Voting system
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Voters_at_the_voting_booths_in_1945.jpeg
Voting systems are methods (algorithms) for groups of people to select one or more options from many, taking into account the individual preferences of the group members. Voting is best known for its use in elections and is often seen as the defining feature of democracy, where citizen preferences are used to determine the composition of government. In addition, voting 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 (See consensus decision making for disciplined consensus methods and how they relate to voting).
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1.1 The ballot |
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 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.
Party-list systems
In party-list proportional representation systems, candidates can be aligned with, or nominated by, parties, and the party's list of candidates plays a functional role within the system. These parties may in turn be aligned with other parties, to form coalitions, which can play roles beyond those played by the party. These systems are designed to ensure proportional representation, the idea that the candidates selected from a given party (or, in non-party-list systems, informal grouping) should be in proportion to the votes cast for that party. Some of these systems, however, 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 very small parties from participating in a parliament, in order to maintain stability of governments.
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; 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
Single-winner systems
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).
- Motion and amendment - treating the choice like another substantial motion, subject to amendment and possibly debate.
- Approval voting (AV) - 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
- 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
- Instant-runoff voting (IRV, also known as alternative vote or "preference voting")
- Tied rankings sometimes 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 (a.k.a. Schwartz sequential dropping (SSD), cloneproof Schwartz sequential dropping (CSSD), beatpath method, beatpath winner, path voting, path winner)
- Copeland's method
- Bucklin voting: approval runoff; voters vote for more candidates each round until a candidate reaches a majority
- Condorcet method, actually several families of systems that satisfy Condorcet's criterion:
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
- Non-party-list systems
- Plurality/majority
- Block voting - Also called Plurality-at-large
- Semiproportional
- Plurality/majority
- Party-list proportional representation. Allocation methods:
- Mixed Systems
- Additional Member System (also called Mixed Member Proportional)
- Parallel voting (also called Supplementary Member system)
Criteria in evaluating voting systems
Various criteria are used in evaluating voting systems. These criteria define potentially desirable properties of voting systems mathematically, so that different systems can be compared using the same criteria.
It is impossible for one voting system to pass all criteria in common use. For example, Arrow's impossibility theorem demonstrates that several desirable features of voting systems are mutually contradictory. For this reason, someone implementing a voting system has to decide which criteria are important for the election.
These criteria include:
- Majority criterion - Does the first choice of a majority win?
- Mutual majority criterion - If a majority prefers every choice in a set to all other choices, is a member of the set selected?
- Monotonicity criterion - Is it impossible to cause a choice to lose by ranking it higher, or win by ranking it lower?
- Consistency criterion - If the electorate is divided in two and a choice wins in both parts, does it win overall?
- Participation criterion - Is it always better to vote honestly than to not vote?
- Condorcet criterion - If a choice beats every other choice in pairwise comparison, does it win?
- Smith criterion - If every choice inside a set beats every choice outside the set in pairwise comparison, is a member of the set selected?
- Independence of irrelevant alternatives - Does the winner never change from A to B just because an unrelated choice C enters the race?
- Independence of clone candidates - If multiple similar choices are available, is the result of the election unaffected by their presence, or do they help or hurt each other?
A more extensive list of criteria is on the voting system criteria page.
Voting systems are also judged with less-mathematical criteria:
- Simplicity
- Speed of vote-counting
- Reduction of potential for fraud or disputed results
- Resistance to strategic voting
- Proportionality (proportional representation), for multiple-winner methods
| Majority | Monotonicity | Participation | Condorcet | Consistency | IA independence | clone independence | |
|---|---|---|---|---|---|---|---|
| Approval | No | Yes | Yes | No | Yes | Yes | Yes |
| Borda | No | Yes | Yes | No | Yes | No | No (teaming) |
| Copeland | Yes | Yes | No | Yes | No | Local | No (crowding) |
| IRV | Yes | No | No | No | No | No | Yes |
| Plurality | Yes | Yes | Yes | No | Yes | No | No (vote-splitting) |
| Range voting | No | Yes | Yes | No | Yes | Yes | Yes |
| Ranked Pairs | Yes | Yes | No | Yes | No | Local | Yes |
| Schulze | Yes | Yes | No | Yes | No | Local | Yes |
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 Instant-Runoff require centralization, and others such as multi-round runoff require multiple polling rounds.
