Talk:Pareto efficiency

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[edit] Took out some unneccessary qualifiers from the Criticisms section

It seemed to be POV in the current wording, using words like "widely criticized" and "strongly" where they were not warranted

Akshayaj 21:01, 12 July 2007 (UTC)



MISTAKE: In the criticism, the fact that one person can have no slice and someone else has 2 slice being pareto optimal assumes a linear utility function (i.e. that marginal utility doesn't decrease with wealth). Otherwise, the equitable allocation would be the best as everyone would have the highest possible utility for their slice. Hence this would be pareto optimal and not the inequitable solution. --203.158.33.213 06:26, 19 August 2006 (UTC)

I agree that a discussion of the different utility functions is badly needed in the article. Rather than to talk about a pie an example with fruit could be used: a boy got an apple and a girl received a banana from their respective fathers. However, both the two children preferred the other child's fruit compared with its own. Therefore, by changing fruits there would be a Pareto efficient solution. To a large, extent different utility functions are a reason why trade occur. Also, it might be a good idea to mention the common assumption that the extra utility from each extra piece of good decreases with each piece. In other words the first apple tastes better than the second and the second tastes better than the third etc. This influences the utility functions of all people for all sorts of goods and services. With different utility functions and different amounts of goods and services with different individuals it's clear that the total utility will increase if the goods and services are redistributed. This is the basic idea behind Pareto efficiency. In history there have been different ideas for how to accomplish this effect. The idea of (utopian) communism was that people would voluntarily hand over goods and services to people with great needs. Even without considering that people are too egoistic for this to work out, in a in world with many different kinds of goods and services and many individuals an information problem occur. How to collect and distribute information about the individuals’ utility functions, the number of different goods available, etc? In a market economy this is no problem since the relative utility functions of the population and the relative scarcity of goods in reflected in the price level for all goods and services. At the very beginning of the 20th century (before the Russian revolution) there was a debate between economists whether an adequate allocation of resources could be achieved in communism, since information about the relative scarcity was not given. Perhaps I should not get into depth on the different arguments in this extremely interesting discussion. Anyway critics of communism foresaw basically problems, which later occurred in economy of the Soviet Union. Strangely enough it's generally considered that the debate was won by the proponents of communism. The reason is that they came up with the concept that there should be artificial trading giving sort of market prices in an economy without personal ownership. In the Soviet Union the main sort of allocation was through administrative action. Therefore after a while changes in individuals' and companies' utility functions as well as relative scarcity of goods and services were no longer reflected in the prices of goods and services. This is one of the main reasons why it was so difficult for the Soviet Union to achieve Pareto efficient solutions. In short, Pareto efficient solutions can be reached in different ways, but in a system with flexible prices such solutions are easiest to attain through trade. Somehow these ideas should be added to the article in one way or the other.Smallchanges 18:34, 9 October 2006 (UTC)

This is facinating. Any references for further reading about this would be appreciated. 74.210.53.170 03:06, 16 June 2007 (UTC)

I don't understand why it is considered better for someone to benefit at another's expense, rather than benefiting at no one's expense. Is it based on the assumption that if it is possible(to benefit at no one's expense), then resources were not being used properly? If this is true, it still seems that it would be desirable, as long as everyone was content, since no one would need to be made less content for others to become more content.

That basically is the idea behind Pareto efficiency. If something is not pareto efficient, then resources are not being used properly, since someone can be made better off without making any one else worse off. Is the page somehow confusing that? Jrincayc 14:49, 23 Nov 2003 (UTC)


"A change that can make at least one individual better off, without making any other individual worse off is called a pareto improvement."

"If an economic system is not Pareto efficient, then it is the case that some individual can be made better off without anyone being made worse off.

Aren't these contradictory? If the change makes someone better off without making anyone else worse off, it is an improvement. However, if the system is not pareto efficient, then you can make someone better off without anyone else being made worse off. So it's an improvement to make the system less pareto-efficient?

