Electoral system

Voting systems or election methods are methods for groups of people to select one or more options from many, taking into account the individual preferences of the group members. Voting is often seen as the defining feature of democracy, and is best known for its use in elections — but it can also be used to award prizes, to select between different plans of action, or as a means for computer programs to evaluate which solution is best for a complex problem.

A key property of voting systems is that, because they are algorithms, they must be formally defined. Consensus, for example, which is sometimes put forward as a voting system, is more properly a broad way of working with others, analogous to democracy or anarchy.

Several of the popular voting methods, categorized by their important properties

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.

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 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.

None of the above option

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, all candidates or poll options are excluded from a subsequent election.

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.

Government formation

The formation of the government happens after the election and can be done in multiple ways. This is independent of the elections themselves. There are many systems of government, each of which has an electoral system and a system of government formation as components. Typical parliamentary systems use a two-step process, first, an election is called where the representatives are elected by citizens through a balloting system, then the government is formed from the representatives through its own process.

Criteria in evaluating voting systems

Various criteria are used in evaluating voting systems. However, it is impossible for one voting system to pass all criteria in common use. For example, Arrow's impossibility theorem demonstrates that the following criteria are mutually contradictory:

• The voting system should always give a result
• If a voter improves the ranking of a particular option, that option should not be disadvantaged (monotonicity criterion)
• Removing a candidate should not change the winner of an election unless that candidate is the winner (independence of irrelevant alternatives)
• Every possible outcome should be achievable
• Non-dictatorship (i.e. more than one person's vote matters)

Other criteria which have been used to judge voting systems include:

• Proportionality
• Simplicity - speed
• Resistance to strategy
• Reduction of potential for dispute after the fact
• Reduction of potential for fraud
• Monotonicity criterion (MC)
• Consistency Criterion (ConC)
• Broadness Criterion (BC)
• Condorcet Criterion (CC)
• Generalized Condorcet criterion (GCC)
• Strategy-Free criterion (SFC)
• Generalized Strategy-Free criterion (GSFC)
• Strong Defensive Strategy criterion (SDSC)
• Weak Defensive Strategy criterion (WDSC)
• Favorite Betrayal criterion (FBC)
• Participation criterion (PC)
• Summability criterion (SC)

Voting systems can be abstracted as mathematical functions that select between choices based on the utility of each option for each voter. This greatly resembles a social welfare function as studied in welfare economics and many of the same considerations can be studied. For aspects such as simplicity, dispute, and fraud, the practical implementation is far more important than the abstract function. However, the choice of abstract function puts some constraints on the implementation. For instance, certain voting systems such as First Past the Post, Schulze, or Borda Count can be tallied in one distributed step, others such as IRV require centralization, and others such as multi-round runoff require multiple polling rounds.

List of Parliamentary Systems

Regional Systems

Single Member systems

• Plurality Voting: A valid vote can choose only one candidate
  • Single Member Plurality
  • Random ballot
• Ordinal Voting: A valid vote can rank candidates 1,2,3... (Tied rankings are permitted in some methods but not others)
  • Tied rankings not permitted
    • 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
  • Tied rankings permitted
    • Condorcet method, actually several families of systems that satisfy Condorcet's criterion:
    • Ranked Pairs (RP) and variants such as Maximize Affirmed Majorities and Maximum Majority Voting
    • Schulze, which is also known as "Beatpath Method" or "Cloneproof Schwartz Sequential Dropping"
    • Copeland's method
  • Condorcet-compliant methods
    • VOTE-123: another name for Condorcet methods, stands for Virtual One-on-one Tournament Elections using 1st, 2nd, & 3rd choices
    • Majority voting or Maximum Majority voting: another term often used for Condorcet methods
  • Bucklin voting: approval with virtual runoff; each voters' ballot is counted for more candidates each round until some candidate reaches a majority
• Cardinal Voting: voting A valid vote allows independent numerical values to be associated with each candidate. (The set of valid values is limited.)
  • Approval Voting
  • Score Voting
  • STAR voting
  • Majority Choice Approval
  • Median Ratings

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.

Multi-Member Systems

• Bloc Systems
  • Bloc Approval Voting: Each voter chooses (no ranking) as many candidates as desired. Only one vote is allowed per candidate. Voters may not vote more than once for any one candidate. Add all the votes. Elect the candidates with the most votes until all positions are filled.
  • Bloc Plurality Voting: Each voter chooses as many candidates as there are seats to be elected. Add all the votes. Elect the candidates with the most votes until all positions are filled.
  • Bloc Score Voting: Each voter scores all the candidates on a scale with three or more units. Starting the scale at zero is preferable. Add all the votes. Elect the candidates with the highest scores until all positions are filled.
  • Cumulative voting
• Sequential Systems
  • Sequential Proportional Approval Voting
  • Proportional approval voting
  • Reweighted Range Voting
  • Sequential Monroe
  • Allocated Score
  • Sequentially Subtracted Score
  • Single transferable vote
  • Single non-transferable vote
• Optimal Systems
  • Harmonic Voting

Partisan Systems

• Party-list proportional representation. Allocation methods:
  • Highest averages methods
    • Sainte-Laguë method
    • d'Hondt method
  • Largest remainder methods

Mixed Systems

• Mixed Member Proportional
  • parallel mixed system
  • mixed compensatory system

Famous theoreticians of voting systems

• Andrew Inglis Clark (promoted the use of STV in Tasmania)
• Jean-Charles de Borda (devised the Borda count)
• Marquis de Condorcet (proposed the Condorcet criterion)
• Maurice Duverger (observed effects of proportional vs. majoritarian systems)
• Thomas Hare (devised STV a.k.a. the Hare Method)
• Victor d'Hondt (devised a method of seat allocation under proportional representation)
• Kenneth Arrow (mathematically demonstrated the limitations of voting systems)

See also

• Disapproval voting (anyone not disapproved, effectively wins - this method is more associated with reality game shows than with public elections)
• Duverger's law
• Electoral reform
• Electoral Systems: A Comparative Introduction ISBN 0333801628
• Party system
• Seniomeritocracy
• Spoiler effect
• Table of voting systems by nation
• Tactical voting

External links

• pSTV -- Software for computing a variety of voting systems including IRV, STV, and Condorcet
• Condorcet with Dual Dropping PERL scripts
• Administration and Costs of Elections Project documents on electoral systems
• The history of voting
• Center for Voting and Democracy
• Voting Tasks and Voting Systems @AccurateDemocracy
• ODP category on voting systems
• Election Methods Education and Research Group
• defensive strategy criteria page
• Preferential Voting FAQ (see glossary at the end)
• Emocracy Emocratic Elections Investigation
• James Green-Armytage's voting methods page Includes a beginner-friendly introduction and a helpful in-depth tutorial
• A New Monotonic and Clone-Independent Single-Winner Election Method (PDF) by Markus Schulze (mirror1, mirror2)
• A different way to vote by AugustinMa. Of interest is the modified version of the popular phpBB bulletin board that can be found here. The board allows the users to create plurality, approval and Condorcet (Schulze) polls and cast their ballots.

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