Can we compare risks of lotteries?
You might be looking for the concept of stochastic dominance:

Roughly speaking, first order stochastic dominance of distribution A over distribution B, means that for every possible outcome gamble A pays out weakly more and in at least one state it pays out strictly more. Roughly speaking, second order stochastic dominance means that distribution A has the same risk as distribution B but a higher mean (but not necessarily weakly-higher in every state of the world. Alternatively, you preserve the mean of distribution B and you "scrunch" the probability mass to create distribution A. "All risk-averse expected-utility maximizers (that is, those with increasing and concave utility functions) prefer a second-order stochastically dominant gamble to a dominated one." 

The seminal paper is Rules for Ordering Uncertain Prospects (Hadar and Russell (1969))