It is confusing at first read because the first sentence refers to an economic activity (change) whereas the second refers to an economic system. Simply put, they just say that an economic system will not be perfectly Pareto effecient if there are opportunities to engage in economic activities that contribute to Pareto efficiency. The second statement could be reformulated tautologically to say "If an economic system is not Pareto efficient, then a Pareto improvement would be possible. mydogategodshat 20:19, 7 May 2004 (UTC)

[edit] Local nature of optimization

Suggested addition, along the lines of:

A key drawback of Pareto optimality is its localization. As the dictator example illustrates, there can be very many Local optimum points. The Pareto improvement criterion does not even define any Global optimum. Under a reasonable criterion, many Pareto-optimal solutions may be far inferior to the global solution. However, it might be argued that under all reasonable criteria the global optimum will also be Pareto-optimal. Indeed Pareto optimality might be one test of reasonableness.

I think I understand what you're trying to say, but I don't think that quite works. While it is important to stress in the article that there are almost always many Pareto optimal solutions, and that depending on the weighting factors (I think that's what you mean by criterion) some will be optimal while others will be suboptimal, you can't say that the number of Pareto optimal points is necessarily a disadvantage. In fact, for people who use Pareto fronts, that's normally considered an advantage. It lets you apply human judgement after seeing a range of solutions, instead of having to choose your weighting factors up front. moink 18:34, 28 Jul 2004 (UTC)

With that in mind, I would emphasize that Pareto efficiency is not really optimality in the ordinary sense, and only provides optimality, albeit robust optimality, in the most limited and local sense. Alex Stark 02:21, 2004 Aug 10 (UTC)

Good point. I'll add it. 137.222.40.132 17:14, 4 April 2006 (UTC)

[edit] 'Corollary'

I removed the text:

A corollary of a Pareto efficient economy that is desirable is that all workers make the same wage and all firms operate with the same profit margins.

I tend to think that this is value judgement. If the writer meant this in general, then they are saying that a coal miner (a dangerous, dirty job) should recieve the same wage as a librarian in a small town. Since the jobs are different, having the same wage would be unfair. Even Twin Oaks provides slightly different benefits to workers who do different jobs. Profit margins in industries are also likely to be different for reasons such as different risk and different capital startup costs. I have no objection to the idea in general that equality is good, but I would hesitate to call it a corollary, and inso much as it is mentioned in an article on Pareto efficientcy, it should probably be mentioned that it is trying for a different idea. Jrincayc 16:13, 3 Jan 2005 (UTC)

Reply by 69.107.96.61 5 Jan 2005. Hi Mr. Jrincayc. I am not a professional economist (like you?) but I believe that the corollary is not a value judgement but in fact a consequence of a pareto efficient economy (one that is at the boundary of the production possibility curve). This I recall from memory, years ago, from my Econ 101 class. I could be mistaken, but I think that once you reach the boundary, by definition all wage differentials, at the margin, will equal zero. That is, suppose that a wage differential exists for rocket scientists. A bunch of people will 'retool' and become rocket scientists, which will drive down the wage differential to zero. (In fact, in the aerospace industry, that's exactly what happened! Too many smart people in aeronautics, that's why I switched majors and became a lawyer). So, in a 'steady-state', long-term, quisscent 'Pareto optimal' economy, everybody makes the same amount of money (kinda like Communism and Sweden, but different). Anyhoo, I could be mistaken so I will let your revision stand. PS--I see we share some similar interests: IP and programming. Try C#.NET for a cool, easy to learn OOP language.--Cheers, User:69.107.96.61

