Social welfare function

Function that ranks states of society according to their desirability

For a discussion of the same concept in the context of voting and politics, see electoral systems.

A joint Politics and Economics series

Social choice and electoral systems

* Social choice
* Mechanism design
* Comparative politics
* Comparison
* List (By country)

Single-winner methods

Single vote - plurality methods

* First preference plurality (FPP)
* Two-round (US: Jungle primary)
* Partisan primary
* Instant-runoff
* UK: Alternative vote
* US: Ranked-choice (RCV)

* * *

Condorcet methods

* Condorcet-IRV
* Round-robin voting
* Minimax
* Schulze
* Ranked pairs
* Maximal lottery

* * *

Positional voting

* Plurality (el. IRV)
* Borda count (el. Baldwin)
* Antiplurality (el. Coombs)

* * *

Cardinal voting

* Score voting
* Approval voting
* Majority judgment
* STAR voting

Proportional representation

Party-list

* Apportionment
* Highest averages
* Largest remainders
* National remnant
* Biproportional
* List type
* Closed list
* Open list
* Panachage
* List-free PR
* Localized list

* * *

Quota-remainder methods

* Hare STV
* Schulze STV
* CPO-STV
* Quota Borda

* * *

Approval-based committees

* Thiele's method
* Phragmen's method
* Expanding approvals rule
* Method of equal shares

* * *

Fractional social choice

* Direct representation
* Interactive representation
* Liquid democracy
* Fractional approval voting
* Maximal lottery
* Random ballot

* * *

Semi-proportional representation

* Cumulative
* SNTV
* Limited voting

Mixed systems

By results of combination

* Mixed-member majoritarian
* Mixed-member proportional

* * *

By mechanism of combination

* Non-compensatory
* Parallel (superposition)
* Coexistence
* Conditional
* Fusion (majority bonus)
* Compensatory
* Seat linkage system
* UK: 'AMS'
* NZ: 'MMP'
* Vote linkage system
* Negative vote transfer
* Mixed ballot
* Supermixed systems
* Dual-member proportional
* Rural–urban proportional
* Majority jackpot

* * *

By ballot type

* Single vote
* Double simultaneous vote
* Dual-vote

Paradoxes and pathologies

Spoiler effects

* Spoiler effect
* Cloning paradox
* Frustrated majorities paradox
* Center squeeze

* * *

Pathological response

* Perverse response
* Best-is-worst paradox
* No-show paradox
* Multiple districts paradox

* * *

Strategic voting

* Lesser evil voting
* Exaggeration
* Truncation
* Turkey-raising

* * *

Paradoxes of majority rule

* Dominance paradox
* Tyranny of the majority
* Discursive dilemma
* Conflicting majorities paradox

Social and collective choice

Impossibility theorems

* Arrow's theorem
* Majority impossibility
* Moulin's impossibility theorem
* McKelvey–Schofield chaos theorem
* Gibbard's theorem

* * *

Positive results

* Median voter theorem
* Condorcet's jury theorem
* May's theorem
* Condorcet dominance theorems
* Harsanyi's utilitarian theorem

* Politics portal
* Economics portal

Mathematics portal

* v
* t
* e

Part of a series on

Economics

* History
* Outline
* Index

Branches and classifications

* Applied
* Econometrics
* Heterodox
* International
* Micro / Macro
* Mainstream
* Mathematical
* Methodology
* Political
* JEL classification codes

Concepts, theory and techniques

* Economic systems
* Economic growth
* Market
* National accounting
* Experimental economics
* Computational economics
* Game theory
* Operations research
* Middle income trap
* Industrial complex

