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That's talking about the average across the population of whole lives, not the average of times within a life. That is, according to the average view in population ethics, the value of a world is given by the average of x1, x2, x3 .... where each xn is the lifetime well-being of a different individual who ever lives in that world. And each xn value is NOT itself an average.

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OK, I think I follow you. So roughly speaking, what do you propose for f(x_n) that differs significantly from just f(x_n) being their lifetime average utility?

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