Glossary of Terms and Acronyms

Alphabetical Listing

AMS = Additional Member System

See Mixed Member System.

Anti-Borda Count

The anti-vector that corresponds to the Borda Count vector. Unusually, these two vectors are in fact identical. [See also Anti-Vector, Conjugate Vector and Borda Count.]

Anti-CHPV

The anti-vector that corresponds to the Consecutively Halved Positional Voting vector. [See also Anti-Vector, Conjugate Vector and CHPV.]

Anti-GV

The anti-vector that corresponds to the Geometric Voting vector. [See also Anti-Vector, Conjugate Vector and GV.]

Anti-Plurality

The anti-vector that corresponds to the Plurality vector. A voting system in which voters cast one vote for every candidate except their least favourite and the candidate with the most votes wins. Alternatively, this equates to each voter casting a single vote against their least favourite candidate; the anti-vector version of this voting system. [See also Anti-Vector, Conjugate Vector, Plurality and Coombs Method.]

Anti-Vector

For the vector {w₁, w₂, w₃, ..., w_N-2, w_N-1, w_N} its anti-vector is {-w_N, -w_N-1, -w_N-2, ..., -w₂, -w₁, -w₁}. An anti-vector always generates the same resultant candidate ranking as its corresponding conjugate vector. For GV, anti-vector format is only appropriate when conjugate vector format rather than vector format is employed. [See also Normalization, Vector, Conjugate Vector and GV.]

Approval Voting

A voting system in which voters cast one vote for every candidate they 'approve of' and the candidate with the most votes wins. [See also Plurality and Anti-Plurality.]

AV = Alternative Vote

A voting system in which the single winner requires over 50% of the vote. Candidates with the fewest votes are successively eliminated until a winner emerges. Each vote for an eliminated candidate is transferred to the next preferred candidate. [See also Supplementary Vote.]

AV+ = Alternative Vote Plus

A multiple-winner voting system that employs the Alternative Vote (AV) in multiple constituencies to elect local-area members and then employs a party list to add further members to ensure that the overall outcome is more party proportional. [See also AV.]

Balanced (Unbiased)

The vector (or a particular preference) neither promotes consensus candidates nor polarized ones. [See also Consensus Bias and Polarized Bias.]

Borda Count

A positional voting system where the sequence of points allocated to the preferences forms a declining arithmetic progression. There is hence a common difference in value between adjacent preferences. The candidate with the most points wins. [See also Positional Voting and Common Difference.]

Broad Support

Candidate preferences with a high mean rank position. The candidate with the highest mean rank position has the broadest support. [See also Strong Support, Consensus Candidate and Borda Count.]

Bucklin Voting

A voting system that is identical to FPTP in its first round. Until a majority of votes is achieved, the next lower rank of preferences as additional votes are accumulated into the vote tallies during each subsequent round. [See also FPTP.]

Burying

The tactical option of lowering the sincere rank of a less preferred candidate so as to advantage a more preferred one. [See also Compromise Lifting, Sincere Ballot and Tactical Voting.]

CHPV = Consecutively Halved Positional Voting

Geometric Voting (GV) with a common ratio of 1/2. [See also GV and Common Ratio.]

Clones

Where two or more candidates are identical and no voter can distinguish between them when attempting to rank them on a single-winner election ballot, such candidates are known as clones and they form one particular clone set. [See also Fraternal Clones and Identical Clones.]

Cloning Map

A square that represents all the possible levels of support for the forward slate of the clone set or its reverse by supporters and opponents of the clone set. It indicates which levels (map areas) give rise to teaming or to vote splitting. [See also Teaming, Vote Splitting, Teaming Threshold and Teaming Index.]

Common Difference

The fixed difference in value between any two adjacent preference weightings. [See also Borda Count.]

Common Ratio

The fixed ratio in value between any two adjacent preference weightings. [See also GV and CHPV.]

Compromise Lifting

The tactical option of compromising results from raising the sincere rank of a possible winning candidate above that for a probable losing one. [See also Burying, Sincere Ballot and Tactical Voting.]

Condorcet Loser

If there is one, the candidate that loses to each and every other candidate in a straight pairwise comparison. [See also Condorcet Method and Pairwise Comparison.]