By application

* Agricultural
* Behavioral
* Business
* Cultural
* Democracy
* Demographic
* Development
* Digitization
* Ecological
* Education
* Engineering
* Environmental
* Evolutionary
* Expeditionary
* Feminist
* Financial
* Geographical
* Happiness
* Health
* Historical
* Humanistic
* Industrial organization
* Information
* Institutional
* Knowledge
* Labour
* Law
* Managerial
* Monetary
* Natural resource
* Organizational
* Participation
* Personnel
* Planning
* Policy
* Public
* Public choice / Social choice theory
* Regional
* Rural
* Service
* Socio
* Sociological
* Solidarity
* Statistics
* Urban
* Welfare

Notable economists

* de Mandeville
* Quesnay
* Smith
* Malthus
* Say
* Ricardo
* von Thünen
* List
* Bastiat
* Cournot
* Mill
* Gossen
* Marx
* Walras
* Jevons
* George
* Menger
* Marshall
* Edgeworth
* Clark
* Pareto
* von Böhm-Bawerk
* von Wieser
* Veblen
* Fisher
* Pigou
* Heckscher
* von Mises
* Schumpeter
* Keynes
* Knight
* Polanyi
* Frisch
* Sraffa
* Myrdal
* Hayek
* Kalecki
* Röpke
* Kuznets
* Tinbergen
* Robinson
* von Neumann
* Hicks
* Lange
* Leontief
* Galbraith
* Koopmans
* Schumacher
* Friedman
* Samuelson
* Simon
* Buchanan
* Arrow
* Baumol
* Solow
* Rothbard
* Greenspan
* Sowell
* Becker
* Ostrom
* Sen
* Lucas
* Stiglitz
* Thaler
* Hoppe
* Krugman
* Piketty
* more

Lists

* Glossary
* Economists
* Publications (journals)
* Schools

* Business portal
* Money portal

* v
* t
* e

In welfare economics and social choice theory, a social welfare function—also called a social ordering, ranking, utility, or choice function—is a function that ranks a set of social states by their desirability. A social welfare function may yield several possible outcomes; each person's preferences are combined in some way to determine which outcome is considered better by society as a whole.[1]

Social choice functions are studied by economists as a way to identify socially-optimal decisions, giving a procedure to rigorously define which of two outcomes should be considered more desirable for society as a whole (e.g. to compare two different possible income distributions).[2] They are also used by democratic governments to choose between several options in elections, based on the preferences of voters.

The notion of social utility is analogous to the notion of a utility function in consumer choice. However, a social welfare function is different in that it is a mapping of individual utility functions onto a single output, in a way that accounts for the judgments of everyone in a society.

There are two different notions of social welfare used by economists:

* Ordinal (or ranked voting) functions use only ordinal information.
* Cardinal (or rated voting) functions additionally incorporate cardinal information, with agents stating how much better one choice is compared to another.

Arrow's impossibility theorem is a key result on social welfare functions, showing an important difference between social and consumer choice: whereas it is possible to construct a rational (non-self-contradictory) decision procedure for consumers based only on ordinal preferences, it is impossible to do the same in the social choice setting, making any such ordinal decision procedure a second-best.

## Terminology and equivalence

[edit]

Some authors maintain a distinction between three closely-related concepts:

1. A social choice function selects a single best outcome (a single candidate who wins, or multiple if there happens to be a tie).
2. A social ordering function lists the candidates, from best to worst.
3. A social scoring function maps each candidate to a number representing their quality. For example, the standard social scoring function for first-preference plurality is the total number of voters who rank a candidate first.

Every social ordering can be made into a choice function by considering only the highest-ranked outcome. Less obviously, though, every social choice function is also an ordering function. Deleting the best outcome, then finding the new winner, results in a runner-up who is assigned second place. Repeating this process gives a full ranking of all candidates.[3]

Because of this close relationship, the three kinds of functions are often conflated by abuse of terminology.

