okcupid does exactly this. Most of their questions are submitted by the users themselves, and they have hundreds if not thousands of them, but they present the questions to you in the order of most differentiating first. You can answer as many or as few as you want, but matches get better as you answer more, with monotonically diminishing returns. You also get to say which answers you would accept from your match (doesn't have to include your answer) and how much it matters if at all.

My gut tells me it's akin to doing principle component analysis. To find the most differentiating question, do 1 dimensional PCA, and the question most aligned with the resulting dimension is question #1. Then do 2 dimensional PCA fixing the first dimension as the first question. The result is question #2. And so on.

OF FAR GREATER CONCERN: They are collecting email addresses associated with personality questions. There is no privacy policy, other than the statement "If there's a match, we'll email you. (You will not be emailed under any other circumstances: no promos, no newsletters, nothing except news of a match.)" You don't know to whom you are giving this information, as there is no named legal entity, just a gmail address and a domain name whose registered owner is hidden in whois databases.

I suspect OKC can make much more accurate predictions than this site, as they have vastly more data (some users answer thousands of questions, most users who are active for more than a few months have answered a couple hundred), vastly more users to compare, and they are pretty savvy about statistical analysis (reading their old blog posts is quite educational on the subject).

But, even given all that data...I find about half of my 99% matches (of which I've talked to maybe a half dozen and gone on a date with maybe four) aren't particularly compatible or interesting, to me. There seem to be other factors at play that just aren't measurable. And, heck, maybe being just like someone else isn't what makes an ideal friend/lover/partner.

It's like a Gram-Schmidt process. You take one question, then you look at other questions given (quotiented by, projected on, etc) that question, and so on.

> My gut tells me it's akin to doing principle component analysis

Or a decision tree, maybe

Since I can't edit, here are some more details on what OkCupid does http://blog.okcupid.com/index.php/page/3/

or like Akinator: http://en.akinator.com/

This site is amazing.