Well, assuming that everyone was alike, there would still be differences in the amount that different jobs payed since the jobs themselves are different. A dangerous, dirty job that required lots of education would pay better than an safe easy job that required no education because if the jobs payed the same, then a person in the hard job would switch to the easy job. What would happen if everyone was the same is that the wages would hit a point so that people would be indifferent between the jobs, because the wage difference would exactly compensate for the differences in danger, effort and education... So the benefit of each job would be the same, but the monetary wage would be different. Since people are different, not even this happens completely, but there are effects to even out the overall benefits of different jobs. Jrincayc 13:58, 6 Jan 2005 (UTC)
Not to beat a dead horse, but I think confusion is with transient versus steady-state effects. "You" are thinking more transient, while "I" am thinking equilibrium (end-point) steady state. At the "steady state" time is infinity, so while people are different, and some jobs take more time to learn, and are more dangerous than others, and should and do initially yield more than safe, easy to learn jobs, at the limit (t = infinity) the wage differential goes to zero regardless of the job (so crab fisherman in Alaska, the world's most dangerous job next to conflict diamond mining in Angola, make the same as a desk receptionist in Peoria). Of course in the 'real world' this would never happen, but keep in mind Pareto optimal is a mathematical construct, not necessarily a real-world event (kinda like Adam Smith's 'perfect competition' where nobody has market power). Another corollary of Pareto optimal efficiency, as I recall, was that all investments and all corporations returned and earned an equal amount of money. The same principle applied: risky investment prices were 'bid up' by eager investors, until the return was the same as what the bank gives you. In fact, in a book called "Triumph of the Optimists: 101 Years of Global Investment Returns" by Elroy Dimson, Paul Marsh, Mike Staunton (good book if you can find a copy), it has been shown, on rather sketchy data, that in fact over the last 100 years, world wide, risky investments yielded about the same as riskless investments (I can relate to that--since the mid 90s my investments are running at about 3% a year compounded! Dang dot-com crash!). But let's agree to disagree on this one. For one thing, I support Wikipedia (have given money to them) but I think long-term it is best to keep the explanation of topics simple, for high-school kids and for quick rough outlines of topics rather than get into grad level discourse, which tends to confuse in an abbreviated format such as here. Cheers, 69.107.96.61 6 Jan 2005
I think that we may be in violent agreement. Let me try and define what I am talking about for the wages. First of all for a given job you have benefits you recieve such as money, health care, retirement and so forth. For a given job you also have costs such as your time, risk of death and dismemberment, physical effort, mental effort and so forth. You also have effort to get the job which includes things such as education, security clearences, licences and so forth. Lets call these benefit, cost, and obtain respectively. First, assuming that obtain is the same for two jobs, I would expect that under the long run people are the same assumetions (LRPS) for any two jobs a and b with the same obtain, benfit_a - cost_a = benfit_b - cost_b. I am pretty sure that this is the invariant, since if say benefit_a - cost_a > benefit_b - cost_b, then more people would want to work at job a than at job b. Since there are extra people trying for job a, and too few people trying for job b, supply and demand would tend to raise the benefits for job b and lower the benefits for job a. So, in the long run, I expect that benefit_a - cost_a = benefit_b - cost_b for all jobs a and b where obtain is the same. Note that this says that benefit_a = benefit_b only if cost_a = cost_b, and I am pretty sure that cost_a and cost_b will be different for many jobs (risk of death, physical effort and so forth vary for jobs). Now, how to deal with obtain. I hope we can agree that being a grocery clerk and being a professor of physics have different obtaining costs. One requires around a month or so of training, and the other requires around a 6-10 years of training (beyond high school). So, there is a different obtaining cost for each. Now, in the LRPS equilibrium, you will only choose a job with a higher obtain if you get greater net benefits later on. So, I think the equilibrium equation is: lifetime(benefits_a - costs_a) - obtain_a = lifetime(benefits_b - costs_b) - obtain_b. Lifetime is a rather complicated intergral that incorperates things like discounting and so forth (that I lack the interest to really calculate), but taking it as the sum of yearly benifits - cost for every working year is a reasonable aproximation. Now, if this is higher for job a than job b, then again, you would expect that there would be supply and demand mismatch issues, so benefits would be raised and lowered to fix that problem. So, as long as the obtain cost and the regular cost are different for different jobs, the benefits of each job will be different in the long run people same assumptions. However, each person will be indifferent to which job that they get (I think this is what you are remembering from your economics class).
As for businesses, I agree that in the long run, each business sector should be earning the same economics profits (but very different accounting profits). I hope this makes sense. If it doesn't tell me where so I can try and figure out if I made a mistake or I am being unclear. Jrincayc 16:20, 7 Jan 2005 (UTC)

[edit] Removed material

I have removed:

The Pareto conjecture hypothesizes that the real world does not contain any Pareto optimizations.

I have not heard of this conjecture. Please cite verifiable sources if you wish to return this sentence. It describes a dark world view indeed! mydogategodshat 00:48, 21 September 2005 (UTC)


Has anyone heard of BitTorrent? Check out http://bittorrent.com to learn about Bram Cohen's creation, which was created as a pareto efficient system.



