Probably maybe
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When I say that the probability of throwing 3 heads in succession is 1/8, that refers to the fact that if I toss three coins a large number of times, I believe that the number of times I get three simultaneous heads will asymptotically approach a ratio of 1/8. Each individual throw is of course governed by well understood mechanical laws, but the sequence of uncontrolled tiny effects at the start of and during each coin toss effectively produces a pseudo-random result.
When I say the probability of Ron Paul getting elected is small, I don’t refer to an ensemble of identical events at all. Randomness doesn’t come into it either. I think that what I really mean is that I CANNOT EASILY IMAGINE A PLAUSIBLE DETERMINISTIC SERIES OF EVENTS THAT WILL CAUSE THAT TO HAPPEN.
These are two very different uses of the word probability. There should probably be a different word for the second use. All of this makes me increasingly suspicious of the use of probabilities in describing societal events.
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Would you then describe the intrade odds of future societal events as implied probabilities?
I might say likelihood, or in this instance simply plausibility might work.
Likelihood vs probability?
Unfortunately, changing English in such a way is hard. I am curious whether other natural languages better make these kinds of distinctions.
Meanwhile, I’ve been happy that because of the financial meltdown of 2008, “uncertainty” vs. “risk” seems to have partially entered the public consciousness. I’m still waiting for “accuracy” vs. “precision” to do so.
I like likelihood for the second kind of probability, but the statisticians have appropriated it as in Maximum Likelihood. How about ‘conceivability‘?
Likelihood is a good choice. Possibility is also reasonable substitute, “The possibility of Ron Paul getting elected is small.”