Related terminology
- voting strategy
- Any way of voting, when it's discussed in terms of its possible or intended affect on the outcome.
- strategic or tactical voting
- When a voter self-consciously marks a ballot in a manner different from their actual preferences, in the hope of optimizing the outcome. (While the adjectives 'strategic' and 'tactical' usually have nearly opposite meanings when used to describe other things, in this case, they commonly both have the meaning given here.)
Famous theoreticians of voting systems
- Kenneth Arrow (mathematically demonstrated the limitations of voting systems)
- Jean-Charles de Borda (devised the Borda count)
- Steven Brams (one of the inventors and chief academic proponents of Approval Voting)
- Andrew Inglis Clark (promoted the use of STV in Tasmania)
- Peter Fishburn (for his multiple proofs demonstrating the mathematical possibilities of voting systems.)
- Marquis de Condorcet (proposed the method of pairwise comparison and the Condorcet criterion; discovered the Condorcet paradox)
- Maurice Duverger (observed effects of proportional vs. majoritarian systems)
- Alan Gibbard and Mark Satterthwaite (for the Gibbard-Satterthwaite theorem that demonstrates any deterministic voting system with three or more alternatives is subject to either some form of Arrovian dictatorship or strategic voting)
- Thomas Hare (devised STV a.k.a. the Hare Method)
- Victor d'Hondt (devised a method of seat allocation under proportional representation)
- Ramon Llull (for his independent discovery of a method similar to Condorcet's method of pairwise comparison and possibly the Borda count centuries before Borda or Condorcet)
- Edward J. Nanson (devised Nanson's method from the Borda count which selects the Condorcet winner if one exits)
- Donald G. Saari (http://www.math.uci.edu/~dsaari/shortcv.pdf) (devised new methods for mathematical analysis of positional voting systems, and demonstrated the advantages of the Borda count over other positional voting methods)
- Nicolaus Tideman (proposed ranked pairs and "comparison of pairs of outcomes by single transferable vote")
See also
- Center for Voting and Democracy
- Disapproval voting
- Duverger's law
- Electoral reform
- Grassroots democracy
- Party system
- Political scientists
- Politics
- Representative democracy
- Spoiler effect
- Table of voting systems by nation
- Tactical voting
- Vote counting systems
References
- Electoral Systems: A Comparative Introduction ISBN 0333801628
External links
(alphabetical by title)- Accurate Democracy: Voting Tasks and Voting Systems (http://accuratedemocracy.com/voting_systems.htm) by Rob Loring
- Administration and Costs of Elections Project documents on electoral systems (http://www.aceproject.org/main/english/es/es.htm)
- Analysis of Democratic Institutions: Structure, Conduct and Performance (http://home.uchicago.edu/~rmyerson/research/perspec.pdf) Article by Roger B. Myerson.(PDF)
- PhD seminar on Choice Theory (http://faculty.fuqua.duke.edu/~rnau/choice/choice09.pdf) (PDF) Article by Robert Nau.
- Common Voting Rules as Maximum Likelihood Estimators (http://www-2.cs.cmu.edu/~conitzer/MLEvotingUAI05.pdf) Article by Vincent Conitzer and Tuomas Sandholm.(PDF)
- Condorcet.org election methods resource (http://condorcet.org/emr/) by Blake Cretney
- Deliberative Democracy and the Problem of Voting (http://pressurecooker.phil.cmu.edu/Academic/Papers/MS-thesis.htm) Article by David Emmanuel Gray.
- A different way to vote (http://www.masquilier.org/republic/election/) by AugustinMa. Of interest is the modified (http://www.masquilier.org/libre/phpbb/) version of the popular phpBB bulletin board that can be found here (http://www.masquilier.org/agora/). The board allows the users to create plurality, approval and condorcet (Schulze) polls and cast their ballots (http://www.masquilier.org/agora/viewforum.php?f=7).
