Pareto efficiency

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Pareto efficiency, or Pareto optimality, is a state of allocation of resources in which it is impossible to make any one individual better off without making at least one individual worse off. The term is named after Vilfredo Pareto (1848–1923), an Italian economist who used the concept in his studies of economic efficiency and income distribution.[citation needed] The concept has applications in academic fields such as economics, engineering, and the life sciences.

Given an initial allocation of goods among a set of individuals, a change to a different allocation that makes at least one individual better off without making any other individual worse off is called a Pareto improvement. An allocation is defined as "Pareto efficient" or "Pareto optimal" when no further Pareto improvements can be made.

Pareto efficiency is a minimal notion of efficiency and does not necessarily result in a socially desirable distribution of resources: it makes no statement about equality, or the overall well-being of a society.[1][2] The notion of Pareto efficiency can also be applied to the selection of alternatives in engineering and similar fields. Each option is first assessed under multiple criteria and then a subset of options is identified with the property that no other option can categorically outperform any of its members.

Overview[edit]

A production-possibility frontier is an example of a Pareto Efficient Frontier. The connected line of red points represent Pareto optimal choices of production.

If economic allocation in any system is not Pareto efficient, there is potential for a Pareto improvement—an increase in Pareto efficiency: through reallocation, improvements can be made to at least one participant's well-being without reducing any other participant's well-being.

It is important to note, however, that a change from an inefficient allocation to an efficient one is not necessarily a Pareto improvement. Thus, in practice, ensuring that nobody is disadvantaged by a change aimed at achieving Pareto efficiency may require compensation of one or more parties. For instance, if a change in economic policy eliminates a monopoly and that market subsequently becomes competitive and more efficient, the monopolist will be made worse off. However, the loss to the monopolist will be more than offset by the gain in efficiency. This means the monopolist can be compensated for its loss while still leaving a net gain for others in the economy, a Pareto improvement.

In real-world practice, such compensations have unintended consequences. They can lead to incentive distortions over time as agents anticipate such compensations and change their actions accordingly. Under certain idealized conditions, it can be shown that a system of free markets will lead to a Pareto efficient outcome. This is called the first welfare theorem. It was first demonstrated mathematically by economists Kenneth Arrow and Gérard Debreu. However, the result only holds under the restrictive assumptions necessary for the proof (markets exist for all possible goods so there are no externalities, all markets are in full equilibrium, markets are perfectly competitive, transaction costs are negligible, and market participants have perfect information). In the absence of perfect information or complete markets, outcomes will generically be Pareto inefficient, per the Greenwald–Stiglitz theorem.[3]

Weak Pareto efficiency[edit]

A "weak Pareto optimum" (WPO) is an allocation for which there are no possible alternative allocations whose realization would cause every individual to gain. Thus an alternative allocation is considered to be a Pareto improvement only if the alternative allocation is strictly preferred by all individuals. When contrasted with weak Pareto efficiency, a standard Pareto optimum as described above may be referred to as a "strong Pareto optimum" (SPO).

Weak Pareto-optimality is "weaker" than strong Pareto-optimality in the sense that any SPO also qualifies as a WPO, but a WPO allocation is not necessarily an SPO.

Use in engineering[edit]

Example of a Pareto frontier. The boxed points represent feasible choices, and smaller values are preferred to larger ones. Point C is not on the Pareto Frontier because it is dominated by both point A and point B. Points A and B are not strictly dominated by any other, and hence do lie on the frontier.

The notion of Pareto efficiency is also useful in engineering. Given a set of choices and a way of valuing them, the Pareto frontier or Pareto set or Pareto front 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 tradeoffs within this set, rather than considering the full range of every parameter.

Algorithms for computing the Pareto frontier of a finite set of alternatives have been studied in computer science, power engineering,[4] sometimes referred to as the maximum vector problem or the skyline query.[5][6]

See also[edit]

References[edit]

  1. ^ Barr, Nicholas (2012). "3.2.2 The relevance of efficiency to different theories of society". Economics of the Welfare State (5th ed.). Oxford University Press. p. 46. ISBN 978-0-19-929781-8. 
  2. ^ Sen, Amartya (October 1993). "Markets and freedom: Achievements and limitations of the market mechanism in promoting individual freedoms" (PDF). Oxford Economic Papers 45 (4): 519–541. JSTOR 2663703. 
  3. ^ Greenwald, Bruce; Stiglitz, Joseph E. (1986). "Externalities in economies with imperfect information and incomplete markets". Quarterly Journal of Economics 101 (2): 229–264. doi:10.2307/1891114. JSTOR 1891114. 
  4. ^ Tomoiagă, B.; Chindriş, M.; Sumper, A.; Sudria-Andreu, A.; Villafafila-Robles, R. Pareto Optimal Reconfiguration of Power Distribution Systems Using a Genetic Algorithm Based on NSGA-II. Energies 2013, 6, 1439-1455.
  5. ^ Kung, H.T.; Luccio, F.; Preparata, F.P. (1975). "On finding the maxima of a set of vectors.". Journal of the ACM 22 (4): 469–476. doi:10.1145/321906.321910. 
  6. ^ Godfrey, Parke; Shipley, Ryan; Gryz, Jarek (2006). "Algorithms and Analyses for Maximal Vector Computation". VLDB Journal 16: 5–28. doi:10.1007/s00778-006-0029-7.