### Example

[edit]

Consider an instant-runoff election between Top, Center, and Bottom. Top has the most first-preference votes; Bottom has the second-most; and Center (positioned between the two) has the fewest first preferences.

| Round 1  | Round 2

|
|

Top  | 40  | 53
Center  | ~~26~~ | Eliminated
Bottom  | 34  | 47

Under instant-runoff voting, Top is the winner. Center is eliminated in the first round, and their second-preferences are evenly split between Top and Bottom, allowing Top to win.

To find the second-place finisher, we find the winner if Top had not run. In this case, the election is between Center and Bottom.

Runner-up  | Round 1

|

—  | Excluded
Center  | 66
Bottom  | 34

(Note that the finishing order is not the same as the elimination order for sequential elimination methods: despite being eliminated first, Center is the runner-up in this election.)

## Ordinal welfare

[edit]

This section has multiple issues. Please help improve it or discuss these issues on the talk page. (Learn how and when to remove these messages)

This section may be too technical for most readers to understand. Please help improve it to make it understandable to non-experts, without removing the technical details. (March 2024) (Learn how and when to remove this message)

|

This section may require copy editing for grammar, style, cohesion, tone, or spelling. You can assist by editing it. (March 2024) (Learn how and when to remove this message)

|

This section needs additional citations for verification. Please help improve this article by adding citations to reliable sources in this section. Unsourced material may be challenged and removed.
Find sources: "Social welfare function" – news · newspapers · books · scholar · JSTOR (March 2024) (Learn how and when to remove this message)

|

This section may need to be rewritten to comply with Wikipedia's quality standards. You can help. The talk page may contain suggestions. (March 2024)

|

(Learn how and when to remove this message)

In a 1938 article, Abram Bergson introduced the term social welfare function, with the intention "to state in precise form the value judgments required for the derivation of the conditions of maximum economic welfare." The function was real-valued and differentiable. It was specified to describe the society as a whole. Arguments of the function included the quantities of different commodities produced and consumed and of resources used in producing different commodities, including labor.

Necessary general conditions are that at the maximum value of the function:

* The marginal "dollar's worth" of welfare is equal for each individual and for each commodity
* The marginal "dis-welfare" of each "dollar's worth" of labor is equal for each commodity produced of each labor supplier
* The marginal "dollar" cost of each unit of resources is equal to the marginal value productivity for each commodity.

Bergson argued that welfare economics had described a standard of economic efficiency despite dispensing with interpersonally-comparable cardinal utility, the hypothesization of which may merely conceal value judgments, and purely subjective ones at that.

Earlier neoclassical welfare theory, heir to the classical utilitarianism of Bentham, often treated the law of diminishing marginal utility as implying interpersonally comparable utility. Irrespective of such comparability, income or wealth is measurable, and it was commonly inferred that redistributing income from a rich person to a poor person tends to increase total utility (however measured) in the society. But Lionel Robbins (1935, ch. VI) argued that how or how much utilities, as mental events, change relative to each other is not measurable by any empirical test, making them unfalsifiable. Robbins therefore rejected such as incompatible with his own philosophical behaviorism.

Auxiliary specifications enable comparison of different social states by each member of society in preference satisfaction. These help define Pareto efficiency, which holds if all alternatives have been exhausted to put at least one person in a more preferred position with no one put in a less preferred position. Bergson described an "economic welfare increase" (later called a Pareto improvement) as at least one individual moving to a more preferred position with everyone else indifferent. The social welfare function could then be specified in a substantively individualistic sense to derive Pareto efficiency (optimality). Paul Samuelson (2004, p. 26) notes that Bergson's function "could derive Pareto optimality conditions as necessary but not sufficient for defining interpersonal normative equity." Still, Pareto efficiency could also characterize one dimension of a particular social welfare function with distribution of commodities among individuals characterizing another dimension. As Bergson noted, a welfare improvement from the social welfare function could come from the "position of some individuals" improving at the expense of others. That social welfare function could then be described as characterizing an equity dimension.

