This would cause a few problems…
I’d say that when I was a freshman in High School (I’m 19 now) at least 75% of students didn’t give a damn about politics in any way shape or form (right now in my college I’d say its about half and half, now that its getting to be election time a few more college students care).
Youth that don’t care would take their parents side and would probably go and vote if mom and dad do (especially so if the families are like those described two paragraphs below), something they wouldn’t do if they didn’t live at home. A couple (which quite often but not always votes alike) could then get half a vote or more representation for their politician. As a side note, this might cause a slight tip of the scale to pro-life/traditional catholic demographics, though that is a slight stretch.
Youth that do care also would probably have a skewed political standpoint that is unrealistically radical. Yes, I know you can support any political group or ideas that you want in America, but I admit that when I was 14 my knowledge of politics and the American political system was significantly less than it is today. Also, my views have changed drastically since then to a point where they, while most definitely not in the average, are more relevant to the issues and are more reasonable (in the sense that I understand and want realistic political compromise).
To make the situation worse, those that do care but do not agree on politics with their parents risk major family disagreements and (in some cases, though responsible parents wouldn’t do this) situations where parents punish or otherwise make their kids life miserable because of how they vote. And on top of that there’s the potential of having youth voters in the midst of their rebel stages voting against the parent’s party out of spite, negating not only their own parent(s) vote(s), but potentially others. Again, I might be stretching it, but single parent families have the greatest potential to harm the democratic system, as they might have a stressed mom or dad with a 14 year old, a 16 year old, and a 17 year old, all in traditional adolescent revolt, taking half a vote from a random citizen as well as their parent’s whole vote.
Yes, I know these kind of things happen in the adult world as well. People are be Democratic or Republican because dad, granddad, and so on was. People go into the booth and vote while flipping a coin. Just as many 14 year olds, many people believe, as is their right, in extremely radical political ideas. In the 18+ voting world, though, there are fewer such potential situations where fraud could take place. Under the current system (I hope I’m right) a greater percentage of those educated on the issues by the media and society are voting compared to those who choose their votes based upon uninformed beliefs. To be clear, I’m not saying that once you turn 18 you’re transformed from an adolescent ignorant of politics to an informed person. I know of a great many well rounded and well informed young people as well as (sadly) a great many adults who know shit about current political issues. Another benefit of the system we have in place now is that an 18 year old is legally able to be separate from their parents, providing a good wall against potential parental coercion.
Youth-fractional-voting could also lead to (I might be stretching it again here, but maybe not all that far) discrimination against those who are single. Politicians would tweak their policies to benefit families. Some might say that for once schools would get real funding (as they should, as we spend the equivalent of the next fifty nations’ military budget combined on U.S. armed forces while we consistently lag FAR behind in education), but it would probably be a better idea to keep it simple and maybe try to gain support for greater representation for parents on school budget issues (though, admittedly, this is just a very rough idea that came to me, I know it would cause an outcry amongst single people and families without children as well as the less legitimate but far more influential rich citizens).
Politics would become showbiz (even more so than now) as politicians try to appeal to the even younger youth vote that doesn’t care either. Al Gore did the macarena, I’ll let you come up with your own potential horror story.
And lastly, the line where society traditionally considers a person an “adult” might be skewed beyond what it is today with 21 being the drinking age. In the eyes of society (though officially not law), those under 21 are sometimes lowered to the same status as kids begging their older friends to buy them cigs even when they’re not drinking. I wasn’t alive when the age was changed, but at least from what I’ve heard 18 year olds were viewed more as adults in how society treated them in non-drinking situations than they are today. God only knows if something like this would backfire and harm younger citizens in how the nation views its youth.