HOME

TheInfoList



OR:

Pareto efficiency or Pareto optimality is a situation where no action or allocation is available that makes one individual better off without making another worse off. The concept is named after
Vilfredo Pareto Vilfredo Federico Damaso Pareto ( , , , ; born Wilfried Fritz Pareto; 15 July 1848 – 19 August 1923) was an Italians, Italian polymath (civil engineer, sociologist, economist, political scientist, and philosopher). He made several important ...
(1848–1923), Italian civil engineer and economist, who used the concept in his studies of economic efficiency and
income distribution In economics, income distribution covers how a country's total GDP is distributed amongst its population. Economic theory and economic policy have long seen income and its distribution as a central concern. Unequal distribution of income causes ec ...
. The following three concepts are closely related: * Given an initial situation, a Pareto improvement is a new situation where some agents will gain, and no agents will lose. * A situation is called Pareto-dominated if there exists a possible Pareto improvement. * A situation is called Pareto-optimal or Pareto-efficient if no change could lead to improved satisfaction for some agent without some other agent losing or, equivalently, if there is no scope for further Pareto improvement. The
Pareto front In multi-objective optimization, the Pareto front (also called Pareto frontier or Pareto curve) is the set of all Pareto efficient solutions. The concept is widely used in engineering. It allows the designer to restrict attention to the set of eff ...
(also called Pareto frontier or Pareto set) is the set of all Pareto-efficient situations. Pareto originally used the word "optimal" for the concept, but as it describes a situation where a limited number of people will be made better off under finite resources, and it does not take equality or social well-being into account, it is in effect a definition of and better captured by "efficiency". In addition to the context of efficiency in ''allocation'', the concept of Pareto efficiency also arises in the context of ''efficiency in production'' vs. ''
x-inefficiency X-inefficiency is the divergence of a firm’s observed behavior in practice, influenced by a lack of competitive pressure, from efficient behavior assumed or implied by economic theory. The concept of X-inefficiency was introduced by Harvey Leib ...
'': a set of outputs of goods is Pareto-efficient if there is no feasible re-allocation of productive inputs such that output of one product increases while the outputs of all other goods either increase or remain the same. Pareto efficiency is measured along the production possibility frontier (PPF), which is a graphical representation of all the possible options of output for two products that can be produced using all factors of production. Besides economics, the notion of Pareto efficiency has been applied to the selection of alternatives in
engineering Engineering is the use of scientific principles to design and build machines, structures, and other items, including bridges, tunnels, roads, vehicles, and buildings. The discipline of engineering encompasses a broad range of more speciali ...
and
biology Biology is the scientific study of life. It is a natural science with a broad scope but has several unifying themes that tie it together as a single, coherent field. For instance, all organisms are made up of cells that process hereditary i ...
. Each option is first assessed, under multiple criteria, and then a subset of options is ostensibly identified with the property that no other option can categorically outperform the specified option. It is a statement of impossibility of improving one variable without harming other variables in the subject of
multi-objective optimization Multi-objective optimization (also known as multi-objective programming, vector optimization, multicriteria optimization, multiattribute optimization or Pareto optimization) is an area of multiple criteria decision making that is concerned with ...
(also termed Pareto optimization).


