The psychology is that people tend not to add answers to questions that have accepted answers.
And people tend to be accepting answers too early, not giving enough opportunity for others to add their answers, which may in fact turn out to be better.
So the solution is to recommend that people should try to hold off accepting an answer until there are at least three of them.
Personally, I often wait a few weeks or even a month or two on Stack Overflow without accepting an answer on my programming questions. It definitely results in more answers, and often I find myself accepting one that was added later.
See also: Why Are We Accepting Answers So Fast?Why Are We Accepting Answers So Fast?
That said, our APQ of 2.9 that we have as I write this is good. Anything over 2.5 is good. So really, this is not currently a problem. See http://area51.stackexchange.com/proposals/43502/genealogy-family-history