Feel free to add anything or correct me.

First past the post:

Voters only vote for one candidate. The candidate with the most votes wins. Very susceptible to 'spoiler' candidates and reinforces a two party system.

Australia: Preferential Voting
America: Instant Runoff Elections
Canada: Single Transferable Vote

Voters rank all or some of the candidates in order of preference. If you give your first preference to the candidate with the lowest number of first preference votes, that candidate will be struck out of the race and your vote goes to your second preference. This continues until one candidate has over 50% of the vote.

Proportional Representation: Voters don't get to elect a single local candidate - instead they elect a group of people. The number of members of parliament each party (or individual) gets is proportional to the percentage of the popular vote. This favours the minor parties the most and is used in Israel and the Australian Senate (on a state by state basis). It can be combined with preferential voting (I'd say it needs to be otherwise the spoiler problems get very unpredictable). You can allow people to vote for specific candidates or parties. In the Australian system each state elects six Senators. When a party or candidate gets 1/7th of the vote (after preferences are distributed if necessary) then one candidate gets elected - until 6/7ths of the vote has been used to elect six people and the remaining candidate in first position has less than 1/7th of the vote and just misses out.

Spoiler Candidate:

First past the post elections are only suitable for 2 candidates. A third (minor) candidate will tend to take more votes from one of the major players than the other. If 55% of the public prefer candidate A over candidate B, but 15% out of that 55% vote for minoar candidate C, the candidate B wins with 45% (A:40%, C: 15%), even though candidate A would win in a runoff election. This is the reason for instant runoff elections.

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Australia: Preferential Voting
America: Instant Runoff Elections
Canada: Single Transferable Vote
United Kingdom: Alternative Vote?

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Runoff Election: This is actually two elections. The second election is a runoff between the two leading candidates from the first election. Both elections run on a first past the post basis (which works just as well as instant runoff for the election with only two candidates). There is still a risk of strategic voting and spoiler candidates. In the first election, voters will tend to vote for the preferred option from the three leading candidates in order to get them into the top two and into the next election. In one year this resulted in a runoff between two right wing candidates for the French presidency, because of all the left wing spoiler candidates. Compare this to the first past the post system where voters tend to vote for the top two candidates. The problems with runoff elections are sometimes mistakenly associated with instant runoff elections, to which they do not apply.

Strategic Voting: not voting for a spoiler candidate even if he or she is your favourite because you would be throwing your vote away. Sometimes referred to as insincere voting.

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another term for instant runoff voting:

http://en.wikipedia.org/wiki/Instant-runoff_voting

The San Francisco Department of Elections (http://www.ci.sf.ca.us/site/election_page.asp?id=24269) prefers the term "Ranked Choice Voting" because "the word 'instant' might create an expectation that final results will be available immediately after the polls close on election night."

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Majority winner: a candidate with more than 50% of the vote

Plurality winner: a candidate with more votes than any other candidate. This is not necessarily a majority. It is possible for a candidate to be the plurality winner under a FPTP system (above), even if the majority of voters prefer another candidate.

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AMS - Additional Member System

http://en.wikipedia.org/wiki/Additional_member_system

two different forms:

SUP - Parallel Voting/Supplimentary member - half the candidates are elected by single member electorates, the other from a proportional representation system. You vote twice - once for your local rep and once for the other system.

MMP - mixed member proportional (aka top-up) AMS usually implies this system. Most representatives elected from single member electorates, but the number of sitting representatives is topped up with candidates who only just lost so that the representation is proportional. Examples are New Zealand and Germany.

These systems get rid of the problems associated with having safe vs swing seats. It encourages active campaigns in all electorates and prevents people in safe seats from feeling that their vote won't make a difference. MMP maintains the highest level of local representation while also achieving proportional representation.

These systems usually use FPTP to elect the local reps, though there is no reason why they couldn't use IRV with the proportional stuff based on first preferences.

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Duverger's law - a FPTP system tends to create artificially reinforced two party dupolies:

http://en.wikipedia.org/wiki/Duverger's_law

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http://en.wikipedia.org/wiki/Tactical_voting

short-term instrumentally rational: describes the way most people vote strategically and why Duverger's law tends to hold - because people vote rationally assuming that they want to be 'instrumental' (ie have an effect) in the short term. This means that they will vote based mainly on the outcome of the current election. This leads to people voting for the two major parties under FPTP systems. If on the other hand if they voted strategically based on long term concerns they would vote for their favourite party even if it meant a significant short term loss in the form of a strong spoiler effect.

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