Now, let’s pretend you are an egalitarian. You still want to satisfy everyone’s goals, and so you go behind the veil of ignorance, and forget who you are. The difference is that now you are not trying to maximize expected expected utility, and instead are trying to maximize worst-case expected utility.
Nitpick: I think this is a somewhat controversial and nonstandard definition of egalitarianism. Rather, this is the decision theory underlying Rawls’ ‘justice as fairness’; and, yes, Rawls claimed that his theory was egalitarian (if I remember correctly), but this has come under much scrutiny. See Egalitarianism against the Veil of Ignorance by Roemer, for example.
Nitpick: I think this is a somewhat controversial and nonstandard definition of egalitarianism. Rather, this is the decision theory underlying Rawls’ ‘justice as fairness’; and, yes, Rawls claimed that his theory was egalitarian (if I remember correctly), but this has come under much scrutiny. See Egalitarianism against the Veil of Ignorance by Roemer, for example.