- Efficiency in Polling (http://www.newuniversity.org/print.php?id=1032) Article by Courtney Baird.
- electionmethods.org by Russ Paielli
- Electowiki (http://wiki.electorama.com/wiki/Main_Page) A wiki that focuses on voting theory, which covers some topics not found in wikipedia. Also contains older versions of some wikipedia voting articles.
- Election methods list (http://electorama.com/em): A mailing list containing technical discussions about election methods
- Evaluating Voting Methods (http://theorem.ca/~mvcorks/code/voting_methods.html) Article by Matt Corks
- The history of voting (http://www-gap.dcs.st-and.ac.uk/~history/HistTopics/Voting.html)
- How Large a Coalitional Should Be to Manipulate an Election? (http://www.math.auckland.ac.nz/~slinko/Research/IC6.pdf) (PDF) Article by Arkadii Slinko.
- May the Best Man Lose (https://www.discover.com/issues/nov-00/features/featbestman/) article on Approval voting and Borda Count by Dana Mackenzie.
- Minimal Monotonic Extensions of Scoring Rules (http://www.hss.caltech.edu/Events/SCW/Papers/erdeo.pdf) Article by Orhan Erdem and M. Remzi Sanver. (PDF)
- A New Monotonic and Clone-Independent Single-Winner Election Method (http://www.mcs.vuw.ac.nz/~ncj/comp303/schulze.pdf) (PDF) by Markus Schulze (mirror1 (http://www.citizensassembly.bc.ca/resources/submissions/csharman-10_0409201706-143.pdf), mirror2 (http://lists.gnu.org/archive/html/demexp-dev/2003-09/pdflQW7IlpAfC.pdf))
- On the Likelihood of Condorcet's Profiles (http://www.eco.fundp.ac.be/cahiers/filepdf/c223.pdf) (PDF) Article by V. Merlin, M. Tataru, and F. Valognes.
- On the impact of indifferent voters on the likelihood of some voting paradoxes (http://www.hss.caltech.edu/Events/SCW/Papers/merlv.pdf) (PDF) Article by Vincent Merlin and Fabrice Valognes.
- ODP category on voting systems (http://dmoz.org/Society/Politics/Campaigns_and_Elections/Voting_Systems/)
- In Praise of Manipulation (http://personal.lse.ac.uk/DOWDING/Files/Manipulaiton_web_04_05.pdf) (PDF) Article by Martin van Hees and Keith Dowding.
- Preferential Voting FAQ (http://www.braindoll.net/vote) (see glossary at the end)
- President Perot or fundamentals of voting theory illustrated with the 1992 election (http://mason.gmu.edu/~atabarro/Perot.pdf) (PDF) Article by Alexander Tabarrok.
- pSTV -- Software for computing a variety of voting systems including IRV, STV, and Condorcet (http://stv.sourceforge.net/)
- A Statistical Investigation of Social Choice Rules (http://www.math.auckland.ac.nz/~slinko/Research/rules3.pdf) Article by Arkadii Slinko and Wayland Leung. (PDF)
- Single winner page (http://www.barnsdle.demon.co.uk/vote/sing.html) by Mike Ossipoff
- Student's Social Choice (http://www.maa.org/editorial/knot/LiberalArts.html) A column by Alex Bogomolny using java applets to illustrate various concepts of choice.
- Universal voting protocol tweaks to make manipulation hard (http://www-2.cs.cmu.edu/~conitzer/tweakIJCAI03.pdf) (PDF) An article by Vincent Conitzer and Tuomas Sandholm.
- Vote Aggregation Methods (http://lorrie.cranor.org/pubs/diss/node4.html) An article by Lorrie Cranor evaluating voting methods.
- Voting by Adaptive Agents in Multi-candidate Elections (http://www.pubchoicesoc.org/papers2005/Moser.pdf) Article by Scott Moser.(PDF)
- Voting, Elections, Democracy, Republicanism, and the Electoral College (http://webspeedreader.com/articles/voting.htm) by William C. Spaulding
- Voting methods: tutorial and essays (http://fc.antioch.edu/~james_green-armytage/voting.htm) by James Green-Armytagede:Wahlsystem
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