Probability bounds lower than other bounds

[Anne Paulson]

Let's say, hypothetically, that we have two probability bound formulae. Let's say we evaluate them for some arguments, and we find that formula A yields 2, and formula B yields 3. We are asked which bound is smaller. Do we say, formula A's bound is smaller, because our ace arithmetic skills allow us to compare two numbers and say which is smaller? Or do we say, they are equal, because neither 2 nor 3 is a probability, so neither of them bounds the probability of the event in any way?

[yaser]

Originally Posted by Anne Paulson

Let's say, hypothetically, that we have two probability bound formulae. Let's say we evaluate them for some arguments, and we find that formula A yields 2, and formula B yields 3. We are asked which bound is smaller. Do we say, formula A's bound is smaller, because our ace arithmetic skills allow us to compare two numbers and say which is smaller? Or do we say, they are equal, because neither 2 nor 3 is a probability, so neither of them bounds the probability of the event in any way?

Of course one can argue both ways, but the first (2 is better than 3) would be the correct formal answer since as a bound, 2 is closer to the actual value than 3. The fact that there is another bound which is better than both, in this case an obvious bound, does not really concern the question being asked