Historically, self-financed candidates have tended to lose. The National Institute on Money in State Politics recently found that of those candidates who received more than half of all campaign contributions from themselves or an immediate family member, only 11 percent won from 2000 to 2009.
It’s not much of a puzzle, since I gave away the answer in the header. Just to spell it out, if we assume that candidates with a higher likelihood of winning will attract more funding, the “more than half self-funded” criterion selects against popularity. There is reverse causation, from weak political prospects to poor fund-raising to greater self-finance.
This is a nice example if you teach stats. Just don’t label it the way I did.