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Sarunas comments on 2014 Less Wrong Census/Survey - Less Wrong
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I think it might have been better to ask people to estimate what are the odds that a given statement is true. If a probability of a statement is close to zero or close to one, it gives us better precision without having to worry about digits after the decimal point (however, if a probability is close to one half, it is probably better to ask for a probability). Although it is easy to convert odds to probabilities, how many people in this survey actually took the mental effort to remind themselves to calculate the odds first and only then to express them as probabilities? I might be wrong, but I guess that only a minority. An idea for the next year survey - it might be interesting to compare the answers of two groups, one of which would be asked to estimate probabilities, the other one to estimate the odds.
Yes, odds are good (and log-odds are even better), but people are bad at both dealing with very large absolute values and dealing with very fine precisions. I think that the survey is correct to put in a cut-off (whether an ϵ for probabilities, an N for log-odds, or one of each for odds); it should just tell us where. (Edit: put in stuff about log-odds properly.)
Are you using "odds" to refer to percentages and "probabilities" to refer to fractions? I don't think there is actually any difference in meaning between the two terms.
Colloquial language doesn't make this distinction, but by technical convention, they are different.
Specifically, ‘odds’ refers to expressions like ‘5 to 3 against’; numerically, that's the fraction 5/3, or rather (because of the ‘against’) its reciprocal, 3/5. Thus odds run from 0 (impossible) to infinity (certain), with odds of 1 being perfectly balanced between Yes and No. In contrast, probabilities run only from 0 to 1. An event with odds of 5 to 3 against, or equivalently odds of 3/5, has a probability of 3/(3+5) = 3/8. So the numbers are different. The conversion formulas are O = P/(1 − P) and P = O/(1 + O).
Then there are log-odds; this is log₂ O bits. (You can also use other bases than 2 and correspondingly other units than bits.) Now 0 indicates perfect balance between Yes and No; a positive number means more likely Yes than No, and a negative number means less likely Yes than No. Log-odds run from negative infinity (impossible) to infinity (certain).
Oh right, I forgot about that definition. The main probability conversions that I was aware of involved converting between fractions and percentages, sometimes expressed instead as probabilities between 0 and 1. Theoretically, it makes sense that odds can also be converted to or from probabilities, now that I think about it. Thanks for your explanation.