A little known or discussed fact of life in the US is that, while we are a younger nation than most European countries, our constitution and our voting system is older than any of theirs. Why? Because they have updated their constitutions and/or voting systems while ours have remained static since their inception over 200 years ago. While other countries have taken the pragmatic view that upgrading (taking into account advances in voting theory) might be a good idea, our voting system along with all other aspects of our constitution (not to mention our economic system) might as well have been set in stone. To even question their continued validity or possible improvement is considered by some to be unpatriotic.
Our voting system is called plurality voting. This means that only one candidate out of however many are running for office is chosen by each individual voter, and then the votes are tallied and the one with the most votes wins providing he or she has a sizable enough percentage of the total votes cast. Otherwise there's a runoff. The literature is full of the pitfalls of this method of voting. Suffice it to say it practically eliminates more than two parties. Another disadvantage of our political system is that the US is divided up into districts with each district returning one representative to the bicameral House while each state returns two Senators to the Senate. So each voter is represented in Congress by only three people: one member of the House and two Senators. That's a very small proportion of the total number of lawmakers when you consider that there are 435 Congressmen and women in the House and 100 Senators. 3 out of 535? 0.5%? How does that make you feel, voters, to know that less than 1% of the lawmakers in Washington represent you or that you had anything to do with electing them? In addition there are the problems of the Electoral College (the President is not elected by a direct vote of the public) and gerrymandering which is an artificial way of dividing up political districts in such a way that favors one party or another. Of course, the party in power gets to do this in order to guarantee itself as many seats in perpetuity as possible. A more sensible way to choose a President is by a majority of all the votes cast eliminating the Electoral College altogether, and a more sensible way of choosing legislators would be a system in which each voters gets a chance to vote for more than three legislators. 
Fortunately, voting theorists have not been inactive. There are at least three methods which promise to be an improvement over the current state of affairs vying for the hearts and minds of the public - at least some members of the public, the cognoscenti, who have bothered to consider such things: range voting (RV - not to be confused with those behemoth gas guzzlers), instant runoff voting (IRV) and approval voting (AV). Each method has its supporters, defenders, detractors, protagonists, antagonists and critics. Approval voting is simple enough. Instead of voting for one out of however many candidates are running, you vote for all the candidates you approve of. Instead of marking the ballot once in each race, you mark it multiple times. Obviously, it wouldn't make sense to mark it for every candidate who is running although I'm sure there are many who would. IRV is more complicated, but you can Google it and find out more than you really wanted to know. That leaves range voting.
You are already familiar with it as this is the method used to score Olympic athletes. You would rate each candidate on a scale from 1 to 10 or 0 to 20 or -99 to +99. The actual limits to the range are somewhat arbitrary as long as each voter can assign ratings over the same range. Then you tote up the score for each candidate and the one with the most points wins. Or you can take the average and the one with the highest average wins. There is one refinement, however, with reference to the above linked website. You do not have to actually vote for each candidate. If there are 100 running and you actually rate only 50 filling in an X for the remaining fifty, then the average is computed by dividing the total (over all voters) votes cast for a candidate divided by the sum of all the voters who actually cast a vote for that candidate (Xs excluded). A candidate needs a quorum of votes to win where a quorum is defined as half the total points of the highest point getter. So, theoretically, a candidate with half the total points of the highest total point getter could win the election if sufficiently few voters actually voted for him or her while sufficiently many voters put down an X for him or her. This seems to introduce a certain amount of arbitrariness to the method, but, obviously, something would have to be done to prevent a candidate whom only a handful of voters voted for (all presumably giving him the highest score) from winning. An alternative way of handling this situation would be to just use total point scores forcing each voter to make a decision regarding each candidate. For candidates unfamiliar to any particular voter, that voter could use a proxy rating. A proxy rating would be provided by an expert of the voter's own political persuasion or someone trusted by the voter who is familiar with the candidate. It could be a rating provided by the voter's political party. Without having done an extensive analysis, this seems somewhat less arbitrary to me.
Donald Saari is a proponent of the Borda count. Steven Brams is a proponent of Approval Voting and Warren D Smith is a proponent of Range Voting. I also independently came up with a version of range voting which I called the Lawrence Count. Due to the serendipity of the internet, someone perusing my website, Social Choice and Beyond, brought to my attention that, unbeknownst to me at the time, there exists a major website promoting and expounding on a similar voting method. Thus are like-minded people all over the world brought into contact with one another thanks to the world wide web! This is truly amazing! As I said on my webpage: "The Lawrence Count is a modified Borda Count which seems so obvious that maybe someone has already discovered it. If so, I relinquish the name and any claim to being its progenitor." So I will change my webpage to indicate that I'm no longer pretentious enough to name something after myself especially if someone else has already discovered it. By the way Warren D Smith doesn't claim to have discovered it either so I guess it was too obvious for anyone to have discovered it, and Smith claims that actually the ants and honey bees discovered it.
The three gentlemen named above go round and round trying to prove that their method is the best and showing the pitfalls of all the others. My opinion is that approval voting is a step above plurality voting but is too simple to take into account the range of expression a voter may wish to demonstrate. It's as if Olympic ice skaters were either approved or disapproved by the judges and then their scores computed. Would you be satisfied with that? The Borda count is too rigid. It has the anomaly that, if one candidate drops out of the race, point values must be reassigned with the result that someone could win who previously was ranked last. Range Voting, in my opinion, is a modified Borda count in that the underlying grid remains constant whether or not candidates enter or drop out of the election. Point values remain the same except for some strategic considerations which, again in my opinion, the voter has a right to take into consideration. There is maximum expressivenesss in that the voter not only gets to rank the candidates but also gets to indicate to an extent how much he or she favors one over another. If each voter gives his or her most favored candidate the highest possible score and his least favored the lowest posssible, then he or she will be getting the most strategic value out of his or her vote. If there is one candidate who is so horrible compared to all the others in the mind of a particular voter, it would not only be honest but strategically advantageous to give the horrible candidate a zero and all others the highest possible rating. Likewise, if there is one candidate who is far and away the most superior compared to the other candidates, it would be honest and strategic to give that candidate the highest rating and all others a zero. Another point is that the point spread from lowest to highest score (say 1 to 99) need only be as great as the sensitivity of the most sensitive voter where sensitivity is defined as the most perceptive voter's ability to make a one point distinction between two candidates. Presumably some voter would be able to rate some candidate in a meaningful way as a 53 and another as a 54, for example.
One reason for the lack of agreement regarding voting methods is Arrow's Impossibility Theorem which states in general terms that there is no democratic voting system which obeys certain rational and ethical criteria. This has given rise to the field of social choice theory. Not everyone would agree with Arrow's choice of rational and ethical criteria but, be that as it may, in over 60 years no one has been able to show that Arrow didn't know what he was talking about. So even if in some sense democratic voting systems are impossible, elections are still held and some voting methods are definitely better than others, and, even though there is no general agreement, there is still hope that we will be able to do better in the future than we have done in the past. Hope springs eternal!
