Right but which metric is reasonable can (and I believe should) change with scale. I'm risk-preferring when it comes to small amounts -- opportunities to make such decisions come up all the time, so I'll be likely to realize the mean. But I'm risk-averse when it comes to large amounts -- I may only get to make one such decision in my life. Better to minimize the variance here.

This not only explains why people play lottery and buy insurance (playing the lottery non-compulsively involves risking only small amounts of money; not having insurance involves risking large amounts of money), but it also explains why those close to retirement should have risk-averse portfolios, while the young should have risk-preferring portfolios (those close to retirement have few "samples" left to take as it were).