How to have same utility function for two persons?
Strictly speaking, infinitely different utility functions can give the same preferences over lotteries. If person A has utility function $f(x)$ then person B with utility function $g(x)=A+B\cdot f(x)$, $B&gt;0$ will make identical decisions over all lotteries. There would be no way to know which individual was actually using utility function $f(x)$ and which was using $g(x)$ because they would always make the same decisions.