Samuelson (1947, p. 221) himself stressed the flexibility of the social welfare function to characterize any one ethical belief, Pareto-bound or not, consistent with:

* a complete and transitive ranking (an ethically "better", "worse", or "indifferent" ranking) of all social alternatives and
* one set out of an infinity of welfare indices and cardinal indicators to characterize the belief.

As Samuelson (1983, p. xxii) notes, Bergson clarified how production and consumption efficiency conditions are distinct from the interpersonal ethical values of the social welfare function.

Samuelson further sharpened that distinction by specifying the welfare function and the possibility function (1947, pp. 243–49). Each has as arguments the set of utility functions for everyone in the society. Each can (and commonly does) incorporate Pareto efficiency. The possibility function also depends on technology and resource restraints. It is written in implicit form, reflecting the feasible locus of utility combinations imposed by the restraints and allowed by Pareto efficiency. At a given point on the possibility function, if the utility of all but one person is determined, the remaining person's utility is determined. The welfare function ranks different hypothetical sets of utility for everyone in the society from ethically lowest on up (with ties permitted), that is, it makes interpersonal comparisons of utility. Welfare maximization then consists of maximizing the welfare function subject to the possibility function as a constraint. The same welfare maximization conditions emerge as in Bergson's analysis.

For a two-person society, there is a graphical depiction of such welfare maximization at the first figure of Bergson–Samuelson social welfare functions. Relative to consumer theory for an individual as to two commodities consumed, there are the following parallels:

* The respective hypothetical utilities of the two persons in two-dimensional utility space is analogous to respective quantities of commodities for the two-dimensional commodity space of the indifference-curve surface
* The Welfare function is analogous to the indifference-curve map
* The Possibility function is analogous to the budget constraint
* Two-person welfare maximization at the tangency of the highest Welfare function curve on the Possibility function is analogous to tangency of the highest indifference curve on the budget constraint.

Kenneth Arrow's 1963 book demonstrated the problems with such an approach, though he would not immediately realize this. Along earlier lines, Arrow's version of a social welfare function, also called a 'constitution', maps a set of individual orderings (ordinal utility functions) for everyone in society to a social ordering, which ranks alternative social states (such as which of several candidates should be elected).

Arrow found that contrary to the assertions of Lionel Robbins and other behaviorists, dropping the requirement of real-valued (and thus cardinal) social orderings makes rational or coherent behavior at the social level impossible. This result is now known as Arrow's impossibility theorem. Arrow's theorem shows that it is impossible for an ordinal social welfare function to satisfy a standard axiom of rational behavior, called independence of irrelevant alternatives. This axiom says that changing the value of one outcome should not affect choices that do not involve this outcome. For example, if a customer buys apples because he prefers them to blueberries, telling them that cherries are on sale should not make them buy blueberries instead of apples.

John Harsanyi later strengthened this result by showing that if societies must make decisions under uncertainty, the unique social welfare function satisfying coherence and Pareto efficiency is the utilitarian rule.

## Cardinal welfare

[edit]

A cardinal social welfare function is a function that takes as input numeric representations of individual utilities (also known as cardinal utility), and returns as output a numeric representation of the collective welfare. The underlying assumption is that individuals utilities can be put on a common scale and compared. Examples of such measures include life expectancy or per capita income.

For the purposes of this section, income is adopted as the measurement of utility.

The form of the social welfare function is intended to express a statement of objectives of a society.

