0 to 1, and restrict utility to R+.
But why would you? It doesn’t offer any benefit over regular artihmetic expected value calculations.