Condorcet Method

Any electoral method that ensures that the Condorcet Winner (if there is one) is always ranked top. [See also Condorcet Winner and Majority Rule.]

Condorcet Winner

If there is one, the candidate that beats each and every other candidate in a straight pairwise comparison. [See also Condorcet Method and Pairwise Comparison.]

Conjugate Vector

For the vector {w₁, w₂, w₃, ..., w_N-2, w_N-1, w_N} its conjugate vector is {1-w_N, 1-w_N-1, 1-w_N-2, ..., 1-w₂, 1-w₁, 1-w₁}. A conjugate vector always genetates the same resultant candidate ranking as its corresponding anti-vector. For GV conjugate vectors, the sum of its normalized weightings is not less than N/2 where N is the number of preferences employed; otherwise GV vector format is used instead. [See also Normalization, Vector, Anti-Vector and GV.]

Consensus Bias

The vector (or a particular preference) promotes consensus candidates over polarized ones. [See also Balanced (Unbiased) and Polarized Bias.]

Consensus Candidate

A candidate who is awarded the same rank of preference by every voter. Unless otherwise stated, the second preference is the common rank. [See also Polarized Candidate.]

Consensus Index (CI)

A linear scale from zero (polarized) through one half (balanced) to one (consensus) that enables a comparison to be made between two preferences or rival positional voting systems. [See also Polarized Bias, Balanced (Unbiased) and Consensus Bias.]

Consistency Criterion

If the electorate within a constituency is divided into any two arbitrary districts and the same candidate is ranked top in both these districts, then this candidate must always win when the constituency is undivided. [See also Constituency and District.]

Constituency

An area within which one electorate votes to elect candidates to fill one or more seats. It may or may not be subdivided into districts for the sole purpose of electoral administration. [See also District and Seat.]

Coombs Method

A voting system in which voters cast one vote for every candidate except their least favourite. In each subsequent round the least popular candidate is eliminated until only one winning candidate emerges. [See also Anti-Plurality.]

D'Hondt Method

A highest averages party-list method. The divisors used are 1, 2, 3, 4 and so on. [See also Highest Averages and Party List.]

Disproportionality Index

See Least Squares Index (LSI).

District

An arbitrary subdivision within a constituency. [See also Constituency.]

Domain

The portion of a multiple-winner multiple-party map in which all election profiles result in the same election outcome in terms of the number of seats for each party. [See also Party Map.]

Droop Quota

One vote more than the number of votes divided by one more than the number of seats/winners; 1 + {V/(1+W)}. [See also Hagenbach-Bischoff Quota and Hare Quota.]

Factorial

The name given to the positional voting vector with the formula w_n = 1/n!. [See also Positional Voting and Vector.]

Forward Slate

A slate that ranks the clone set in the order sincerely preferred by that set. [See also Slate and Reverse Slate.]

FPTP = First-Past-The-Post

A single-round plurality voting system. The candidate with the most votes wins. [See also Plurality.]

Fraternal Clones

Clones are fraternal when they are always ranked in the same order in adjacent positions by voters strictly preferring that clone set to other candidates. [See also Forward Slate, Clones and Identical Clones.]

GV = Geometric Voting

A positional voting system where the sequence of preference weightings forms a declining geometric progression (geometric decay). There is hence a common ratio between adjacent preference weightings. The single winner is the candidate with the highest tally. [See also Positional Voting and Common Ratio.]

Hagenbach-Bischoff Quota

The number of votes divided by one more than the number of seats/winners; V/(1+W). [See also Droop Quota and Hare Quota.]

Hare Quota

The number of votes divided by the number of seats/winners; V/W. [See also Hagenbach-Bischoff Quota and Droop Quota.]

Highest Averages

A proportional party-list voting method that divides the tally for each party by a sequence of divisors. For W seats, the W highest resulting quotients (averages) are identified and one seat is awarded to a party for each such 'highest average'. [See also Party List, Party-List CHPV, D'Hondt Method and Sainte-Laguë Method.]

Identical Clones

A clone is identical when it is just as likely to be ranked before any other member of the clone set as after it. [See also Clones and Fraternal Clones.]

