1. You can assume that people start equal. A rich person already got a lot of utility, while the poor person already lost some. You can still do the math that derives utilitarianism in the final utilities just fine.

2. Utility =/= Money. Under the VNM model I was using, utility is defined as the thing you are risk-neutral in. N units of utility is the thing which a 1/N chance of is worth the same as 1 unit of utility. So my statement is trivially true.

Let's say, in a certain scenario, each person i has utility ui. We define U to be the sum of all the ui, then by definition, each person is indifferent between having ui and having a ui/U chance of U and a (1-u_i)/U chance of 0. Since everyone is indifferent, this scenario is as good as the scenario in which one person, selected according to those probabilities, has U, and everyone else has 0. The goodness of such a scenario should be a function only of U.

1. Politics is the mind-killer, don't bring controversial figures such as Dick Cheney up.

2. The reason it is just to harm the unjust is not because their happiness is less valuable. It is because harming the unjust causes some to choose justice over injustice.