I'm not so sure it makes sense for maximization of average utility to cover the past; it seems like the average-utilitarian's goal should be to maximize his average future utility.That sounds sensible, but it also creates a problem of time inconsistency. Suppose you’re 30, and your life up to now has been “great.” You expect the next 20 years (up to age 50) to be “fantastic.” And you expect all years after that to be “pretty good.” Every year after age 50 will lower the average quality of future years. So from your current 30-year-old perspective, if you want to maximize the average quality of future years of life, you should plan to commit suicide at age 50. (Indeed, you should bind yourself to commit suicide at 50, if there’s any way to do so.) However, by the time you reach age 50, the intervening decades will have become the past and thus irrelevant to the goal of maximizing the quality of future years. You should therefore repudiate your plan to commit suicide.
This time inconsistency is, to me, further evidence that maximizing average utility of life is not the right goal. An analogous inconsistency occurs for average utilitarianism of the interpersonal variety, once we consider multiple generations. Right now, present and foreseeable future generations of humanity seem likely to have higher expected utility than the average of prior generations, since the mass of human beings throughout history have lived in conditions of squalor and deprivation. So average utilitarianism would recommend continued existence for humanity. But what if we reached a point in history at which humankind’s condition declined rapidly and seemed to likely to continue that way (perhaps as in Battlestar Galactica)? In that case, an average utilitarianism that considered all lives, past and future, would recommend immediate mass suicide. An average utilitarianism that only looked to the future, on the other hand, could allow continued existence for humanity for a period of time – but if humanity’s condition were expected to drop even further at some point in the more distant future, it would make sense to adopt a time-delayed suicide pact.