[edit] about pareto efficiency in public finance

I have a homework about pareto efficiency in drug markets. question is "standart public finance theory suggest that patent rights on drugs must be protected because such rights guarantee pareto efficiency.is this true or false.discuss in details" if you can help to me I will be happy thanksssss

I think that is covered in WP:WINYH, which is to say Wikipedia is Not Your Homework. --Brokenfixer 06:46, 18 January 2006 (UTC)


[edit] Pareto efficient is socialist

This is a socialist hypothesis. It is utterly false in a free market, because there is no way to improve someone without consequences for someone else. Any regulation of the market breaks the definition of the free market that must have unknowable elements, such as new technology or competition for new ways and means--it is how the market become efficient in a free market by competition. The horse-carriage, by example, is no longer popular, but has been used since time immemorial and was replaced by the automobile (every new automobile took away from horse-carriage makers), and this means no economy could be Pareto efficient because the definitions of efficient are inadequate and incomplete. Automobiles dramatically increased the efficiency of Western World societies, and any regulation to prevent changes to make a fake efficient system would be quickly overrun by the other nations willing to throw out Pareto efficient and make the technology advances. Pareto efficient does not explain the modern technology markets and new efficiencies they develop.

This isn't a hypothesis, it's a mathematical concept. It has nothing to do with political philosophies, so please keep politics out of this article.
In any case, you're contradicting yourself. If there is no way to "improve someone without consequences for someone else" then that's Pareto efficient by definition.
Pareto efficiency is defined on a ceteris paribus basis, so whether new technologies emerge in future is irrelevant. 137.222.40.132 17:09, 4 April 2006 (UTC)
The condition for pareto inefficiency is not that improvements must have no consequences for somebody else in the absolute sense. There must simply be a net gain from an efficiency change after any "losers" are compensated. Please see below and also in the article for more on this.

Also, new productivity increasing technologies move the [production possibilities frontier] outwards, ie, increase what can be produced. This means that when a new technology becomes available not adopting it creates a pareto inefficiency, because the economy is not producing to its full potential.

Pareto is not socialist. Socialism advocates the redistribution of wealth from top down, person A makes 100 person B and C make 25, everyone therefore should make 50, while this may be communist insert a number slightly higher say 60, 45, 45 to make is socialist. Pareto, from what I learned of it in a class I took involving it, would say this is NOT PARETO OPTIMAL. for it to be pareto optimal, NO ONE GOES DOWN, and at least one person goes up. therefore, to characterize it as socialist is incorrect, because in Socialism the wealthy serve to bring up the poor, which might serve to highlight an overall utility model of society, but not one that guards against any downswing and only goes for the upswing (in an attempt to guard against the situation in Mills' utilitarianism, whereby one person suffering to prop up the rest is acceptable if the average utility or happiness goes up.)

Also, to say that there is no way to improve someone without hurting someone else, shows a great deal of misunderstanding concerning economics and trade. In a situation with perfect information, (the ideal all free markets strive for), or even in the real world without perfect info for everyone, there are many situations where people can make mutually advantageous trades (this is the basis of capitalism as a whole). Trade is not a zero sum game, someone might have one good, and another something else, and to trade half of each stockpile would benefit both parties.

[edit] Dictator analogy, pie example

I have removed the bit about a dictator being an undesirable Pareto efficiency. Pareto efficiency deals with markets, something definitionally unapplicable to dictatorships. This is also applicable to the silly bit above about it being somehow "socialist." Pareto efficiency is not about the winners winning more than the losers lose. Rather, it says that in a free market losers' loss will be negated by some other market compensation. 68.98.158.194

I reintroduced the example as it is very easy to understand, being somewhat extreme. If you don't like the dictator thing, maybe it would be better to reword the example than to remove it AdamSmithee 18:18, 13 May 2006 (UTC)

I removed the dictator example again but not because of any political preference. Unfortunately it was based on a common misunderstanding of the "better off with no worse off" necessary condition for Pareto efficiency. Acheivement of Pareto efficiency only creates the potential for this condition, but does not necessarily distribute wealth like this in practice. This is acheived in practice by compensation to those hurt by the policy change, with the efficiency gain outweighing the amount of compensation required and resulting a net gain. Thus, the case that a dictatorship is always a Pareto efficient economy is not correct, if a re-organisation can result in a net economic gain after the dictator has been compensated for his/her loss. Please see the other part of my edit in the begining section for changes explaining this.

