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, an Italian economist who used the
concept in his studies of economic efficiency and income distribution. 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. 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
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. In the
absence of perfect information or complete markets, outcomes will generically be Pareto
inefficient, per the Greenwald–Stiglitz theorem.
Weak Pareto efficiency A "weak Pareto optimum" 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". 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
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,
sometimes referred to as the maximum vector problem or the skyline query.
See also Admissible decision rule, analog in decision
theory Arrow's impossibility theorem
Bayesian efficiency Fundamental theorems of welfare economics
Constrained Pareto efficiency Deadweight loss
Efficiency Game theory
Kaldor–Hicks efficiency Market failure, when a market result is not
Pareto optimal Maximal element, concept in order theory
Multiobjective optimization Nash equilibrium
Robinson Crusoe economy Social Choice and Individual Values for the
'(weak) Pareto principle' Welfare economics
References
Fudenberg, D.; Tirole, J.. "1.2.4 Multiple Nash Equilibria, Focal Points, and Pareto
Optimality". Game Theory. MIT Press. p. 18. ISBN 0-262-06141-4.
Ng, Yew-Kwang.
Welfare Economics. Macmillan. ISBN 0-333-97121-3. Osborne, Martin J.; Rubinstein, Ariel. Course
in Game Theory. MIT Press. pp. 6–. ISBN 978-0-262-65040-3. Mathur, Vijay K.. "How Well Do We Know Pareto
Optimality?". Journal of Economic Education 22: 172–8. doi:10.2307/1182422.