 and \(P_4\succ P_3\) iff \(u(5)w(0.1)&gt;u(1)w(0.11)\). This implies that the preferences will be recovered by having \(w\) be such that \(w(1)-w(0.99)&gt;w(0.11)-w(0.1)\), so that a difference in probability of \(0.01\) has a greater impact at the higher end of the probability scale than it does towards its relatively lower  end.[9]