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Why not say "I assign 'The Democrats will win the election.' probability greater than 50%." instead?
Because that may sound weird to certain people. (What about “I think Democrats are more likely than not to win the next election”?)
Why not just say "The democrats are more likely than not to win the next election?"
Because next-election-winningness is not an attribute of the democrats, it's an attribute of your mental model of the democrats.
I'm not quite sure what you even mean by this comment.
I have a mental model in which the Democrats won the 2008 U.S. Presidential election.
Is that election-winningness, on your view, an attribute of the Democrats? Or of my mental model of Democrats? Or both?
I phrased badly: that should have been "likelihood-of-democrats-winning-next-election" corresponds to your mental model of the democrats, not the democrats themselves. The democrats will either win or they won't, but if you don't know which you'll say "I think/believe the democrats will win the next election". Since the democrats actually did win the 2008 election, your mental model does correspond to the real world, so it doesn't matter whether you're referring to your mental model or the real world. Since you have less confidence in your mental model of future democratic performance, it makes sense to use different phrases for each ("I believe the democrats will win the next election" feels different than "The democrats won the last election").
Well, I certainly agree that it makes sense to use different phrases to indicate different levels of confidence in an assertion, and I agree that the distinction between "X" and "I believe X" is often used this way.
I'd say “I think” if I only have poor knowledge of the facts, have to heavily rely on my priors and my intuition, and hence I could easily shift my probability assignment (and narrow what E.T. Jaynes calls my Ap distribution) by (e.g.) looking stuff up, if I could be bothered to. I'd omit it if I already had as much relevant information as I could reasonably gather, and so I don't expect my probability assignment to shift or my Ap distribution to narrow in the near future.
Because that's four extra syllables, and it shifts emphasis from the statement to the meta-statement about probability.
(These aren't good reasons to speak imprecisely, but it's a broadly observed fact of linguistics that people favor shorter ways of saying things when their meaning is sufficiently similar.)
I think the main issue about language is the question of who you're talking to. If you're speaking to a friend with a very weak grasp of Rationality and Probability the sentence that sentence will not make sense, and be needlessly convoluted.
To me it looks like Eliezer is trying to set up a new standard (perhaps just for this sequence) about when and how we are allowed to use the loaded words 'truth' and 'rationality'. So it doesn't make sense to try to apply this to every single conversation (especially outside of Less Wrong).