C.G.P. Grey has a series of four videos on YouTube that help explain different issues with voting in a democracy. All of these videos were published in 2011, but I find them extremely relevant giving our current fiscal problems here in the United States.
The first video explains the problems with first-past-the-post voting. In this system of voting the person with the most votes wins the election.
The second video explains a the alternative vote. It is commonly known as instant-runoff voting. The alternative vote could help the United States move away from the 2 party system and allow room for a third party. This video resonates with me given that I am unhappy with both parties.
The third video explains gerrymandering and a gives a few solutions on how to fix it.
The fourth video explains mixed-member proportional representation. It is an interesting voting system that the video explains better than I can.