In his recent post, rhollerith wrote,
I am more likely than not vastly better off than I would have been if <I had made decision X>
This reminded me of the slogan for the water-filtration system my workplaces uses,
We're 100% sure it's 99.9% pure!
because both sentences make a claim and give an associated probability for it. Now in this second example, the actual version is better than the expectation-value-preserving "We're 99.9% sure it's 100% pure", because the actual version implies a lower variance in outcomes (and expectation values being equal, a lower variance is nearly always better). But this leads to the question of why rhollerith didn't write something like "I am almost certainly at least somewhat better off than I would have been...".
So I ask: when writing nontechnically, do you prefer to give a modest conclusion with high confidence, or a strong conclusion with moderate confidence? And does this vary with whether you're trying to persuade or merely describe?
(Also feel free to post other examples of this sort of statement from LW or elsewhere; I'd search for them myself if I had any good ideas on how to do so.)
When writing non technically, I prefer to give the most accurate answer available. If I'm highly confident of a modest conclusion, I state that. If I'm moderately confident of a strong conclusion, I state that. They are two entirely different statements, and, while there are cases where both apply, by no means are they equivalent.
In the relationship context, "better off" tends to come in large, uncertain chunks, so what rhollerith said is reasonable, what you suggested he might say seems very unlikely to be the case.
They're obviously not completely equivalent, but in cases where your measurements form some Gaussian (or similar) distribution, which is very common, the you have the choice of saying things like (to use the water-purifying example), "we're 85% confident it's at least 99.97% pure", "we're 97.7% confident it's at least 99.3% pure", "We're 99.9% confident it's at least 98.5% pure", etc., etc., each of which... (read more)