To be more specific: If ϵ ≥ 5 × 10⁻ⁿ (which it must be for some n, if it is a positive real number), then I only need to figure out my probability to n + 1 digits. Upon doing so, if it’s all 0s, then my probability is no more than ϵ, so I can enter 0. Otherwise, I should enter something larger. (And a similar thing holds on the other end.) Specifying ϵ serves the practical purpose of telling us how much work to put into estimating our probabilities. Since I had no guideline for that, I chose to default to ϵ = 1⁄2 (in percentage points), rather than try to additionally work out how small ϵ was supposed to be.
If, instead of bringing up ϵ, the survey had instructed us to use as many decimals as we need to avoid ever answering either 0 or 100, then I probably would have done more work. (There are reasons why this is bad, since the results will be increasingly unreliable, but still it could have said that.) But since I knew that at some point my work would be ignored, I didn’t do any.
(Edits: minor grammar and precise phrasing of inequalities.)
I took epsilon to be simply 0.5, on the basis of “the survey can take decimals but I’m going to use whole numbers as suggested, so 0 means I rounded down anything less than 0.5”. This is imprecise but gives me greater confidence in my answers, and (as you say), I have some tendency towards laziness.
Epsilon is a minuscule amount. It’s vanishingly small, but it’s still there.
Yes, but which minuscule amount?
To be more specific: If ϵ ≥ 5 × 10⁻ⁿ (which it must be for some n, if it is a positive real number), then I only need to figure out my probability to n + 1 digits. Upon doing so, if it’s all 0s, then my probability is no more than ϵ, so I can enter 0. Otherwise, I should enter something larger. (And a similar thing holds on the other end.) Specifying ϵ serves the practical purpose of telling us how much work to put into estimating our probabilities. Since I had no guideline for that, I chose to default to ϵ = 1⁄2 (in percentage points), rather than try to additionally work out how small ϵ was supposed to be.
If, instead of bringing up ϵ, the survey had instructed us to use as many decimals as we need to avoid ever answering either 0 or 100, then I probably would have done more work. (There are reasons why this is bad, since the results will be increasingly unreliable, but still it could have said that.) But since I knew that at some point my work would be ignored, I didn’t do any.
(Edits: minor grammar and precise phrasing of inequalities.)
I took epsilon to be simply 0.5, on the basis of “the survey can take decimals but I’m going to use whole numbers as suggested, so 0 means I rounded down anything less than 0.5”. This is imprecise but gives me greater confidence in my answers, and (as you say), I have some tendency towards laziness.
Yes, that’s what I did too (0.5%).