Overview

Formally, a state is Pareto-optimal if there is no alternative state where improvements can be made to at least one participant's well-being without reducing any other participant's well-being. If there is a state change that satisfies this condition, the new state is called a "Pareto improvement". When no Pareto improvements are possible, the state is a "Pareto optimum". In other words, Pareto efficiency is when it is impossible to make one party better off without making another party worse off. This state indicates that resources can no longer be allocated in a way that makes one party better off without harming other parties. In a state of Pareto Efficiency, resources are allocated in the most efficient way possible. Pareto efficiency is mathematically represented when there is no other strategy profile ''s’'' such that ''ui (s’) ≥ ui (s)'' for every player ''i'' and ''uj (s’) >  uj (s)'' for some player ''j''. In this equation ''s'' represents the strategy profile, ''u'' represents the utility or benefit, and ''j'' represents the player. Efficiency is an important criterion for judging behavior in a game. In a notable and often analyzed game known as Prisoner’s Dilemma, depicted below as a
normal form game In game theory, normal form is a description of a ''game''. Unlike extensive form, normal-form representations are not graphical ''per se'', but rather represent the game by way of a matrix. While this approach can be of greater use in identifyi ...
, this concept of efficiency can be observed, in that the strategy profile (Cooperate, Cooperate) is more efficient than (Defect, Defect). Using the definition listed above, ''u(Ci)'' ≥ ''u(Di)'' for ''i ∈'' , thus yielding this strategy as a Pareto efficient strategy. In other words, both players receive an increase in payoff by selecting Cooperate over Defect. A special case of a state is an allocation of resources. The formal presentation of the concept in an economy is the following: Consider an economy with n agents and k goods. Then an allocation \ , where x_i \in \mathbb^k for all ''i'', is ''Pareto-optimal'' if there is no other feasible allocation \ where, for utility function u_i for each agent i , u_i(x_i') \geq u_i(x_i) for all i \in \ with u_i(x_i') > u_i(x_i) for some i.. Here, in this simple economy, "feasibility" refers to an allocation where the total amount of each good that is allocated sums to no more than the total amount of the good in the economy. In a more complex economy with production, an allocation would consist both of consumption vectors and production vectors, and feasibility would require that the total amount of each consumed good is no greater than the initial endowment plus the amount produced. Under the assumptions of the first welfare theorem, a
competitive market In economics, competition is a scenario where different economic firmsThis article follows the general economic convention of referring to all actors as firms; examples in include individuals and brands or divisions within the same (legal) firm ...
leads to a Pareto-efficient outcome. This result was first demonstrated mathematically by economists
Kenneth Arrow Kenneth Joseph Arrow (23 August 1921 – 21 February 2017) was an American economist, mathematician, writer, and political theorist. He was the joint winner of the Nobel Memorial Prize in Economic Sciences with John Hicks in 1972. In economics ...
and Gérard Debreu. However, the result only holds under the assumptions of the theorem: markets exist for all possible goods, there are no
externalities In economics, an externality or external cost is an indirect cost or benefit to an uninvolved third party that arises as an effect of another party's (or parties') activity. Externalities can be considered as unpriced goods involved in either co ...
, markets are perfectly competitive, and market participants have perfect information. In the absence of perfect information or complete markets, outcomes will generally be Pareto-inefficient, per the Greenwald–Stiglitz theorem. The
second welfare theorem There are two fundamental theorems of welfare economics. The first states that in economic equilibrium, a set of complete markets, with complete information, and in perfect competition, will be Pareto optimal (in the sense that no further exchang ...
is essentially the reverse of the first welfare theorem. It states that under similar, ideal assumptions, any Pareto optimum can be obtained by some
competitive equilibrium Competitive equilibrium (also called: Walrasian equilibrium) is a concept of economic equilibrium introduced by Kenneth Arrow and Gérard Debreu in 1951 appropriate for the analysis of commodity markets with flexible prices and many traders, and se ...
, or
free market In economics, a free market is an economic system in which the prices of goods and services are determined by supply and demand expressed by sellers and buyers. Such markets, as modeled, operate without the intervention of government or any ot ...
system, although it may also require a
lump-sum A lump sum is a single payment of money, as opposed to a series of payments made over time (such as an annuity). The United States Department of Housing and Urban Development distinguishes between " price analysis" and "cost analysis" by whether ...
transfer of wealth.


Variants


Weak Pareto efficiency

Weak Pareto efficiency is a situation that cannot be strictly improved for ''every'' individual. Formally, a strong Pareto improvement is defined as a situation in which all agents are strictly better-off (in contrast to just "Pareto improvement", which requires that one agent is strictly better-off and the other agents are at least as good). A situation is weak Pareto-efficient if it has no strong Pareto improvements. Any strong Pareto improvement is also a weak Pareto improvement. The opposite is not true; for example, consider a resource allocation problem with two resources, which Alice values at , and George values at . Consider the allocation giving all resources to Alice, where the utility profile is (10, 0): * It is a weak PO, since no other allocation is strictly better to both agents (there are no strong Pareto improvements). * But it is not a strong PO, since the allocation in which George gets the second resource is strictly better for George and weakly better for Alice (it is a weak Pareto improvement) its utility profile is (10, 5). A market doesn't require
local nonsatiation In microeconomics, the property of local nonsatiation of consumer preferences states that for any bundle of goods there is always another bundle of goods arbitrarily close that is strictly preferred to it.''Microeconomic Theory'', by A. Mas-Colel ...
to get to a weak Pareto optimum.


