Voting Rules for

Different uses for voting need different types of voting.

PoliticalSim software

A Glossary of Democracy

Tools for developing democracy

Click the top row of the table to sort the terms into concept groups or an alphabetical list.

Concept Groups
Legitimate Power
Political Economy
Single-Winner Elections
Multi-Winner Elections
Spatial Simulations
Tally Criteria
Voting Strategies
     Other Tally Rules Defined
Single-Winner Systems
Policy Voting
Budget Voting
Future Rules
001 Accurate democracy elects central and diverse reps for ensemble councils. It enacts the one policy that beats all others, and it gives spending power in proportion to popularity. It is introduced in the illustrated primer on voting systems.
010  Legitimate Power 
012 Mandate, is the authority that votes convey from voters to winners. More effective votes build a stronger mandate.
014 Effective votes are just enough to elect a candidate. Votes for losers do not count, nor do surplus votes that give a winner more than enough. It might make sense to exclude also the votes that elect reps for the opposition party(s), because under old voting rules they get no power to affect laws or budgets. Antonym wasted votes. See quota.
015 Surplus votes give a winner more than enough votes to win. aka excess votes.
016 Threshold of victory, is the number of votes a voting rule requires a candidate to win. aka the quota, the finish line.
018 Wasted votes are votes for a losing candidate and surplus votes which give a winner more than enough to win. Any vote that has no effect is a wasted vote. Perhaps this should include votes for reps who have no power. Synonym dead votes. Antonym effective votes.
020  Political Economy 
021 Government is a means to secure the rights of life, liberty and the pursuit of happiness; "to secure these rights, Governments are instituted among Men, deriving their just powers from the consent of the governed."
022 Free Market implies free from regulation by voters and their reps. This gives power to the tiny elite who own or control monopolies.
023 Open Markets make competition possible through low “barriers to entry” for new companies. Perhaps “competitive market” is the best term for an efficient economy.
024 Government regulation can help lower the barriers to entry, maintain a healthy number of competitors and so prevent monopolies. Or it can do the opposite, thus helping a powerful elite and hurting others.
025 Market Failures are a major ethical and economic reason for government regulation of public activity. The failures include economic “externalities” (for example, those who cause pollution might not pay for the harm it does to other people and property), the “tragedy of the commons” (for example, a fishery decimated by users who take too much from the shared resource), and abuse of “natural monopolies” (for example, those who own a distribution network of pipes, wires, rails or roads could use their monopoly to control markets).
030  Single-Winner Elections 
031 Condorcet candidate is the one who could beat each of the others in separate pair-wise contests. Majorities of voters prefer him or her to each of the other candidates. aka Condorcet winner.
032 Voting Cycle occurs when candidate A beats B, B beats C, and C beats A. There is no Condorcet winner when the leading candidates are in such a tie of three or more.
033 Condorcet completion method is a voting system that chooses the Condorcet candidate, if one exists, and specifies a contingency rule if the strongest candidates are tied in a voting cycle.
034 Condorcet efficiency measures how often a voting system elects the Condorcet candidate when one exists. Given as a percentage. The Condorcet efficiency of a Condorcet completion method is 100%.
035 Transitivity. A voter’s preference order is said to be transitive if whenever the voter prefers A over B and B over C, he also prefers A over C. A similar definition applies to a group's social preference ordering.
036 Smith Set is the smallest set of candidates each of whom can win a pairwise Condorcet election over every candidate outside of the set.
039 Tally methods for single-winner elections.
040  Multi-Winner Elections 
041 Multi-candidate. A multi-candidate election is an election in which there are three or more candidates.
042 Multi-seat election or multi winner decision. A multi-candidate election is an election with three or more candidates.
047 Mixed-Member Proportional. MMP makes voters elect representatives through two different voting systems. The first is usually a plurality system. The second is usually a List PR system. The seats a party wins under the first system reduce its seats allocated under the second system.
048 Parallel System elects a mixed-member legislature; the voters elect representatives through two different systems. The first is usually a plurality/majority system. The second is a Proportional Representation system. The seats a party wins under the first system do not reduce its seats allocated under the second system. In contrast under MMP, a party's district seats count toward filling its share of the PR seats.
060  Transferable Vote Terms 
061 Weight. A voter’s ballot starts with a weight of 1 vote (or 1 share of money). If the ballot helps elect a candidate, part or all of its weight is spent.
110  Tally Criteria  based on Phillip Straffin’s Topics in the Theory of Voting. out of print; Boston: UMAP, 1980. Chapter 2.
112 Majority criterion: If a majority of voters (1 out of every 2, 50%) have an alternative X as their first choice, a voting rule should choose X. A tie is possible.
113 Pareto criterion: If every voter prefers an alternative X to an alternative Y, a voting rule should not produce Y as a winner.
114 Condorcet winner criterion: If there is an alternative X which could obtain a majority of votes in pairwise Condorcet contests against every other alternative, a voting rule should choose X as the winner.
116 Kemeny distance. The Kemeny distance between two preference orders is the number of adjacent pairwise switches needed to convert one preference order to the other.
117 Monotonicity criterion. A voting system violates monotonicity if a voter can raise a candidate in the social ordering by lowering that candidate in his individual ordering or vice versa.
130  Voting Strategy Terms 
132 Insincere voting. A voter’s ballot is insincere if his reported preference order differs from his true preference order.
133 Strategic voting. Strategic voting involves any decision by the voter in marking his ballot intended to improve the outcome from his point of view. In addition to insincere voting, it includes, under approval voting for example, expansion or truncation used to optimize a voter’s effect on the outcome.
136 Free rider is someone who chooses not to help a group, yet who benefits from their efforts.
In economics, a free rider uses an object or service he did not help to buy, analogy.
In elections, a free rider does not waste his vote on a candidate who is certain to win, even if that is his first choice. He takes a free ride on other voters as they use their strength to elect that candidate and he gives his vote to help a marginal candidate.
A free-rider amendment attaches an unrelated (and often unpopular) motion to a popular or essential bill. It takes a free ride on the votes for the main bill.
137 A Killer or poison-pill amendment attaches a widely unpopular motion to a bill. The amended bill then is likely to lose.
140  Political Reform Terms 
142 Sabbatical terms make elections more competitive, forcing current reps to run against former winners. Sabbaticals cannot work with list PR because members can rotate off the list to work in a party job for a term, then rotate back onto the list.
170  Spatial Simulation Terms 
171 Simulation. A simulation is an experiment run as a model of reality. The simulations reported in these pages were computer simulations, that is, they were run on computers using mathematical models. They use mathematical distributions to simulate the variety of political positions and opinions of voters and candidates.
172 Social utility. The social utility of a candidate is the total (alternatively, the average) utility of the candidate over all voters
173 Social-utility efficiency. The social utility efficiency of a voting system is the normalized ratio between the expected social utilities of the candidate selected by the system and the candidate maximizing social utility.
174 Correlation. The correlation between two random variables is a statistical measure of the tendency of the two variables to vary together. with each other A negative correlation means one goes up as the other goes down. Finding a correlation does not prove a cause and effect relationship between the two variables.
175 Dimension of a spatial model. The dimension of a spatial model denotes the number of coordinates designated in each point in space. Each such coordinate may be intended to represent the position of a participant (voter or candidate) on a specific issue or characteristic.
176 Polarized society. A polarized society is an electorate in which two or more (usually disparate) preference orders predomin¬ate. Such a society with exactly two dominating preference orders is called a dual culture.
177 Random society. A random society is a model for an electorate in which, for each voter, candidate utilities are drawn independently from a uniform distribution. = an impartial culture?
178 Relative dispersion. In a spatial model of voting, the relative dispersion of candidates to voters is the ratio of the standard deviation of the candidates’ positions to that of the voters.
179 Impartial culture. An impartial culture is a model of an electorate in which all preference orders (for a set of candidates) are equally likely.
180 Standard deviation. Standard deviation is a measure of the variation of a random variable; namely, the square root of the average squared deviation of the mean.
181 Normal distribution. The normal (or Gaussian or bell-shaped) distribution of probability specifies that probability follow the density
f (x) = (1/σ √2π) exp[ - (x - μ)2/2σ2]
Where σ (sigma) equals the standard deviation, and μ equals the mean.
182 Squeeze effect is the drop in votes for one candidate when (in terms of a real or simulated spatial model) nearby candidates surround and draw support away from the one candidate.

