Stochastic Dominance: A Betterness Relationship

Stochastic dominance is the idea that when one option does stochastically dominates the other then any sane view of betterness of prospects will regard the first as a better prospect than the second. So here's an example that establishes that. It's called it swap and sweeten. The agent's choice set is either do nothing or do A or do B. We don't really care about the do nothing option. That's only there to define how much difference you make if you do A or B. What we're interested in is whether you do A Or Whether You Do B.