Constrained Pareto efficiency

Constrained Pareto efficiency is a weakening of Pareto optimality, accounting for the fact that a potential planner (e.g., the government) may not be able to improve upon a decentralized market outcome, even if that outcome is inefficient. This will occur if it is limited by the same informational or institutional constraints as are individual agents. An example is of a setting where individuals have private information (for example, a labor market where the worker's own productivity is known to the worker but not to a potential employer, or a used-car market where the quality of a car is known to the seller but not to the buyer) which results in
moral hazard In economics, a moral hazard is a situation where an economic actor has an incentive to increase its exposure to risk because it does not bear the full costs of that risk. For example, when a corporation is insured, it may take on higher risk ...
or an
adverse selection In economics, insurance, and risk management, adverse selection is a market situation where buyers and sellers have different information. The result is that participants with key information might participate selectively in trades at the expe ...
and a sub-optimal outcome. In such a case, a planner who wishes to improve the situation is unlikely to have access to any information that the participants in the markets do not have. Hence, the planner cannot implement allocation rules which are based on the idiosyncratic characteristics of individuals; for example, "if a person is of type ''A'', they pay price ''p''1, but if of type ''B'', they pay price ''p''2" (see Lindahl prices). Essentially, only anonymous rules are allowed (of the sort "Everyone pays price ''p''") or rules based on observable behavior; "if any person chooses ''x'' at price ''px'', then they get a subsidy of ten dollars, and nothing otherwise". If there exists no allowed rule that can successfully improve upon the market outcome, then that outcome is said to be "constrained Pareto-optimal".


Fractional Pareto efficiency

Fractional Pareto efficiency is a strengthening of Pareto efficiency in the context of
fair item allocation Fair item allocation is a kind of a fair division problem in which the items to divide are ''discrete'' rather than continuous. The items have to be divided among several partners who value them differently, and each item has to be given as a whol ...
. An allocation of indivisible items is fractionally Pareto-efficient (fPE or fPO) if it is not Pareto-dominated even by an allocation in which some items are split between agents. This is in contrast to standard Pareto efficiency, which only considers domination by feasible (discrete) allocations.Barman, S., Krishnamurthy, S. K., & Vaish, R.
"Finding Fair and Efficient Allocations"
''EC '18: Proceedings of the 2018 ACM Conference on Economics and Computation'', June 2018.
As an example, consider an item allocation problem with two items, which Alice values at and George values at . Consider the allocation giving the first item to Alice and the second to George, where the utility profile is (3, 1): * It is Pareto-efficient, since any other discrete allocation (without splitting items) makes someone worse-off. * However, it is not fractionally Pareto-efficient, since it is Pareto-dominated by the allocation giving to Alice 1/2 of the first item and the whole second item, and the other 1/2 of the first item to George its utility profile is (3.5, 2).


Ex-ante Pareto efficiency

When the decision process is random, such as in
fair random assignment Fair random assignment (also called probabilistic one-sided matching) is a kind of a fair division problem. In an ''assignment problem'' (also called '' house-allocation problem'' or '' one-sided matching''), there ''m'' objects and they have to be ...
or random social choice or fractional approval voting, there is a difference between ex-post and ex-ante Pareto efficiency: * Ex-post Pareto efficiency means that any outcome of the random process is Pareto-efficient. * Ex-ante Pareto efficiency means that the ''lottery'' determined by the process is Pareto-efficient with respect to the ''expected'' utilities. That is: no other lottery gives a higher expected utility to one agent and at least as high expected utility to all agents. If some lottery ''L'' is ex-ante PE, then it is also ex-post PE. ''Proof'': suppose that one of the ex-post outcomes ''x'' of ''L'' is Pareto-dominated by some other outcome ''y''. Then, by moving some probability mass from ''x'' to ''y'', one attains another lottery ''L'' that ex-ante Pareto-dominates ''L''. The opposite is not true: ex-ante PE is stronger that ex-post PE. For example, suppose there are two objects a car and a house. Alice values the car at 2 and the house at 3; George values the car at 2 and the house at 9. Consider the following two lotteries: # With probability 1/2, give car to Alice and house to George; otherwise, give car to George and house to Alice. The expected utility is for Alice and for George. Both allocations are ex-post PE, since the one who got the car cannot be made better-off without harming the one who got the house. # With probability 1, give car to Alice, then with probability 1/3 give the house to Alice, otherwise give it to George. The expected utility is for Alice and for George. Again, both allocations are ex-post PE. While both lotteries are ex-post PE, the lottery 1 is not ex-ante PE, since it is Pareto-dominated by lottery 2. Another example involves
dichotomous preferences In economics, dichotomous preferences (DP) are preference relations that divide the set of alternatives to two subsets: "Good" versus "Bad". From ordinal utility perspective, DP means that for every two alternatives X,Y: : X \preceq Y \iff X \in ...
. There are 5 possible outcomes and 6 voters. The voters' approval sets are . All five outcomes are PE, so every lottery is ex-post PE. But the lottery selecting ''c'', ''d'', ''e'' with probability 1/3 each is not ex-ante PE, since it gives an expected utility of 1/3 to each voter, while the lottery selecting ''a'', ''b'' with probability 1/2 each gives an expected utility of 1/2 to each voter.


