I'm writing a conference paper in English... My Japanese colleague told me that I should use "○" for YES and "x" for NO in my paper, but I think the right symbols should be "✓" for YES and "x" for NO. Which one is correct?
Ok, most of the answers here are spot on. You're more correct, but Y and N are much clearer in general. Two things people don't seem to have mentioned so far:
Where is the conference?
All of the answers so far assume an international or anglophone venue with many native speakers. In that case, you should explain to your Japanese colleague that (almost?) no other culture uses those symbols in that way. As near as China, people have only seen it in Japanese contexts if at all and they should never be used in international settings. (You could include a guide, but why bother? Just use something more commonly understood.)
But if the conference is in Japan and you're submitting a paper that will mostly be read by Japanese speakers of English, he is right and you should adopt the convention that is most easily understood by them. △ is a terrible symbol for the sense being used but, if your readers already grok it and ? would cause more difficulty, then go ahead and use it.
How are you using these symbols?
Some people are telling you to use checks or boxes, but those are only appropriate for forms and tables within your paper.
In running text, you should just use "yes(es)" and "no(es)" in discussion of anything other than votes, which sometimes get the archaic "yea(s)" and "nay(s)". If you're discussing a yes response as a response, you might set it off with all caps: "Respondent 17 selected YES when asked if s/he was an above-average driver, despite reporting elsewhere that s/he can no longer purchase insurance due to repeated collisions involving guard rails, other cars, and small buildings." You might replace that YES with a 'yes' or a yes or a yes or a Y; you might describe R17 as "checking yes"; but you wouldn't just say s/he "selected ✓" or "○".