Yes, if you drop continuity, all you get is lexicographic preferences, which isn’t much of a change. But situations where you want to break ties don’t come up much. There is usually the opportunity to measure more closely the first-order goal, rather than to try to control the tie-breaker.
Yes, if you drop continuity, all you get is lexicographic preferences, which isn’t much of a change. But situations where you want to break ties don’t come up much. There is usually the opportunity to measure more closely the first-order goal, rather than to try to control the tie-breaker.