Bayesian Pareto efficiency

Bayesian efficiency is an adaptation of Pareto efficiency to settings in which players have incomplete information regarding the types of other players.


Ordinal Pareto efficiency

Ordinal Pareto efficiency is an adaptation of Pareto efficiency to settings in which players report only rankings on individual items, and we do not know for sure how they rank entire bundles.


Pareto efficiency and equity

Although an outcome may be considered a Pareto improvement, this does not imply that the outcome is satisfying or equitable. It is possible that inequality persists even after a Pareto improvement. Despite the fact that it is frequently used in conjunction with the idea of Pareto optimality, the term "efficiency" refers to the process of increasing societal productivity. It is possible for a society to have Pareto efficiency while also have high levels of inequality. Consider the following scenario: there is a pie and three persons; the most equitable way would be to divide the pie into three equal portions. However, if the pie is divided in half and shared between two people, it is considered Pareto efficient meaning that the third person does not lose out (despite the fact that he does not receive a piece of the pie). When making judgments, it is critical to consider a variety of aspects, including social efficiency, overall welfare, and issues such as diminishing marginal value.


Pareto efficiency and market failure

In order to fully understand market failure, one must first comprehend market success, which is defined as the ability of a set of idealized competitive markets to achieve an equilibrium allocation of resources that is Pareto-optimal in terms of resource allocation. According to the definition of market failure, it is a circumstance in which the conclusion of the first fundamental theorem of welfare is erroneous; that is, when the allocations made through markets are not efficient. In a free market, market failure is defined as an inefficient allocation of resources. Due to the fact that it is feasible to improve, market failure implies Pareto inefficiency. For example, excessive consumption of depreciating items (drugs/tobacco) results in external costs to non-smokers, as well as premature death for smokers who do not quit. An increase in the price of cigarettes could motivate people to quit smoking while also raising funds for the treatment of smoking-related ailments.


Approximate Pareto efficiency

Given some ''ε'' > 0, an outcome is called ''ε''-Pareto-efficient if no other outcome gives all agents at least the same utility, and one agent a utility at least (1 + ''ε'') higher. This captures the notion that improvements smaller than (1 + ''ε'') are negligible and should not be considered a breach of efficiency.


Pareto-efficiency and welfare-maximization

Suppose each agent ''i'' is assigned a positive weight ''ai''. For every allocation ''x'', define the ''welfare'' of ''x'' as the weighted sum of utilities of all agents in ''x'': : W_a(x) := \sum_^n a_i u_i(x). Let ''xa'' be an allocation that maximizes the welfare over all allocations: : x_a \in \arg\max_x W_a(x). It is easy to show that the allocation ''xa'' is Pareto-efficient: since all weights are positive, any Pareto improvement would increase the sum, contradicting the definition of ''xa''. Japanese neo- Walrasian economist
Takashi Negishi is a Japanese neo- Walrasian economist. Career Negishi graduated Faculty of Economics, University of Tokyo in 1956 and received a PhD in Economics from University of Tokyo in 1963. Contributions Negishi's research has provided a wide range of e ...
proved that, under certain assumptions, the opposite is also true: for ''every'' Pareto-efficient allocation ''x'', there exists a positive vector ''a'' such that ''x'' maximizes ''Wa''. A shorter proof is provided by
Hal Varian Hal Ronald Varian (born March 18, 1947 in Wooster, Ohio) is Chief Economist at Google and holds the title of emeritus professor at the University of California, Berkeley where he was founding dean of the School of Information. Varian is an eco ...
.


