Science Fair Project Encyclopedia
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 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 (See consensus decision making for disciplined consensus methods and how they relate to voting).
Additionally to the basic process of voting in local districts, the forming of a government forms the basics of a democracy.
Aspects of voting systems
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.
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.
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?
- Participation criterion - Is there ever an advantage to not voting?
- Summability criterion - Can the vote-tallying process be distributed across many locations?
- Condorcet criterion - If a choice is preferred by a majority over every other choice, does it win?
- Consistency criterion - If the electorate is divided in two and a choice wins in both parts, does it win overall?
- Independence of irrelevant alternatives - Can the winner be changed from A to B when an unrelated choice C enters the race?
- Independence of clone candidates - If multiple similar choices are available, do they help or hurt each other, or is the result unaffected?
Voting systems are also judged with less-mathematical criteria:
- 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||Summability||Condorcet||Consistency|| Independence of|
| Independence of|
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, Cloneproof Schwartz Sequential Dropping, 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.
List of 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).
- Approval voting (AV) - Voters may vote for as many candidates as they like. Candidate with most votes wins. Sometimes considered a version of Cardinal Rankings (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
- Tied rankings permitted
- Condorcet method, actually several families of systems that satisfy Condorcet's criterion:
- Bucklin voting: approval runoff; voters vote for more candidates each round until a candidate reaches a majority
Rated voting methods
- Cardinal Ratings (CR) (Also called range voting) - voters give whole number points (example 1-10) to each candidate, totaled in single round
- Rated ballots may also be used for ranked voting methods, in cases where tied rankings are allowed.
- Non-party-list systems
- Party-list proportional representation. Allocation methods:
- Mixed Systems
- 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)
- Stephen 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 Condorcet criterion)
- Maurice Duverger (observed effects of proportional vs. majoritarian systems)
- Alan Gibbard and Mark Satterthwaite (for the Gibbard-Satterwaite Theorem that demonstrates any deterministic voting system with three or more alternatives is subject to either to 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 the Condorcet method and possibly the Borda count centuries before Borda or Condorcet, which received little attention due to his excommunication by the Roman Catholic Church, which was later revoked by the Church in the 19th century. Note, that Condorcet and Borda did investigate their respective methodologies with mathematical rigor.)
- Donald G. Saari (devised new methods for mathematical analysis of positional voting systems, and demonstrated the advantages of the Borda count over other positional voting methods)
- Center for Voting and Democracy
- 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
- Grassroots democracy
- Party system
- Political scientists
- Representative democracy
- Spoiler effect
- Table of voting systems by nation
- Tactical voting
- Vote counting systems
- pSTV -- Software for computing a variety of voting systems including IRV, STV, and Condorcet
- Administration and Costs of Elections Project documents on electoral systems
- The history of voting
- Voting Tasks and Voting Systems @AccurateDemocracy
- ODP category on voting systems
- Election Methods Education and Research Group
- defensive strategy criteria page
- Condorcet.org definitions
- Preferential Voting FAQ (see glossary at the end)
- Emocracy Emocratic Elections Investigation
- May the Best Man Lose article on Approval voting and Borda Count by Dana Mackenzie.
- 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 (Cloneproof Schwartz Sequential Dropping) polls and cast their ballots.
- Evaluating Voting Methods Article by Matt Corks
- Student's Social Choice A column by Alex Bogomolny using java applets to illustrate various concepts of choice.
- Vote Aggregation Methods An article by Lorrie Cranor evaluating voting methods.
- Robust Voting An article by Gilbert W. Bassett, Jr. and Joseph Persky.
- Voting, Elections, Democracy, Republicanism, and the Electoral College Discusses voting, elections, democracy, republicanism, and the Electoral College. Includes a procedural guide to the electoral college, parts of the Constitution and constitutional amendments regarding voting and elections, and includes the original paper by Alexander Hamilton, "Federalist No. 68 - The Mode of Electing the President", which illustrates much of the founding fathers' original thinking regarding the Electoral College.
- President Perot or fundamentals of voting theory illustrated with the 1992 election Article by Alexander Tabarrok.
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