The utilitarian or Benthamite social welfare function measures social welfare as the total or sum of individual utilities:

W = ∑ i = 1 n Y i {\displaystyle W=\sum _{i=1}^{n}Y_{i}}

where  W {\displaystyle W} is social welfare and  Y i {\displaystyle Y_{i}} is the income of individual  i {\displaystyle i} among  n {\displaystyle n} individuals in society. In this case, maximizing the social welfare means maximizing the total income of the people in the society, without regard to how incomes are distributed in society. It does not distinguish between an income transfer from rich to poor and vice versa. If an income transfer from the poor to the rich results in a bigger increase in the utility of the rich than the decrease in the utility of the poor, the society is expected to accept such a transfer, because the total utility of the society has increased as a whole. Alternatively, society's welfare can also be measured under this function by taking the average of individual incomes:

W = 1 n ∑ i = 1 n Y i = Y ¯ {\displaystyle W={\frac {1}{n}}\sum _{i=1}^{n}Y_{i}={\overline {Y}}}

In contrast, the max-min or Rawlsian social welfare function (based on the philosophical work of John Rawls) measures the social welfare of society on the basis of the welfare of the least well-off individual member of society:

W = min ( Y 1 , Y 2 , ⋯ , Y n ) {\displaystyle W=\min(Y_{1},Y_{2},\cdots ,Y_{n})}

Here maximizing societal welfare would mean maximizing the income of the poorest person in society without regard for the income of other individuals.

These two social welfare functions express very different views about how a society would need to be organised in order to maximize welfare, with the first emphasizing total incomes and the second emphasizing the needs of the worst-off. The max-min welfare function can be seen as reflecting an extreme form of uncertainty aversion on the part of society as a whole, since it is concerned only with the worst conditions that a member of society could face.

Amartya Sen proposed a welfare function in 1973:

W G i n i = Y ¯ ( 1 − G ) {\displaystyle W_{\mathrm {Gini} }={\overline {Y}}(1-G)}

The average per capita income of a measured group (e.g. nation) is multiplied with  ( 1 − G ) {\displaystyle (1-G)} where  G {\displaystyle G} is the Gini index, a relative inequality measure. James E. Foster (1996) proposed to use one of Atkinson's Indexes, which is an entropy measure. Due to the relation between Atkinsons entropy measure and the Theil index, Foster's welfare function also can be computed directly using the Theil-L Index.

W T h e i l − L = Y ¯ e − T L {\displaystyle W_{\mathrm {Theil-L} }={\overline {Y}}\mathrm {e} ^{-T_{L}}}

The value yielded by this function has a concrete meaning. There are several possible incomes which could be earned by a person, who randomly is selected from a population with an unequal distribution of incomes. This welfare function marks the income, which a randomly selected person is most likely to have. Similar to the median, this income will be smaller than the average per capita income.

W T h e i l − T = Y ¯ e − T T {\displaystyle W_{\mathrm {Theil-T} }={\overline {Y}}\mathrm {e} ^{-T_{T}}}

Here the Theil-T index is applied. The inverse value yielded by this function has a concrete meaning as well. There are several possible incomes to which a Euro may belong, which is randomly picked from the sum of all unequally distributed incomes. This welfare function marks the income, which a randomly selected Euro most likely belongs to. The inverse value of that function will be larger than the average per capita income.

### Axioms of cardinal welfarism

[edit]

Suppose we are given a preference relation R on utility profiles. R is a weak total order on utility profiles—it can tell us, given any two utility profiles, if they are indifferent or one of them is better than the other. A reasonable preference ordering should satisfy several axioms:[4]: 66–69

1\. Monotonicity: if the utility of one individual increases, while all other utilities remain equal, R should strictly prefer the second profile. For example, it should prefer the profile (1, 4, 4, 5) to (1, 2, 4, 5). Such a change is called a Pareto improvement.

2\. Symmetry: reordering or relabeling the values in the utility profile should not change the output of R. This axiom formalizes the idea that every person should be treated equally in society. For example, R should be indifferent between (1, 4, 4, 5) and (5, 4, 4, 1), because the only difference is whether

3\. Continuity: for every profile v, the set of profiles weakly better than v and the set of profiles weakly worse than v are closed sets.[jargon]

4\. Independence of unconcerned agents: R should be independent of individuals whose utilities have not changed. For example, if R prefers (2, 2, 4) to (1, 3, 4), it also prefers (2, 2, 9) to (1, 3, 9); the utility of agent 3 should not affect the comparison between two utility profiles of agents 1 and 2. This property can also be called locality or separability. It allows us to treat allocation problems in a local way, and separate them from the allocation in the rest of society.

