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Psychohistorian comments on Probability distributions and writing style - Less Wrong
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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 represents a different part of the curve. Now obviously the most complete answer here would be to say "our data are decribed by a Gaussian of mean X and st. dev. Y", but people don't frequently do that in informal contexts, so how do you reduce it to one claim with one confidence?
Would you go into why that is? It doesn't seem intuitive to me at all. Why shouldn't a relationship improve your life by just a small amount?
From the context, it appears there are two basic outcomes different from the current status quo:
Status quo: Relationship, Utility = High
1st option: No relationship, Utility = Low, probability = probably over .5, under .9
2nd option: Relationship, Utility = from highly negative to extremely high, cumulative probability ~.4-.1.
Thus, what would likely happen is that he's not in a relationship. If he is in a relationship, his happiness could be anywhere over the map. Since it's already high, it's unlikely (though possible) that he would be better off (and even less likely that he would be drastically better off). There's some chance he's just a little bit better off, if he were in a slightly worse relationship. And then there's a rather large chance he's much better off, if the alternative is no relationship or a miserable one. Thus, he's probably vastly better off, but he's not almost certainly a little bit better off. At the risk of overgeneralizing, I'd say that a lot of low-certainty, high-stakes personal utility calculations tend to be non-Gaussian.
And of course the probabilities here are purely for illustrative purposes. If he thought that there was, say, a 10% chance of being single and a 45% chance of being in a miserable relationship, you'd get the same results. I'm assuming his language accurately mapped his estimates.