Paretooptimal

Pareto optimality, or Pareto efficiency, is a state of resource allocation in which it is impossible to make any individual better off without making at least one other individual worse off. An allocation that satisfies this condition is Pareto efficient. The concept was developed by Vilfredo Pareto in the late 19th and early 20th centuries and has become a foundational idea in welfare economics and social choice theory.

In a constrained economy, the Pareto frontier (or Pareto set) comprises all allocations that are Pareto efficient given the available resources and technology. A Pareto improvement is a change that makes someone better off without harming anyone else. Pareto efficiency is a partial ordering of allocations: it does not tell us which of the Pareto efficient outcomes is best, only that no further Pareto improvements are possible.

Pareto efficiency focuses on ordinal preferences rather than cardinal utilities and does not by itself address equity or distributional concerns. An allocation can be Pareto efficient but still be viewed as unfair or undesirable from a social-welfare perspective that imposes social or ethical weights on individuals.

Applications of Pareto efficiency appear across economics, engineering, and multiobjective optimization. Limitations include sensitivity to the chosen set of agents and goods, the possibility of multiple Pareto efficient outcomes, and the exclusion of distributional considerations, externalities, and dynamic changes over time.