IIA = Independence of Irrelevant Alternatives

The addition, withdrawal, promotion in rank or demotion in rank of any alternative candidate does not reverse the relative rank order of any two other candidates in the election outcome rankings.

Independence of Clones

The addition or deletion of any clone does not change the winner(s) of an election. [See also Clones.]

Indifference

The indifference vector is one where all weightings have the same value. It is hence an invalid positional voting system and one that cannot be normalized. Nevertheless, with a fixed consensus index of one, it is wholly and consistently consensual and therefore pointless as it cannot discriminate between any two candidates. [See also Consensus Index and Vector.]

Intermediate Indifference

A voting system in which voters cast one vote for one candidate and one vote against another candidate. Its normalized vector is of the form {1, k, ..., k, 0} and the candidate with the highest tally wins. [See also Plurality, Anti-Plurality, Normalization and Vector.]

IRV = Instant Run-Off Voting

Another name for the Alternative Vote (AV). [See also AV.]

Iso-Tally Grid Line

A straight line on a three-candidate election map connecting all points that represent the same average tally per voter.

Largest Remainder

A proportional party-list method that allocates seats according to a specified quota. One seat is awarded to a party for each quota reached. Where necessary, any remaining seats are awarded to the parties with the largest remainders after used quotas for each party have been deducted from their respective tally. [See also Party List, Hare Quota, Hagenbach-Bischoff Quota and Droop Quota.]

Lifting

See Compromise Lifting.

LSI = Least Squares Index

A measure of the disproportionality of any multiple-winner election outcome in terms of the discrepancies between the party shares of the tallies and the party shares of the seats; where 0 ≤ LSI ≤ 1. [See also OPV.]

Majority Criterion

A candidate with first preferences from over one half of the voters always wins. [See also Two-Thirds Majority Criterion and Majority Threshold.]

Majority Rule

In a pairwise comparison, the selected option is the one with the greater support. [See also Plurality Rule.]

Majority Threshold

The proportion of first preferences above which a candidate achieves a simple or higher majority and thereby always wins. This proportion may vary upwards from one half. [See also Majority Criterion and Two-Thirds Majority Criterion.]

Mean-Weighted Preference

The preference that has a weighting equivalent to the mean value of all the N weightings used in an N-candidate election.

Mixed Member System

A proportional voting system in which two types of winners emerge. The first type represents a specific locality having been elected through a specified single-winner contest in that constituency. The second type is elected via a party list to ensure that each party has a more proportional share of the overall vote. [See also Constituency and Party List.]

Monotonicity (Mono-Raise) Criterion

Provided that the relative rank ordering of the other candidates is unchanged, a voter cannot promote the rank of a candidate on their ballot and thereby cause that candidate to be demoted in the election outcome rankings. [See also General Criteria page 3 for further monotonicity criteria.]

Nauru

The name of the state that employs the positional voting vector with the Dowdall formula w_n = 1/n. [See also Positional Voting and Vector.]

Normalization

The process of manipulating a vector so that its first preference is worth one (w₁ = 1) and its last preference is worth zero (w_N = 0). Subtracting the initial value of w_N from all weightings and scaling all the weightings by dividing them by the subsequent w₁ achieves this outcome while ensuring that the resultant rank ordering of the candidates is unaffected (unlike the tallies). Note that anti-vectors are hence normalized such that the first preference is worth zero (w₁ = 0) and the last preference is worth minus one (w_N = -1). Also, conjugate vectors - just like vectors - are normalized such that its first preference is worth one (w₁ = 1) and its last preference is worth zero (w_N = 0). [See also Vector, Anti-Vector and Conjugate Vector.]

Optimality

The proportion of all possible election outcomes that generate the same party seat shares as that by an optimally proportional voting (OPV) system. [See also OPV.]

OPV = Optimally Proportional Voting

A multiple-winner system in which any possible election outcome minimises the discrepancies between the party shares of the tallies and the party shares of the seats. [See also LSI.]

Pairwise Comparison

A straightforward contest between any two candidates from a field of N candidates in which the more popular of the two wins. [See also Condorcet Method and Majority Rule.]

