  Notice that equality of welfare and equal opportunity for welfare do not exhaust the welfarist egalitarian alternatives. Take the example of a view that is oriented to equality of perfectionist achievement (achievement of objectively valuable achievements of a kind that make one's life go better for oneself). One might hold that what is morally valuable and ought to be promoted is equality of achievement, or equal opportunity for achievement, or another view along the lines of equal achievement of one's potential or equal opportunity to achieve one's potential. Say that each person has a native talent for achievement. I have little native talent; you have a lot. Egalitarianism might be construed as requiring that so far as is possible, social arrangements be set so that each of us achieves, or can achieve, the same percentage of his native potential over the course of her life. Everyone's ratio of actual achievement to native potential for achievement should be the same. So my having the opportunity to achieve little, and my actually achieving little, compared to you, on this conception would not necessarily offend against the egalitarian ideal (see McMahan 1996, and for the thought that measurement of achievements on a single scale is chimerical, Raz 1986).