Every preference relation with properties 1–4 can be represented as by a function W which is a sum of the form:

W ( u 1 , … , u n ) = ∑ i = 1 n w ( u i ) {\displaystyle W(u_{1},\dots ,u_{n})=\sum _{i=1}^{n}w(u_{i})}

where w is a continuous increasing function.

### Harsanyi's theorem

[edit]

Introducing one additional axiom—the nonexistence of Dutch Books, or equivalently that social choice behaves according to the axioms of rational choice—implies that the social choice function must be the utilitarian rule, i.e. the weighting function  w ( u ) {\displaystyle w(u)} must be equal to the utility functions of each individual. This result is known as Harsanyi's utilitarian theorem.

### Non-utilitarian

[edit]

By Harsanyi's theorem, any non-utilitarian social choice function will be incoherent; in other words, it will agree to some bets that are unanimously opposed by every member of society. However, it is still possible to establish properties of such functions.

Instead of imposing rational behavior on the social utility function, we can impose a weaker criterion called independence of common scale: the relation between two utility profiles does not change if both of them are multiplied by the same constant. For example, the utility function should not depend on whether we measure incomes in cents or dollars.

If the preference relation has properties 1–5, then the function w must be the isoelastic function:

c 1 − η − 1 1 − η {\displaystyle {\frac {c^{1-\eta }-1}{1-\eta }}}

This family has some familiar members:

* The limit when  η -> − ∞ {\displaystyle \eta \to -\infty } is the leximin ordering.
* For  η = 0 {\displaystyle \eta =0} we get the Nash bargaining solution—maximizing the product of utilities.
* For  η = 1 {\displaystyle \eta =1} we get the utilitarian welfare function—maximizing the sum of utilities.
* The limit when  η -> ∞ {\displaystyle \eta \to \infty } is the leximax ordering.

If we require the Pigou–Dalton principle (that inequality is not a positive good) then  η {\displaystyle \eta } in the above family must be at most 1.

## See also

[edit]

* Aggregation problem
* Arrow's impossibility theorem
* Community indifference curve
* Distribution (economics)
* Economic welfare
* Extended sympathy
* Gorman polar form
* Justice (economics)
* Liberal paradox
* Production-possibility frontier
* Social choice theory
* Welfare economics

## Notes

[edit]

1. ^ Amartya K. Sen, 1970 [1984], Collective Choice and Social Welfare, ch. 3, "Collective Rationality." p. 33, and ch. 3*, "Social Welfare Functions." Description.
2. ^ Tresch, Richard W. (2008). Public Sector Economics. New York: PALGRAVE MACMILLAN. p. 67\. ISBN 978-0-230-52223-7.
3. ^ Quesada, Antonio (2002). "From social choice functions to dictatorial social welfare functions". Economics Bulletin. 4 (16): 1–7.
4. ^ Herve Moulin (2004). Fair Division and Collective Welfare. Cambridge, Massachusetts: MIT Press. ISBN 9780262134231.

## References

[edit]

* Kenneth J. Arrow, 1951, 2nd ed., 1963, Social Choice and Individual Values ISBN 0-300-01364-7
* Abram Bergson (Burk),"A Reformulation of Certain Aspects of Welfare Economics," Quarterly Journal of Economics, 52(2), February 1938, 310–34
* Bergson–Samuelson social welfare functions in Paretian welfare economics from the New School.
* James E. Foster and Amartya Sen, 1996, On Economic Inequality, expanded edition with annexe, ISBN 0-19-828193-5.
* John C. Harsanyi, 1987, “interpersonal utility comparisons," The New Palgrave: A Dictionary of Economics, v. 2, 955–58
* Pattanaik, Prasanta K. (2008), "social welfare function (definition)", in Durlauf, Steven N.; Blume, Lawrence E. (eds.), The new Palgrave dictionary of economics (2nd ed.), Basingstoke, Hampshire New York: Palgrave Macmillan, ISBN 9780333786765.

