Your threshold theory of utility is interesting. In mathematical terms, it suggests [1] poor people have a utility function which is flat up to some critical value (and this critical value is considerably higher than their possible expected income).

For example, U(I) = sqrt(I/$15k), i < $15k, U(I) = 1, $15k < I < $100k, and then U(I) = 2, $100k < I. (I is income. The discontinuity at $100k is not necessary, but the flatness on [$15k, $BIGNUM] is.)

I.e., consider a poor person making $15k/year. If they spend $100/year on lotto (assume 1 in 1 million chance of winning), with virtually no chance of success, that suggests that 1e6 x Utility(big 'thing') > Utility($100 worth of goods/services). In particular, this suggests that the poor person assigns a very low value to an extra $100 worth of goods and services. If this is the case, then the lottery is actually a very efficient tax! It only deprives people of something they barely care about at all.

If correct, this theory would also explain why poor in the US work so little - they don't value the things that the extra money could buy.

[1] Like PaulJoslin, I am implicitly assuming that lottery ticket buyers are rational and inferring their utility function from their choices. It's also possible that lotto buyers simply don't understand probability, in which case all this speculation is irrelevant.