Attitudes toward risk and double inflection utility functions

CFA Level III Portfolio Management
#1

The CFAI text discusses the Friedman Savage double utility functions which says that at low income levels and at very high income levels, individuals are risk averse and they are risk seeking in the middle. That seems fine to me. However, in the same reading, under section 2.2.3, the text says that those with less income prefer a small chance of large gain (sounds like lottery, i.e. risk seeking) and the middle income people prefer small, fair gambles (sounds risk averse).

Don’t the two sound contradictory?

#2

A fair gamble has an expected payment of 0. It is indeed a risk seeking game. Commonly, risk-averse individuals do not accept fair gambles.

What is a risk-seeking scenario?

Preferring strategy A over B, where:

A: 50% probability of getting $1,000 and 50% probability of getting $0

B: 100% probability of getting $500

both A and B has the same expected value ($500), so comparable strategies. A risk-seeker investor will prefer A over B.

I think the book has no contradictory statements.