Pareto efficiency
Pareto efficiency, or Pareto optimality, is a central theory in economics with broad applications in game theory, engineering and the social sciences. Given a set of alternative allocations and a set of individuals, a movement from one alternative allocation to another that can make at least one individual better off, without making any other individual worse off is called a Pareto improvement or Pareto optimization. An allocation of resources is Pareto efficient or Pareto optimal when no further Pareto improvements can be made.
The term is named after Vilfredo Pareto, an Italian economist who used the concept in his studies of economic efficiency and income distribution.
If an economic system is not Pareto efficient, then it is not the case that some individual can be made better off without anyone being made worse off. It is commonly accepted that such inefficient outcomes are to be avoided, and therefore Pareto efficiency is an important criterion for evaluating economic systems and political policies.
In particular, it can be shown that, under certain idealised conditions, a system of free markets will lead to a Pareto efficient outcome. This was first demonstrated mathematically by economists Kenneth Arrow and Gerard Debreu, although the result may not necessarily reflect the workings of real economies because of the restrictive assumptions necessary for the proof (markets exist for all possible goods, markets are perfectly competitive, and transaction costs are negligible). This is called the first welfare theorem.
Not every Pareto efficient outcome will be regarded as desirable. For example, consider a dictatorship run solely for the benefit of one person. This will, in general, be Pareto optimal because it will be impossible to raise the well-being of anyone (excluding the dictator) without reducing the well-being of the dictator, and vice versa. Nevertheless, most people (except by definition the dictator) would not see this as a desirable economic system.
There is often more than one Pareto efficient outcome for a given amount of resources. For example with a dictatorship, both with dictator Alice or with dictator Bob, the outcome will be Pareto efficient because in the first instance it will be impossible to raise the well-being of anyone without reducing Alice's benefit and similarly for Bob.
A strongly Pareto optimal (SPO) allocation is one such that the allocation is strictly preferred by one person, and no other allocation would be as good for everyone. A weakly Pareto optimal (WPO) allocation is one where a feasible reallocation would be strictly preferred by all agents.