Do men with deep voices have more children?

Yes.

Via Gad Saad:

The validity of evolutionary explanations of vocal sexual dimorphism hinges upon whether or not individuals with more sexually dimorphic voices have higher reproductive success than individuals with less dimorphic voices. However, due to modern birth control methods, these data are rarely described, and mating success is often used as a second-rate proxy. Here, we test whether voice pitch predicts reproductive success, number of children born and child mortality in an evolutionarily relevant population of hunter-gatherers. While we find that voice pitch is not related to reproductive outcomes in women, we find that men with low voice pitch have higher reproductive success and more children born to them. However, voice pitch in men does not predict child mortality. These findings suggest that the association between voice pitch and reproductive success in men is mediated by differential access to fecund women. Furthermore, they show that there is currently selection pressure for low-pitch voices in men.

Source: “Voice pitch predicts reproductive success in male hunter-gatherers” from Biology Letters 22 December 2007 vol. 3 no. 6 682-684