Use in engineering

The notion of Pareto efficiency has been used in engineering. Given a set of choices and a way of valuing them, the
Pareto front In multi-objective optimization, the Pareto front (also called Pareto frontier or Pareto curve) is the set of all Pareto efficient solutions. The concept is widely used in engineering. It allows the designer to restrict attention to the set of eff ...
(or Pareto set or Pareto frontier) is the set of choices that are Pareto-efficient. By restricting attention to the set of choices that are Pareto-efficient, a designer can make
trade-off A trade-off (or tradeoff) is a situational decision that involves diminishing or losing one quality, quantity, or property of a set or design in return for gains in other aspects. In simple terms, a tradeoff is where one thing increases, and anot ...
s within this set, rather than considering the full range of every parameter.


Use in public policy

Modern microeconomic theory has drawn heavily upon the concept of Pareto efficiency for inspiration. Pareto and his successors have tended to describe this technical definition of optimal resource allocation in the context of it being an equilibrium that can theoretically be achieved within an abstract model of market competition. It has therefore very often been treated as a corroboration of Adam Smith's "
invisible hand The invisible hand is a metaphor used by the British moral philosopher Adam Smith that describes the unintended greater social benefits and public good brought about by individuals acting in their own self-interests. Smith originally mention ...
" notion. More specifically, it motivated the debate over "
market socialism Market socialism is a type of economic system involving the public, cooperative, or social ownership of the means of production in the framework of a market economy, or one that contains a mix of worker-owned, nationalized, and privately owne ...
" in the 1930s. However, because the Pareto-efficient outcome is difficult to assess in the real world when issues including asymmetric information, signalling, adverse selection, and moral hazard are introduced, most people do not take the theorems of welfare economics as accurate descriptions of the real world. Therefore, the significance of the two welfare theorems of economics is in their ability to generate a framework that has dominated neoclassical thinking about public policy. That framework is that the welfare economics theorems allow the political economy to be studied in the following two situations: "market failure" and "the problem of redistribution".Lockwood B. (2008) ''Pareto Efficiency''. In: Palgrave Macmillan (eds.) ''The New Palgrave Dictionary of Economics''. Palgrave Macmillan, London. Analysis of "market failure" can be understood by the literature surrounding externalities. When comparing the "real" economy to the complete contingent markets economy (which is considered efficient), the inefficiencies become clear. These inefficiencies, or externalities, are then able to be addressed by mechanisms, including property rights and corrective taxes. Analysis of "the problem with redistribution" deals with the observed political question of how income or commodity taxes should be utilized. The theorem tells us that no taxation is Pareto-efficient and that taxation with redistribution is Pareto-inefficient. Because of this, most of the literature is focused on finding solutions where given there is a tax structure, how can the tax structure prescribe a situation where no person could be made better off by a change in available taxes.


Use in biology

Pareto optimisation has also been studied in biological processes. In bacteria, genes were shown to be either inexpensive to make (resource-efficient) or easier to read (
translation Translation is the communication of the meaning of a source-language text by means of an equivalent target-language text. The English language draws a terminological distinction (which does not exist in every language) between ''transla ...
-efficient).
Natural selection Natural selection is the differential survival and reproduction of individuals due to differences in phenotype. It is a key mechanism of evolution, the change in the heritable traits characteristic of a population over generations. Cha ...
acts to push highly expressed genes towards the Pareto frontier for resource use and translational efficiency. Genes near the Pareto frontier were also shown to evolve more slowly (indicating that they are providing a selective advantage).


Common misconceptions

It would be incorrect to treat Pareto efficiency as equivalent to societal optimization, as the latter is a
normative Normative generally means relating to an evaluative standard. Normativity is the phenomenon in human societies of designating some actions or outcomes as good, desirable, or permissible, and others as bad, undesirable, or impermissible. A norm in ...
concept, which is a matter of interpretation that typically would account for the consequence of degrees of inequality of distribution. An example would be the interpretation of one school district with low property tax revenue versus another with much higher revenue as a sign that more equal distribution occurs with the help of government redistribution.


