In this video, C.G.P. Grey explains the Single Transferable Vote, a system in which voters get to specify a second choice in case their primary choice candidate doesn't win -- which can lead to a much more representative result. This system is used around the world, most notably in Australia. (Indeed, when I first heard about this kind of voting, it was explained to me as an "Australian Ballot.") To keep things safely abstract, Grey uses a fictional animal kingdom as a way to talk about different constituencies.*
If you haven't seen Grey's 2011 video The Problems with First Past the Post Voting Explained, that's a useful starting point in case you don't get why there's a problem to begin with. Once you're prepared to get nerdy about voting, let's enjoy some monkey business:
See also: What's Up with the Electoral College?
* = VOTE MONKEY 2014 ALL THE WAY (my name is Monkey McChimperson, and I endorse this message).