At The American Scientist, three researchers look at how vocal pitch may influence which politicians are more likely to be supported by voters, all other things being roughly equal.
The short version is that candidates with lower voices tend to do better overall, even though there's no one-to-one correspondence between lower vocal pitch and election results. Interestingly, although a male with a lower voice is more likely to make a favorable impression when competing against another man, he loses that advantage if he's facing a woman.
Left untouched by the researchers, of course, is what role telling the actual truth would play in how people appreciate their political candidates. Word is the sample size was too small to obtain any usable results.