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Aspects of voting systems...
 The ballot:
Different voting systems have different forms for allowing the individual to express their tolerances or preferences. In ranked ballot or "preference" voting systems, like Instant-runoff voting, the Borda count, or a Condorcet method, voters order the list of options from most to least preferred. In range voting, voters rate each option separately. In first-past-the-post (also known as plurality voting), voters select only one option, while in approval voting, they can select as many as they want. In voting systems that allow "plumping", like cumulative voting, voters may vote for the same candidate multiple times.
In any instance, the use of DRE, or Direct Recording Electronic, voting systems may compromise the secrecy of the ballot, as well as change, lose, or add fake votes. They offer no paper ballot to be verified by the voter, which should serve as the official record. For this and other reasons, electronic systems are not suitable for use without the production of the voter-verified paper ballot, or VVPB.
District (constituency) size:
A voting system may select only one option (usually a candidate, but also an option that represents a decision), in which case it is called a "single winner system", or it may select multiple options, for example candidates to fill an assembly or alternative possible decisions on the measure the ballot posed.
Some countries, like Israel, fill their entire parliament using a single multiple-winner district (constituency), while others, like the Republic of Ireland or Belgium, break up their national elections into smaller, multiple-winner districts, and yet others, like the United States or the United Kingdom, hold only single-winner elections. Some systems, like the Additional member system, embed smaller districts within larger ones.
Proportional representation.....                              back to top
If a given district is electing more than one representative, then proportional representation is possible. (For example, proportional representation can be used to elect a legislature, but it cannot be used to elect an executive.) The basic idea of proportional representation is that if a given party (or any other political grouping) gets X% of the vote, it should also get X% of the seats in the legislature.
Party-list proportional representation
In a party list system, each voter votes for one party, and then a mathematical formula is used to approximately distribute the seats in the legislature in proportion to each party's share of the vote.
In a closed list system, parties publish an ordered list of candidates before the elections, such that if the party wins N seats, the first N candidates on the list will fill those seats. In an open list system, voters for a party have the ability to determine the ordering of the party list by voting for particular candidates.
Parties may in turn be aligned with other parties, forming coalitions that can play roles beyond those played by the party. Some party list systems have election thresholds--minimum numbers of votes cast for a party to win any seats. The purpose of an election threshold is generally to keep small parties from participating in a legislature.
Single transferable vote proportional representation
Single transferable vote is a proportional representation system in which voters rank individual candidates in order of preference. STV uses a fairly complex mathematical formula to process the ranked ballots into a final result. The basic idea is as follows: If your first choice does not have enough votes to win, he or she is eliminated, and your vote is transferred to your next choice, and possibly to subsequent choices in turn. If your first choice has more votes than he or she needs to win, then some fraction of your vote is transfered to your next choice, and possibly to subsequent choices in turn.
None of the above option                                        back to top
In some voting systems, voters may choose to select none of the candidates (or poll options), by voting for a "None of the above" option. If this option wins, the election fails; typically it will be re-run with a new set of candidates or poll options, all previous ones (having lost to "none of the above") being excluded. The philosophy behind having a "None of the above" option is that all possible alternatives should be considered in a decision; this option represents all of the alternatives not considered explicitly.
Write-in candidate - poll option
Some elections allow voters to write in the name of a person (or of the poll option) not on the ballot as their candidate (or as a poll option). Write-in candidates (poll options) rarely win and votes are often cast for ineligible people or fictional characters. This happens because write-in poll options or candidates are not visible to other voters. This is not usually an issue in the case of an e-voting system, where new write-in poll options or candidates can be made visible as the election takes place. Alternatively, some locations require write-in candidates or poll options to be registered before the election.
List of systems....                                                     back to top
Single-winner systems can be classified by ballot type:
Binary voting A valid vote can only give a yes or nothing to a given candidate.
Ranked voting A valid vote can rank candidates 1,2,3... (Tied rankings are permitted in some methods but not others)
Rated voting A valid vote allows independent numerical values to be associated with each candidate. (The set of valid values is limited.)
They can also be classified on how many times votes can be counted. Methods like Plurality, Borda, and Approval with single counting rounds are simpler since voters can be sure to know how their votes will be applied.
Binary voting methods
First-past-the-post (also called Plurality or Relative Majority or Winner-Take-All) - vote for at most one candidate. Most votes wins, even if this is less than a majority.
Runoff systems
Two-round runoff voting - if no majority, hold a new election with only the top two candidates. This system is used for most single-winner elections in France.
Elimination runoff - if no majority, hold a new election with the weakest candidate eliminated. Repeat until there is a majority.
Exhaustive runoff - no eliminations, repeat balloting until there is a majority. Common in committees. This system is used by the Papal Conclave (if one considers every cardinal as a candidate). The political parties in the United States also use this format in their party conventions.
Motion and amendment - treating the choice like another substantial motion, subject to amendment and possibly debate.
Approval voting - Voters may vote for as many candidates as they like. Candidate with most votes wins. Sometimes considered a version of range voting (see below) with a point range of [0,1]
Random ballot - May also be used for multiwinner elections, or as a tiebreaker for other methods
Ranked voting methods                                          back to top
Instant-runoff voting (IRV, also known as alternative vote or "preference voting")
Supplementary vote: simplified IRV process (two rankings, two rounds)
Borda count: single round count, more points for higher-ranked
Coombs' method: disapproval runoff
Condorcet method, actually a family of systems that satisfy Condorcet's criterion, which includes:
Minimax, a.k.a. Simpson-Kramer, successive reversal
Ranked Pairs and variants such as Maximize Affirmed Majorities and Maximum Majority Voting
Schulze (a.k.a. cloneproof Schwartz sequential dropping (CSSD), beatpath method, beatpath winner, path voting, path winner), and variants such as Schwartz sequential dropping (SSD).
Copeland's method
Bucklin voting: approval runoff; voters vote for more candidates each round until a candidate reaches a majority.
Rated voting methods
Range voting - voters give points in a specified range (for example 0-100) to each candidate. The candidate with the highest total is the winner.
Rated ballots may also be used for ranked voting methods, in cases where tied rankings are allowed.
Multiple-winner systems
Not proportional
Block voting - Also called Plurality-at-large
Proportional approval voting
Cumulative voting
Single non-transferable vote
Quota Borda system
Party-list proportional representation. Allocation methods:
Highest averages methods
Sainte-Laguë method
d'Hondt method
Largest remainder methods
Single transferable vote (STV)
Mixed Systems
Additional Member System (also called Mixed Member Proportional)
Parallel voting (also called Supplementary Member system)

Information courtesy of Wikipedia
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