First Past the Post (FPTP)
‘First past the post' is a way of voting combined with a way of counting the votes. It can be used for single and multiple member constituency elections. In a single member election the candidate with the highest number, not necessarily a majority, of votes is elected. When this method is used to elect MPs to parliament in a single member, party based election, this method can result in significant distortions.
The number of MPs elected for each party is unlikely to be proportionate to the number of votes cast nationwide for the different parties. Small parties with thinly spread support may have proportionately fewer MPs elected. Coversely a small party with tightly concentrated support may have proportionately more MPs elected. It is possible for party A to have fewer votes than party B but still have more MPs, and thus be able to form the Government.
FPTP is used in the UK, Canada, and eleswhere. It favours a two political party system

Single Transferable Vote (STV)
The single transferable vote (STV) is a voting system designed to achieve a more proportional result. There are variations of the system. To achieve proportionality the system requires constituencies to be organised as multi member constituencies. A form of preferential voting is used. Counting is complex. Each vote is initially allocated to the voter's preferred candidate. Depending on the number of electors and the number of candidates, each candidate needs a minimum number of votes to be elected. Counting is done in stages. A candidate is eliminated at each stage. When a candidate is eliminated, or has enough votes to be elected, surplus votes are transferred to the remaining candidates. There are different methods of doing this.
While not a strictly proportional electoral system, results may be broadly proportional, although this does depend on the interplay between the numbers of parties competing in the election and the size of the multimember constituencies.
STV is used in Ireland , Australia , and elsewhere.

The Alternative Vote (AV)
The Alternative Vote also known as Instant-runoff voting (IRV), preferential voting, and ranked choice voting, is a voting system used to elect a single winner. Voters rank candidates in order of preference. Counting is in stages. Votes for the first choice candidate are counted as one vote. If a candidate secures a majority of votes cast, that candidate wins. Otherwise, the candidate with the fewest votes is eliminated. The ballots of the eliminated candidate(s) are re-counted as one vote for the highest ranked candidate remaining on the ballot. This process continues until a winning candidate receives a majority of the votes.
AV is used in Australia and elsewhere. It is often to elect leaders of groups, and Mayors.

Alternative Vote Plus (AV+)
The Alternative Vote Plus, is a semi-proportional voting system invented by the 1998 Jenkins Commission.
AV+ is an additional member system. As in the Alternative Vote voting system, candidates are ranked numerically in order of preference. To ensure proportionality, an additional group of members are elected through a regional party lists system. These members are 20% of the whole parliament. Constituency boundaries would need to be redrawn to accommodate a smaller number of constituency MPs.
The system is untried.

Total Representation
Total Representation involves election of Constituency and ‘Party' MPs. Constituency MPs are elected by the FPTP method. Party MPs are elected by pooling all the votes cast for the unsuccessful candidates in all the constituencies and dividing them proportionally among all the parties which fielded candidates in the election.
Constituency boundaries would need to be redrawn to accommodate a smaller number of constituency MPs.
The system is untried.