Uncategorized definitions

Coalitions: A ruling coalition of legislators must continue to agree on policies or else risk a collapse of government that requires a new election. A working coalition may form simply to pass a particular bill.

Cumulative-vote election gives each voter as many votes as there are offices to be filled. He may give all of his votes to one candidate or spread them out among several candidates. The first strategy is always more likely to cast a decisive vote. The candidates which receive the most votes win the seats. A large minority can win a seat if they give all their votes to one candidate, so this is a semi-proportional voting rule.

Several chapters define particular voting rules. The chapter on single-winner elections has a whole page of rivals to the Condorcet rules. The chapters on voting for policies, projects and budgets have several intriguing rules, in addition to the recommended ones.

Recommended social-choice glossaries on the web: FairVoteBlake Cretney'sLorrie Faith Crannor'slegislative terminology; please come back.

The first section was based on Samuel Merrill’s Making Multi-candidate Elections More Democratic. Princeton N.J.: Princeton University Press, 1988. Glossary, pages 133 to 138.


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Searching for more? This discipline is fractured by many synonyms. Even its title varies; some call it public choice; others prefer social choice. The table below has many terms that can help you find similar web sites.

You will find most of these terms include topics other than formulas for calculating winners from ballots. Searching for voting systems will bring you most often to sites that sell voting equipment. So will election systems and ballot systems. Tally rules include tallies of things other than votes. Voting rules seems least ambiguous.

Search Terms Adjectives
Nouns Voting Election Tally Ballot





















Election chapters' terms for electing, nominating or selecting a:
1) chairperson, chair, chairman, chairmen, chairwoman, chairwomen; president, prime minister, judge;
2) representative, minister, delegate;

Legislation chapters' terms to enact, set, pass, fund or budget:
1) policies, laws, rules;
2) projects, grants, earmarks, proposals;
3) budgets, agencies;