Pareto Condition

Where each and every voter prefers candidate A over candidate B then the election outcome reflects this unanimity and also ranks A ahead of B.

Participation Criterion

Adding ballots that prefer candidate A to B never change the winner to B from A.

Party Cloning

In unfairly attempting to gain extra seats, the act of a party in duplicating itself into two (or more) identical parties with each one having its own separate party list. [See also Party List and Strategic Nomination.]

Party List

A voting system in which voters vote for a specific party and seats are awarded in proportion to the share of the vote for each party. Candidates at the top of their party list fill the number of seats won by that party.

Party-List CHPV

The multiple-winner version of Consecutively Halved Positional Voting (CHPV) and a highest averages party-list method. The divisors used are 1, 2, 4, 8 and so on. [See also CHPV, Highest Averages and Party List.]

Party Map

An n-dimensional multiple-winner map for n+1 competing parties in which all possible election profiles and outcomes are represented.

Plurality

A voting system in which voters vote for a single candidate and the one with the most support wins. Where a majority is not achieved during the first round, some versions require further rounds with fewer candidates. The voting vector {1, 0, ..., 0} is used to represent plurality in positional voting. [See also FPTP, Anti-Plurality, Positional Voting and Vector.]

Plurality Rule

During each vote-processing round, a tally is established for each option, the options are ranked according to those tallies and a subset of options with the highest tallies is selected. [See also Majority Rule and Plurality Rule Method.]

Plurality Rule Method

One that complies with the plurality rule. Direct (single-round) methods require a winner to gain a plurality but not a majority of the tallies. Iterative (multiple-round) methods require a winner to gain a majority and a plurality of the tallies. [See also Plurality Rule.]

Polarization Index (PI)

A linear scale from zero (consensus) through one half (balanced) to one (polarized) that enables a comparison to be made between two preferences or rival positional voting systems. [See also Consensus Bias, Balanced (Unbiased) and Polarized Bias.]

Polarized Bias

The vector (or a particular preference) promotes polarized candidates over consensus ones. [See also Balanced (Unbiased) and Consensus Bias.]

Polarized Candidate

A candidate who receives first preferences from some voters and either last or no preference from the remaining voters. [See also Consensus Candidate.]

Positional Voting

A voting system in which voters express their preferences in strict rank order and where these preferences are weighted (or given points) according to their rank position in the ballot. Candidates are then ranked in the order of the tally of weightings (or points) they received with the top-ranked one(s) being elected.

Preferential Voting

Any voting system where voters express their relative preferences for candidates by completing a ranked ballot. [See also Ranked Ballot.]

Range Voting

A voting system in which voters award a score - within a defined range - to each candidate and the one with the highest total score wins.

Ranked Ballot

The means by which voters expresses their individual preferences in rank order from most to least preferred. [See also Preferential Voting and Ranked Ballot CHPV.]

Ranked Ballot CHPV

The single-winner version of the Consecutively Halved Positional Voting (CHPV) system. [See also CHPV.]

Resolvability Criterion

It must be possible to resolve any tie between two or more top-ranked candidates by the addition of the ballot from one voter so that only one winning candidate is chosen.

Reversal Symmetry Criterion

It must not be possible for a uniquely winning candidate to still win when all the strictly ranked preferences on each ballot are reversed in rank order.

Reverse Slate

A slate that ranks the clone set in the reverse order to that sincerely preferred by that set. A candidate that is nth from the top on a forward slate is nth from the bottom on the reverse slate. [See also Clones and Forward Slate.]

Sainte-Laguë Method

A highest averages party-list method. The divisors used are 1, 3, 5, 7 and so on. [See also Highest Averages and Party List.]

Seat

A position to which one winning candidate is elected. [See also Constituency.]

Sincere Ballot

A ranked ballot on which a voter casts their genuine preferences in strict rank order without seeking to manipulate the election outcome. [See also Burying, Compromise Lifting and Tactical Voting.]

Slate

A party list of its own clone candidates in preferential order for a single-winner election. [See also Clones, Forward Slate and Reverse Slate.]

Square

The name given to the positional voting vector with the formula w_n = 1/n². [See also Positional Voting and Vector.]

