Understanding the purpose of sex is a fundamental unresolved problem in evolutionary biology. The difficulty is not that there are too few theories of sex, the difficulty is that there are too many and none stand out. To distinguish between theories, we ask: Why are there no triparental species with offspring composed of the genetic material of three individuals? A successful theory should confer an advantage to biparental sex over asexual reproduction without conferring an even greater advantage to triparental sex. Of two leading theories (red queen and mutational), we show that only one is successful in this sense.