Also available as: a journal article.

* Jan de Van Graaff, 1957, "Theoretical Welfare Economics", 1957, Cambridge, UK: Cambridge University Press.
* Lionel Robbins, 1935, 2nd ed.. An Essay on the Nature and Significance of Economic Science, ch. VI
* ____, 1938, "Interpersonal Comparisons of Utility: A Comment," Economic Journal, 43(4), 635–41
* Paul A. Samuelson, 1947, Enlarged ed. 1983, Foundations of Economic Analysis, pp. xxi–xxiv & ch. VIII, "Welfare Economics," ISBN 0-674-31301-1
* _____, 1977. "Reaffirming the Existence of 'Reasonable' Bergson–Samuelson Social Welfare Functions," Economica, N.S., 44(173), p pp. 81–88. Reprinted in (1986) The Collected Scientific Papers of Paul A. Samuelson, pp. 47–54.
* _____, 1981. "Bergsonian Welfare Economics", in S. Rosefielde (ed.), Economic Welfare and the Economics of Soviet Socialism: Essays in Honor of Abram Bergson, Cambridge University Press, Cambridge, pp. 223–66. Reprinted in (1986) The Collected Scientific Papers of Paul A. Samuelson, pp. 3 –46.
* Sen, Amartya K. (1963). "Distribution, Transitivity and Little's Welfare Criteria," Economic Journal, 73(292), pp. 771–78.
* _____, 1970 [1984], Collective Choice and Social Welfare (description), ch. 3, "Collective Rationality." ISBN 0-444-85127-5
* _____ (1982). Choice, Welfare and Measurement, MIT Press. Description and scroll to chapter-preview links.
* Kotaro Suzumura (1980). "On Distributional Value Judgments and Piecemeal Welfare Criteria," Economica, 47(186), p pp. 125–39.
* _____, 1987, “social welfare function," The New Palgrave: A Dictionary of Economics, v. 4, 418–20

Authority control databases: National |

* Germany

|

* v
* t
* e

Electoral systems

Part of the politics and Economics series

Single-winner|

* Approval voting
* Combined approval voting
* Unified primary
* Borda count
* Bucklin voting
* Condorcet methods
* Copeland's method
* Dodgson's method
* Kemeny–Young method
* Minimax Condorcet method
* Nanson's method
* Ranked pairs
* Schulze method
* Exhaustive ballot
* First-past-the-post voting
* Instant-runoff voting
* Coombs' method
* Contingent vote
* Supplementary vote
* Simple majoritarianism
* Plurality
* Positional voting system
* Score voting
* STAR voting
* Two-round system
* Graduated majority judgment

Proportional|

| Systems|

* Mixed-member
* Mixed single vote
* Party-list
* Proportional approval voting
* Rural–urban
* Sequential proportional approval voting
* Single transferable vote
* CPO-STV
* Hare-Clark
* Schulze STV
* Spare vote
* Indirect single transferable voting

|

Allocation|

* Highest averages method
* Webster/Sainte-Laguë
* D'Hondt
* Largest remainders method

Quotas|

* Droop quota
* Hagenbach-Bischoff quota
* Hare quota
* Imperiali quota

Mixed|

* Parallel voting
* MMP
* Additional member system
* Alternative vote plus
* Mixed single vote
* Mixed ballot transferable vote
* Scorporo
* Vote linkage mixed system

Semi-proportional|

* Single non-transferable vote
* Limited voting
* Cumulative voting
* Satisfaction approval voting

