Additional member system
This electoral system combines some elements of first-past-the-post with some elements of proportional representation. Voters have two votes - one for individual candidates and the other for a party list. The latter element aims to give smaller parties a fairer share of seats.
At present, this system is used for elections to the Scottish Parliament, the Welsh Assembly and the London Assembly.
Alternative vote (AV)
Should electoral reform ever come to Westminster, this method is likely to be the winner. It allows voters to rank candidates in order of preference. If no one receives more than 50 per cent of first-preference votes, the votes for the bottom candidate are redistributed until one candidate has an absolute majority.
In September, Gordon Brown promised to hold a referendum on the alternative vote if Labour is re-elected, but he dismayed campaigners who point out that AV can be even less proportional than first-past-the-post.
Alternative vote plus (AV+)
We have Roy Jenkins (see "Jenkins commission") to thank for this system, which many regard as a perfect marriage of the fairness of proportional representation with the stability offered by majoritarian systems.
AV operates like its bigger brother, but also includes a second vote for a top-up list of MPs, designed to achieve broad proportionality.
Alan Johnson cheered up AV+ fans when he called for a referendum on reform to be held on the same day as the next general election, but the "Clunking Fist" soon crushed his modest proposal.
It is exceptionally rare for individual parties to win a majority of seats under proportional representation, so coalition governments
are the norm. Supporters of electoral reform in Britain argue that coalitions would foster a more consensual approach, one that might guard against divisive decisions such as the one that took Britain into the Iraq war.
With a hung parliament still possible after the next election, Britain could see its first coalition government in decades. A deal between Labour and the Liberal Democrats could hinge on electoral reform.
Paracetamol at the ready? Thankfully, the d'Hondt formula is nowhere near as headache-inducing as it sounds. The system owes
its daunting name to its creator, the Belgian lawyer Victor D'Hondt, but it is more simply known as the "highest-average method".
The formula divides the number of votes cast for a party by the total number of seats gained plus one, which is used to allocate seats in countries with proportional representation.
Under the usual Westminster system, the candidate with the most votes wins the seat regardless of whether he or she has an absolute majority.
The method is still robustly defended by the Tories, who claim that proportional representation would hand power to "political elites".
But critics point to the perverse results it produces. For example, in 1951, the Conservatives won a majority of seats despite winning fewer votes than Labour.
Other countries that use versions of FPTP are Canada, India and the United States.
Here is one phrase that's guaranteed to make electoral reform campaigners a little misty-eyed. Labour set up the commission, named after its chairman, Roy Jenkins, in December 1997. Its task was to investigate alternatives to first-past-the-post.
The result was the sophisticated AV+ system. However, despite some initial warm words, Labour has persistently refused to endorse this method.
The only one of the three main political parties to support proportional representation, the Lib Dems have been persistently penalised under first-past-the-post. In the 2005 general election, they won 22 per cent of the vote but gained only 9.6 per cent of the seats in the House of Commons.
The party favours the single transferable vote, but Nick Clegg has said he would be willing to accept AV+.
The most widely used electoral system in the world, and the purest form of proportional representation (PR) available.
In an open-list system, electors vote for individual candidates, whereas in a closed-list system they vote for parties rather than people.
The closed-list system has been criticised for handing the control of candidate selection to party hierarchies, which tend to favour bland and conformist figures.
The party-list system is currently used for British elections to the European Parliament.
The umbrella term for the range of electoral systems that are designed to reflect the rather reasonable belief that the number of seats
a party wins should reflect accurately the share of the vote that it receives.
Seats in which a party's lead is historically so secure that it is usually guaranteed victory. Think Kensington and Chelsea for the Conservatives or Bolsover for Labour.
Reformers point to this as one of the most undemocratic features of the FPTP system, as it encourages the parties
to focus their policies on a handful of swing voters in marginal constituencies.
Single transferable vote (STV)
This system, which is currently used in Northern Ireland (see page 26), allows voters to list candidates in order of preference from one to five. Should your candidate of choice already have enough votes, or should too few to stand a chance of being elected, your vote will be transferred to your second choice.
This system is similar to AV (see above), but voters are asked to state only a first and second preference. If no candidate achieves an absolute majority, all but the top two candidates are eliminated and their second preferences redistributed. The candidate left with the highest number of votes is declared the winner. This is the system in use for all English mayoral elections.
If a voter's favourite party has no chance of winning, he or she may support an alternative party in order to keep out a more disliked rival. In 1997 and 2001, a significant number of Liberal Democrats voted Labour in order to defeat the Conservatives. Advocates of reform argue that, under proportional representation, electors would be free to vote for their preferred party always.
In a democracy, how can a vote ever be wasted? By voting for losing candidates, or by voting for the winning candidate above the level he or she needs in order to secure the seat. At the last general election, 70 per cent of votes were wasted in this way.
George Eaton writes for Newstatesman.com