Standardisation

The process of ensuring that the first preference weighting of a vector is worth one (w₁ = 1) through scaling and using this same scaling factor on all the remaining weightings. [See also Normalization, Positional Voting, Vector, Anti-Vector and Conjugate Vector.]

Stick Diagram

A visual aid in which lines (sticks) are used to represent a group of associated weightings or tallies. The positions of the points along any stick indicate the values of these grouped tallies when compared to the scale shown alongside it. For CHPV, this scale is a binary logarithmic one.

Strategic Nomination

The act by a party in seeking to affect the outcome of an election through the addition or withdrawal of one or more of its (usually clone) candidates. [See also Clones and Party Cloning.]

Strong Support

High number of first preferences for a candidate. The candidate with the highest number of first preferences has the strongest support. [See also Broad Support, Polarized Candidate and Plurality.]

STV = Single Transferable Vote

A multiple-winner voting system that allocates seats according to a specified quota. A seat is awarded to an individual candidate when they reach the necessary quota. Votes in excess of the quota and the votes awarded to eliminated candidates are consecutively transferred to the remaining candidates and in proportion to next preferences until all the seats are filled. [See also Hare Quota, Hagenbach-Bischoff Quota and Droop Quota.]

Summability Criterion

Where a constituency is subdivided into multiple districts, all the candidate tallies in a constituency-wide election are identical to the summation of all the individual district tallies for those candidates. [See also Constituency and District.]

Supplementary Vote

A voting system in which voters cast a first and second preference only. Where no candidate has a majority of first preferences, all but the two top-ranked candidates are eliminated. The relevant second preferences are then distributed and the more popular candidate of the remaining two wins. [See also Alternative Vote.]

Tactical Voting

The act of a voter in seeking to alter the perceived outcome of an election to their own advantage by ranking candidates on their ballot differently to their genuine preferences. [See also Burying, Compromise Lifting and Sincere Ballot.]

Teaming

The strategic nomination of clone candidate(s) that benefits the clone set (team). The addition of the clone(s) has the effect of depressing (burying) the rankings and hence the tallies for the other competing candidates. [See also Clones and Strategic Nomination.]

Teaming Effect Threshold

A straight line on a cloning map that represents all the conditions where neither teaming nor vote splitting occurs. [See also Cloning Map, Teaming, Teaming Success Threshold, Teaming Threshold and Vote Splitting.]

Teaming Index

The worst-case proportion (largest area) of a cloning map that gives rise to teaming. [See also Cloning Map and Teaming.]

Teaming Success Threshold

A straight line on a cloning map that represents the boundary conditions beyond which teaming changes the election outcome. [See also Cloning Map, Teaming, Teaming Effect Threshold, Teaming Threshold and Vote Splitting.]

Teaming Threshold

A straight line on a cloning map that simultaneously represents all the conditions where neither teaming nor vote splitting occurs and the boundary conditions beyond which teaming changes the election outcome. [See also Cloning Map, Teaming, Teaming Effect Threshold, Teaming Success Threshold and Vote Splitting.]

Truncation

The act of a voter when listing some but not all of the permissible preferences on an untruncated ranked ballot. Some ranked ballots may have one or more truncated low-rank positions that prevent voters from expressing their weakest preferences. [See also Ranked Ballot.]

Two-Thirds Majority Criterion

A candidate with first preferences from over two thirds of the voters always wins. [See also Majority Criterion and Majority Threshold.]

Vector

The sequence of all non-negative weightings in strict rank order from highest to lowest preference employed in an election. For GV vectors, the sum of its normalized weightings does not exceed N/2 where N is the number of preferences employed; otherwise GV conjugate vector format is used instead. [See also Anti-Vector, Conjugate Vector, Normalization and GV.]

Vote-for-X-out-of-N

A positional voting system in which voters cast a vote for X candidates out of a choice of N where 1 < X < N and the candidate with the highest tally wins. [See also Plurality, Anti-Plurality, Positional Voting and Vector.]

Vote Splitting

The strategic nomination of clone candidate(s) that harms the clone set. The addition of the clone(s) has the effect of dividing one tally into two or more tallies hence reducing the size of the largest tally. [See also Clones and Strategic Nomination.]

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