First of all, every election campaign would start pandering to babies, because they're easily manipulated. You'd start seeing billboards that read: "Taxes are poopy. Poopy old taxes." or "Who's a good little voter? Want a banana?" or "phbbdhheztt", because babies can't read anyway.
The next thing would be that babies would start voting for other babies because--have you met babies? Total chauvinists, as far as other babies go. Babies literally believe that babies' shit doesn't stink. And once you start putting babies in the ballot, well, forget about it. Are you gonna vote against a baby? What are you, some kinda asshole?
So you'll have these all-baby debates. Which will be awful. You'll have a right-wing baby going "baba" and a liberal baby going "googah" and then some libertarian baby going on about how the government has no business telling him what he can or can't put in his mouth.