Pareto efficiency

A Pareto optimum (also Pareto - efficient state), named after the economist and sociologist Vilfredo Pareto ( 1848-1923 ), is a state in which it is not possible to improve a property without at the same time worsen another. The set of all Pareto optima is also called Pareto set. The Pareto criterion is the assessment of whether a condition is improved by improving a parameter ( Pareto superiority ) to have to deteriorate without the other parameters. Vilfredo Pareto originally referred to individuals rather than properties / parameters.

In mathematical terms, the tuple is a Pareto optimum ( here: maximum ) of a set of tuples, if there are no other tuples, which is at least as good in all parameters ( and in a really better), so if there is no another tuple in there, so that applies to all: and is valid for at least one.

A Pareto optimum is the result of a Pareto optimization.

Example

Example 1

In the same torque, an engine is better if it has a higher power. For a given power an engine is better if it has a higher torque. Exceeds the improvement of a value to the worsening of the other, so the motors are not Pareto comparable.

Based on the graph are further to the right and continue above values ​​Pareto superior compared to the left and below values. All engines on the red curve are " the best ". You are Pareto- optimal. An increase of a value is then only possible if the other decreases. (On the red line is: " Next to the right " forces to " further down ", conversely forcing " further up " to also having to " further to the left " to go. )

An additional condition or requirement may reduce the Pareto front on a single " ( all ) best " engine (with respect to all three requirements). This can also be a standard, the power and torque transferred to a size that makes the points on the red line and so comparable to a unique optimal solution (with respect to the norm) leads. Depending on how well the sizes are comparable, is sometimes not a norm to find.

Example 2

Sketch of the possible locations for the wells:                       (b1)                       (b2) (b3)                       (B4) (B5)          ===== | A | ===== | B | ===== | C | ======== road =====                     Set A = { b1, b2, b3, b4, b5 }

Parameters are the 3 - tuple elements "Distance to A", " Distance B", and " Distance C":

• B1 ( 158.1 m, 150.0 m, 158.1 m)
• B2 ( 111.8 m, 100.0 m, 111.8 m)
• B3 ( 141.4 m, 111.8 m, 100.0 m)
• B4 ( 70.7 m, 50.0 m, 70.7 m)
• B5 ( 111.8 m, 70.7 m, 50.0 m)

For the first Tupeleintrag ( = "Distance to A") is optimally B4, the second tuple element b4 is also optimal for the third tuple element B5 is optimal.

The Pareto optimum is thus { b4, b5 }.

• The square b1 is not Pareto- optimal, because the place is the square b2 b1 paretomäßig superior (English: Pareto- superior). The square faces b1 b2 for all operators; improvement
• But b2 is not Pareto- optimal, since b4 b2 paretomäßig superior. The place b4 faces b2 for all operators; improvement
• The squares b2 and b3 are not comparable according to the Pareto criterion, as a relocation of the fountain of b2 b3 after both one of the parties is better as well as another interested person, worse. The same applies to a relocation of the fountain of b3 b2 after. A consideration of the advantages and disadvantages of different people is not possible via the Pareto criterion.
• The square b3 is also not a Pareto optimum, since b5 faces b3 for all improved dar.
• The place b4 is Pareto- optimal, since to b4 there is no paretomäßig superior alternative, the (at least) one of the parties is better off without a worse position at the same time another
• The square b5 is however also Pareto- optimal, since any transfer of the fountain on one of the other places would provide individual C worse.
• The squares b4 and b5 are not comparable according to the Pareto criterion, as a relocation of the fountain of b4 b5 after both one of the parties is better as well as worse off another. The same applies to a transfer of b5 b4 after.

The Pareto criterion compared to the criterion of benefit amount

The criterion of Pareto optimality displaced in economic theory the hitherto prevailing utilitarian criterion of " sum of the individual benefits ."

Under the influence of the positivist philosophy of science, the idea of ​​utility as a numerical ( cardinal ) measurable and for different people ( interpersonal ) comparable size was not accepted.

In place addierbarer, cardinal utility sizes are now entering an ordinal ratings in the form of preferences ( is better / as good / worse than / not decidable ). This can usually rank orders ( orders of preference ) form ( first rank, second rank, third rank, etc. or short). It is thereby no interpersonal applicable benefit scale needed because it is individual preference orderings. The weighting of individuals with their interests is made in the Pareto criterion implicitly. The individuals and their interests are treated on an equal weighted, as it does not matter what is asked of individuals each better or worse.

The introduction of a utility scale reduces the parameters of a tuple to a size. Only by eliminating the undecidability of Größer-/Kleinerbeziehung between tuples and allows the exchange as the Pareto optimization.

The Pareto criterion in conjunction with a status quo regulation

In itself, the Pareto criterion is a plausible and unproblematic criterion for societal decisions. It supports any changes that will benefit anyone and harm anyone.

Ethically problematic, however, if it is the so- defined optimality or efficiency is the only consideration.

As has been shown, may exist a large number of Pareto optima in terms of value can not be compared with each other. In economic reality, however, a selection takes place, because - as is usual in legal systems - it remains with the existing condition, the status quo when it comes to any decisions. It therefore comes as long as do not alter the status quo, as any owner so only a disadvantage. By combining the criterion of Pareto optimality with a status quo clause affects the Pareto criterion in favor of existing conditions.

Conditions for efficiency ( Pareto optimality )

Pareto optimality of an economy means that the production factors of optimal use to be supplied. This is the case if the following conditions are met:

In modern economies meet regularly to deviations of several conditions of Pareto optimality. How can impair the functioning of the market mechanism at the same time the monopolies, externalities, information asymmetries and the presence of public goods. In this case, it is unclear according to the theory of the second best, whether a stand-alone measure to prepare the conditions affecting efficiency enhancing.