Criteria|

* Condorcet winner criterion
* Condorcet loser criterion
* Consistency criterion
* Independence of clones
* Independence of irrelevant alternatives
* Independence of Smith-dominated alternatives
* Later-no-harm criterion
* Majority criterion
* Majority loser criterion
* Monotonicity criterion
* Mutual majority criterion
* Participation criterion
* Plurality criterion
* Resolvability criterion
* Reversal symmetry
* Smith criterion
* Seats-to-votes ratio

Other|

* Ballot
* Election threshold
* First-preference votes
* Liquid democracy
* Spoilt vote
* Sortition
* Unseating

Comparison|

* Comparison of voting systems
* Voting systems by country

Portal — Project

* v
* t
* e

Economics

Theoretical|

* Microeconomics
* Decision theory
* Price theory
* Game theory
* Contract theory
* Mechanism design
* Macroeconomics
* Mathematical economics
* Complexity economics
* Computational economics
* Agent-based computational economics
* Behavioral economics
* Pluralism in economics

Empirical|

* Econometrics
* Economic statistics
* Experimental economics
* Economic history

Applied|

* Agricultural
* Behavioral
* Business
* Cultural
* Democracy
* Demographic
* Development
* Digitization
* Ecological
* Education
* Engineering
* Environmental
* Evolutionary
* Expeditionary
* Feminist
* Financial
* Geographical
* Happiness
* Health
* Historical
* Humanistic
* Industrial organization
* Information
* Institutional
* Knowledge
* Labour
* Law
* Managerial
* Monetary
* Natural resource
* Organizational
* Participation
* Personnel
* Planning
* Policy
* Public
* Public choice / Social choice theory
* Regional
* Rural
* Service
* Socio
* Sociological
* Solidarity
* Statistics
* Urban
* Welfare

Schools
(history)

* Mainstream
* Heterodox
* American (National)
* Ancient thought
* Anarchist
* Mutualism
* Austrian
* Behavioral
* Buddhist
* Chartalism
* Modern monetary theory
* Chicago
* Classical
* Critique of political economy
* Democratic
* Disequilibrium
* Ecological
* Evolutionary
* Feminist
* Georgism
* Happiness
* Historical
* Humanistic
* Institutional
* Keynesian
* Neo- (neoclassical–Keynesian synthesis)
* New
* Post-
* Circuitism
* Malthusianism
* Marginalism
* Marxian
* Neo-
* Mercantilism
* Mixed
* Neoclassical
* Lausanne
* New classical
* Real business-cycle theory
* New institutional
* Physiocracy
* Socialist
* Stockholm
* Supply-side
* Thermo

Economists

* de Mandeville
* Quesnay
* Smith
* Malthus
* Say
* Ricardo
* von Thünen
* List
* Bastiat
* Cournot
* Mill
* Gossen
* Marx
* Walras
* Jevons
* George
* Menger
* Marshall
* Edgeworth
* Clark
* Pareto
* von Böhm-Bawerk
* von Wieser
* Veblen
* Fisher
* Pigou
* Heckscher
* von Mises
* Schumpeter
* Keynes
* Knight
* Polanyi
* Frisch
* Sraffa
* Myrdal
* Hayek
* Kalecki
* Röpke
* Kuznets
* Tinbergen
* Robinson
* von Neumann
* Hicks
* Lange
* Leontief
* Galbraith
* Koopmans
* Schumacher
* Friedman
* Samuelson
* Simon
* Buchanan
* Arrow
* Baumol
* Solow
* Rothbard
* Greenspan
* Sowell
* Becker
* Ostrom
* Sen
* Lucas
* Stiglitz
* Thaler
* Hoppe
* Krugman
* Piketty
* more

Lists|

* Glossary
* Economists
* Publications (journals)
* Schools

* Category
* Index
* Lists
* Outline
* Publications
* Business portal
*[US:]:
*[UK:]:
*[el.]:
*[NZ:]:
*[v]: View this template
*[t]: Discuss this template
*[e]: Edit this template