Around this time of the election cycle, we hear a lot about the importance of voting and how every vote counts. However, very little is said about the paradoxes that can make individual votes meaningless – especially with the introduction of a third party. The Exploratorium (A museum that I can’t wait to take my kids to) put together this excellent video that explores the paradox’s involved in voting.
The end of the video touches on Kenneth Arrow mathematically proving that no decision mechanism can eliminate all of these types of paradoxes. Basically, there is no method for constructing social preferences from arbitrary individual preferences without suffering from a known paradox. We can tamp down some paradoxes but only at the cost of creating others (or eliminating democracy altogether).
Wikipedia has an excellent table showing the voting system criteria used in each of the single-winner systems.
That all being said: Remember to go out and vote!