Draft:Glossary of social choice

This glossary of social explains commonly used terms in social choice theory and political science relating to electoral systems, in alphabetical order. Some of these terms have their own pages, like plurality and proportional representation.

A

absolute majority

More than half of the total. It is a subset of a set consisting of more than half of the set's elements. A majority is different from, but often confused with, a plurality, which is a subset larger than any other subset but not necessarily more than half the set.

In social choice theory, an absolute majority

In parliamentary procedure, and common language the term absolute majority has different meanings.

acyclical

additional member system (United Kingdom)

The name of a two vote seat-linkage-based mixed electoral system used in the United Kingdom, a combination of first-preference plurality (on the winner-take-all tier) and closed list proportional representation (on the compensatory tier). Sometimes conflated with the term mixed-member proportional representation.

alternative

An element of the set from which a choice is to be made.

alternative vote

One of the names of the (first-preference) plurality-by-elimination single-winner system also known as instant-runoff voting, primarily in the United Kingdom.

at-large

An type of election or district where multiple winners are elected at once, with the same electoral method. Most commonly used in the context of winner-take-all electoral system and in the United States.

apportionment

Algorithm to determine how many seats are assigned to each electoral list.

approval ballot

A type of ballot where voters may approve (mark) or disapprove (not mark) each candidate, therefore they may approve of any number of candidates (even all or none). most commonly used for approval voting, whether single-winner or multi-winner. See also: single-choice ballot, ranked ballot, score ballot and cumulative ballot

approval voting (AV)

A single-winner cardinal voting system using approval ballots and the plurality rule. In a broader definition includes multi-winner systems using approval ballots, whether they use the plurality rule to determine winners or not.

anti-plurality

A single winner electoral system electing the loser according to the plurality rule in a last-preference plurality system. Voters do not mark their first preference, only their last preference, and the winner is the alternative with the least amount of votes.

anti-plurality loser

The single winner of a last-preference plurality election. See

B

ballot

binary relation

binomial system (Chile)

biproportional apportionment

Method to allocate seats in proportion to two separate characteristics, most commonly parties and regions.

block voting (BV)

block approval voting

bonus

Borda count

C

candidate

An alternative, when the subject of voting is electing people.

candidate method

cardinal system

choice set

choice function

closed list

An electoral list that remains unchanged by voting, where the ordering of candidates is pre-determined and voters have no direct influence on it. --- open list

Condorcet winner

Condorcet winner criterion

Condorcet loser

Condorcet loser criterion

Condorcet method

Condorcet paradox

contingent vote

Coombs' method

cumulative voting

cyclical

D

dictator

dictatorship

divisor

double simultaneous vote (DSV)

A method of conducting multiple elections to separate offices – such as the president and members of a legislature – through a single vote, analogous to a single closed list election. The electoral methods used for the different elections may be different.

Droop quota

dual-member district

A type of multi-member district with two seats up for election (in each election). Some systems use exclusively dual-member districts, like the binomial system or dual-member mixed proportional.

E

electoral system

A set of rules used to determine the results of an election. Also known as a voting system.

elimination

exhaustive ballot

exhausted ballot

equality

equivalence relation

A symmetric quasi-ordering.

F

first-past-the-post voting (FPTP)

Formally called first-preference plurality (FPP), a plurality rule voting system for electing a single winner, most commonly used with a single-choice ballot. The term is sometimes also applied to some forms of block voting.

first-preference plurality (FPP)

A more formal term for first-past-the-post voting, where only the first preferences of each voter are counted and the plurality rule decides the single winner of the election. May be used in single-member districts to elect multiple winners in a single election. FPP is formally a positional type of ranked voting method, however it does not require the use of ranked ballots, a ballot with a single mark is sufficient.

flexible list

see open list

free list

panachage or mixed list, is a variant on the most open list where voters may support candidates on different lists. Candidates are typically elected using either cumulative or block plurality voting. This gives the voters full control over which candidates are elected, not just within a particular party, but even across them.

open list

fusion

Not to be confused with: electoral fusion, fusion voting

G

general ticket

H

history dependence

I

instant runoff voting (IRV)

irrelevant alternative

J

jackpot

jungle primary

L

liberalism

list

largest remainder

M

majority

majority criterion

majority rule

median voter

method of equal shares

mixed ballot

mixed ballot transferable vote (MBTV)

mixed list

see free list

mixed-member system or mixed electoral system

mixed-member majoritarian (MMM) representation

mixed-member proportional (MMP) representation

Type of proportional representation that is achieved by mixed system: some seats are allocated by a winner-take-all method and some by a corrective mechanism. strict definition: the type of mixed electoral systems that provide proportional representation (requires a flexible amount of leveling seats). Broader definition: type of mixed electoral system with generally sufficient compensation to provide roughly proportional representation overall. Not all compensatory systems are mixed-member proportional. In New Zealand, a specific seat linkage system is referred to as MMP, in other countries, generic or specific proposals have also been labelled as MMP, regardless of them being striclty proportional.

mixed-member semi-proportional

mixed single vote (MSV)

monotonicity

multi-member district (MMD)

Electoral district with multiple seats elected at the same time (not staggered).

multiple non-transferable vote

limited (block) voting, block voting, limited (block) approval voting, block approval voting

multiple transferable vote

N

negative vote transfer

negative vote weight

non-partisan primary

A primary election in which all candidates for the same elected office run against each other at once, distinct from a two-round system and partisan primary.

O

ordering

---

A complete quasi-ordering.

ordinal voting

P

panachage

parallel voting

A superposition method of mixed or hybrid electoral systems, where voters have two (independent) votes. Commonly conflated with mixed-member majoritarian representation. See superposition

pareto efficiency

participation criterion

partisan method

An electoral system officially incorporating political parties or other free associations, usually by use of electoral lists.

partisan primary

party-list method

Any voting system using electoral lists, whether proportional or not.

party block voting

pivotal voter

plurality

plurality voting

plurality winner

plurality loser

popular vote

positional voting

positive vote transfer

preference

preferential voting

proportionality

proportional representation (PR)

Q

quasi-ordering

A reflexive and transitive binary relation.

quasi-proportional

quasi-transitive

quota

R

random ballot

Electoral system where the election is decided on the basis of a single randomly-selected ballot.

ranking

ranked voting

ranked-choice voting

remainder

runoff

runoff voting

S

semi-proportional representation

sincere voting

single-member plurality (SMP)

First-preference plurality (FPP) used exclusively in single-member districts (SMD). In practice single-choice ballots are used.

single non-transferable vote (SNTV)

single transferable vote (STV)

social choice

social choice theory

The mathematical analysis of collective decision making, the study of how individuals' preferences over certain alternatives can be aggregated into a social preference.

social welfare function

split-ticket

strategic voting

staggered election

status quo

strict preference

superposition

supplementary vote

supplementary member system

symmetric

T

two-round system (TRS)

two-round majority jackpot

top-up (seats): a form of compensation, typically in mixed electoral systems. Leveling seats, that are allocated in a separate (regionalized or at-large) district via seat linkage are usually referred to as top-up (vote linkage an non compensatory allocation is typically is not).

transferable vote

transitivity

U

unanimity

unrestricted domain

utility

V

vote

voter

vote transfer

W

weak preference

winner

winner compensation

winner-take-all