They only start expressing incompatibilist intuitions when asked to comment on abstract philosophical statements of a kind one would not normally encounter.
This is the Nichols and Knobe hypothesis which argued that people in general are incompatibilists but that language which generates strong affective responses will nonetheless lead people to import moral responsibility. The hypothesis is formed by taking some vignette about free will and making the action significantly more condemnable. So people will think that someone who gives to others in a deterministic world is not responsible but someone who murders others in that world is. Every other feature of the story remains the same. The stories that generate incompatibilist intuitions aren't different from those that generate compatibilist intuitions except in the emotional/morally condemnable content. The former aren't more abstract or philosophical. The better interpretation of this hypothesis is that people's actual intuitions about determinism get overrun by a desire to signal that they do not support the evil action committed in the vignette. Feel free to google Knobe's work in intentionality for evidence that this phenomena is more general.
In any case, the Nichols and Knobe hypothesis isn't the position of the article. The authors set out to test the hypothesis and found it false. Instead, they found that people responded to vignettes mostly consistently. About 60-67% gave incompatibilist responses, 22-9% gave compatibilist responses and mixed/inconsistent responses were returned at a high single digit rate.
As promised, here is the "Q" part of the Less Wrong Video Q&A with Eliezer Yudkowsky.
The Rules
1) One question per comment (to allow voting to carry more information about people's preferences).
2) Try to be as clear and concise as possible. If your question can't be condensed to a few paragraphs, you should probably ask in a separate post. Make sure you have an actual question somewhere in there (you can bold it to make it easier to scan).
3) Eliezer hasn't been subpoenaed. He will simply ignore the questions he doesn't want to answer, even if they somehow received 3^^^3 votes.
4) If you reference certain things that are online in your question, provide a link.
5) This thread will be open to questions and votes for at least 7 days. After that, it is up to Eliezer to decide when the best time to film his answers will be. [Update: Today, November 18, marks the 7th day since this thread was posted. If you haven't already done so, now would be a good time to review the questions and vote for your favorites.]
Suggestions
Don't limit yourself to things that have been mentioned on OB/LW. I expect that this will be the majority of questions, but you shouldn't feel limited to these topics. I've always found that a wide variety of topics makes a Q&A more interesting. If you're uncertain, ask anyway and let the voting sort out the wheat from the chaff.
It's okay to attempt humor (but good luck, it's a tough crowd).
If a discussion breaks out about a question (f.ex. to ask for clarifications) and the original poster decides to modify the question, the top level comment should be updated with the modified question (make it easy to find your question, don't have the latest version buried in a long thread).
Update: Eliezer's video answers to 30 questions from this thread can be found here.