ranked choice voting (a.k.a. instant runnoff voting)

From Wikipedia http://en.wikipedia.org/wiki/Instant-runoff_voting:
"Instant-runoff voting (IRV) is a voting system used for single-winner elections in which voters rank candidates in order of preference. In an IRV election, if no candidate receives a majority of first choices, the candidate with the fewest number of votes is eliminated, and the votes cast for that candidate are redistributed to the remaining candidates according to the voters' indicated preference. This process is repeated until one candidate has a majority among votes for candidates not eliminated."

Here's a demo of IRV that shows the process and results: http://www.demochoice.org/dcballot.php?poll=oakzoo
I've done the demo several times. The clearest illustration of how IRV works comes when you rank the animals in order from first to last as 1. warthog, 2. gibbon, 3. goat, 4. elephant. After ranking and confirming your vote, click the button labeled "how your vote counted". It will step you through the process it used to select a winner.

Why is IRV such a great thing?

1. It allows voters to truly vote their conscience. For example, a liberal could vote for Ralph Nader in 2000 without siphoning a vote away from Al Gore. Or a voter in either party during this year's primaries could vote for Ron Paul or Dennis Kucinich and still have a counting vote for one of the two eventual front-runners in his or her party. with IRV we would have a much clearer picture of the true mood of the electorate.

2. It makes the major parties more accountable to the voters. Democrats could no longer assume that they had your vote because your only viable alternative was to vote for a Republican, and vice versa. Large numbers of people would be free to vote for a third party, such as the Green Party or Libertarian Party, so these parties would keep the major parties honest.

3. Closely related to number 2, it weakens the stranglehold of the two party system. A third party with an inspiring candidate and platform could actually win at some point if the major parties drift too far from the will of their constituencies.

IRV is used in several places around the country and the world, such as San Francisco, Australia, Ireland, United Kingdom, Papua New Guinea, and Pierce County Washington. Numerous localities around the U.S. are in the process of implementing it as well.
The major opponents of IRV in this country are, you guessed it, the Democratic and Republican party machines. They are the ONLY ones with anything to lose by instituting it. The Green Party is a major proponent of IRV, for the same reasons that the big parties oppose it.

You can get active in promoting IRV. Here's more info:

http://www.instantrunoff.com/
http://www.fairvote.org/irv/
http://www.calirv.org/
http://irvwa.org/