Criticism

Some commentators contest that Pareto efficiency could potentially serve as an ideological tool. With it implying that capitalism is self-regulated thereof, it is likely that the embedded structural problems such as unemployment would be treated as deviating from the equilibrium or norm, and thus neglected or discounted. Pareto efficiency does not require a totally equitable distribution of wealth, which is another aspect that draws in criticism. An economy in which a wealthy few hold the vast majority of resources can be Pareto-efficient. A simple example is the distribution of a pie among three people. The most equitable distribution would assign one third to each person. However, the assignment of, say, a half section to each of two individuals and none to the third is also Pareto-optimal despite not being equitable, because none of the recipients could be made better off without decreasing someone else's share; and there are many other such distribution examples. An example of a Pareto-inefficient distribution of the pie would be allocation of a quarter of the pie to each of the three, with the remainder discarded. The
liberal paradox The liberal paradox, also Sen paradox or Sen's paradox, is a logical paradox proposed by Amartya Sen which shows that no means of aggregating individual preferences into a single, social choice, can simultaneously fulfill the following, seemingly ...
elaborated by
Amartya Sen Amartya Kumar Sen (; born 3 November 1933) is an Indian economist and philosopher, who since 1972 has taught and worked in the United Kingdom and the United States. Sen has made contributions to welfare economics, social choice theory, econom ...
shows that when people have preferences about what other people do, the goal of Pareto efficiency can come into conflict with the goal of individual liberty.Sen, A., ''Rationality and Freedom'' (
Cambridge, MA Cambridge ( ) is a city in Middlesex County, Massachusetts, United States. As part of the Boston metropolitan area, the cities population of the 2020 U.S. census was 118,403, making it the fourth most populous city in the state, behind Boston ...
/ London: Belknep Press, 2004)
pp. 92–94
Lastly, it is proposed that Pareto efficiency to some extent inhibited discussion of other possible criteria of efficiency. As
Wharton School The Wharton School of the University of Pennsylvania ( ; also known as Wharton Business School, the Wharton School, Penn Wharton, and Wharton) is the business school of the University of Pennsylvania, a private Ivy League research university in P ...
professor Ben Lockwood argues, one possible reason is that any other efficiency criteria established in the neoclassical domain will reduce to Pareto efficiency at the end.


See also

* Admissible decision rule, analog in
decision theory Decision theory (or the theory of choice; not to be confused with choice theory) is a branch of applied probability theory concerned with the theory of making decisions based on assigning probabilities to various factors and assigning numerical ...
*
Arrow's impossibility theorem Arrow's impossibility theorem, the general possibility theorem or Arrow's paradox is an impossibility theorem in social choice theory that states that when voters have three or more distinct alternatives (options), no ranked voting electoral syst ...
* Bayesian efficiency *
Fundamental theorems of welfare economics There are two fundamental theorems of welfare economics. The first states that in economic equilibrium, a set of complete markets, with complete information, and in perfect competition, will be Pareto optimal (in the sense that no further exchang ...
*
Deadweight loss In economics, deadweight loss is the difference in production and consumption of any given product or service including government tax. The presence of deadweight loss is most commonly identified when the quantity produced ''relative'' to the amoun ...
* Economic efficiency * Highest and best use *
Kaldor–Hicks efficiency A Kaldor–Hicks improvement, named for Nicholas Kaldor and John Hicks, is an economic re-allocation of resources among people that captures some of the intuitive appeal of a Pareto improvement, but has less stringent criteria and is hence appl ...
*
Market failure In neoclassical economics, market failure is a situation in which the allocation of goods and services by a free market is not Pareto efficient, often leading to a net loss of economic value. Market failures can be viewed as scenarios where indi ...
, when a market result is not Pareto-optimal * Maximal element, concept in
order theory Order theory is a branch of mathematics that investigates the intuitive notion of order using binary relations. It provides a formal framework for describing statements such as "this is less than that" or "this precedes that". This article int ...
* Maxima of a point set *
Multi-objective optimization Multi-objective optimization (also known as multi-objective programming, vector optimization, multicriteria optimization, multiattribute optimization or Pareto optimization) is an area of multiple criteria decision making that is concerned with ...
*
Pareto-efficient envy-free division Efficiency and fairness are two major goals of welfare economics. Given a set of resources and a set of agents, the goal is to divide the resources among the agents in a way that is both Pareto efficient (PE) and envy-free (EF). The goal was first ...
* ''
Social Choice and Individual Values Kenneth Arrow's monograph ''Social Choice and Individual Values'' (1951, 2nd ed., 1963, 3rd ed., 2012) and a theorem within it created modern social choice theory, a rigorous melding of social ethics and voting theory with an economic flavor. ...
'' for the "(weak) Pareto principle" * TOTREP *
Welfare economics Welfare economics is a branch of economics that uses microeconomic techniques to evaluate well-being (welfare) at the aggregate (economy-wide) level. Attempting to apply the principles of welfare economics gives rise to the field of public ec ...


References


Further reading

* * * * *
Book preview.
* * {{DEFAULTSORT:Pareto Efficiency Game theory Law and economics Welfare economics Mathematical optimization Electoral system criteria Vilfredo Pareto