I'm not entirely sure of the strict relevance of the pie example to the concept of Pareto efficincy either. It appears to prove that Pareto efficiency can exist alongside inequity due to social choice, but doesn't prove that Pareto efficiency drives inequity. We need a citation by Sen to prove that he was directing his critisism towards Pareto efficiency and that his ideas have not been extrapolated by others here.

I have serious doubts about the pie example as well or the need to invoke magic falling pies produced by no-one. MaxEnt 08:14, 18 July 2006 (UTC)
I don't consider the fact the pie falls out of the sky is a problem. Some real-life situations are very similar: Every year, Alaska gets a tax surplus which it must divide. That's a pie from the sky. They've been dividing it equally among residents, but obviously that's not the only way to divide. Technological advances that create new resources, such as new radio frequencies, are also similar. As an example, the "falling out of the sky" aspect of it is not a big problem to me.
My problem as to do with relating this pie example to Amartya Sen's work. I am (or rather, was) familiar with Sen's Paretian liberal paradox, but I have some difficulty relating that paradox to the pie ending up divided among 2 of the 3 players. Maybe some explanations would help. Haonhien 01:17, 20 September 2006 (UTC)

I don't understand the purpose of the criticism section at all. It seems to do little more than point out that there is inequity in the world, and contributes little to the article. It reads more like a political statement than an attempt to add to the understanding of Pareto optimality. Maybe this section should be rewritten in a more neutral, abstract manner using strictly mathematical examples to show that there are multiple Pareto optimal solutions, not all of which are "fair". If there are no objections, I'll start putting together some examples.

192.165.213.18 21:53, 26 March 2007 (UTC)

[edit] Incorrect affirmation

I removed this affirmation:

Also, the attainment of efficiency requires the presence of perfect competition, and is therefore a theoretical goal, not ever likely to be reached in reality.

as I think it is incorrect. In principle, a social planner could set up a system whitch is Pareto efficient. Please discuss before reintroducing AdamSmithee 18:18, 13 May 2006 (UTC) Bold text

I concur. Lack of perfect competition does not affect Pareto optimality. Transaction costs are another matter. Haonhien 01:19, 20 September 2006 (UTC)


[edit] probably daft question:

is there a typo somewhere in the following? : "If an economic system is Pareto efficient, then it is the case that no individual can be made better off without another being made worse off. It is commonly accepted that outcomes that are not Pareto efficient are to be avoided, and therefore Pareto efficiency is an important criterion for evaluating economic systems and political policies"

or is it a problem in my logic that an outcome in which everyone is made better off is "to be avoided"?

A situation in which everyone could be made better off should be avoided, yes -- rather than holding out on everyone, you should go ahead do whatever needs to be done to make them better off.
Would you want your boss to say that he could give you a raise but isn't going to (in order to prolong the situation of being able to give you a raise), or would you want him to give you the raise and then tell you that you can't have another one? Sanguinity 20:15, 13 November 2006 (UTC)

[edit] Metric Spaces

How do metric spaces play out in the definition of the Pareto set? What is the measure on R^n, and where does it come into effect in defining P(Y)? Sanguinity 20:23, 13 November 2006 (UTC)

In using Pareto sets in engineering, you have some set of inputs, X, that characterize your system (say a rocket or an engine -the set of inputs may be very large). You further have some function with input X and output Y (e.g. different performance characteristics). In order to have one solution dominate another, the criterion vector (output) needs to be a metric space so you can compare them. In the engineering case, the inputs need to be a metric space so you can characterize the differences between solutions. It may be the case that in decision sciences and economics that this criterion may be relaxed such that only Y needs to be a metric space, but I'm not sure if that's the case, and I wasn't able to find any answers in my 20 minute search through papers. If anyone particularly knowledgeable about this comes across this article, please chime in. Similarly, I'm wondering if this article should be broken up into two articles in the future, one that describes the mathematical concept of Pareto efficiency, and another that goes on to the ramifications in economics (and possibly a third into engineering, if we ever get enough written about it... there are a couple commercial and academic software packages that are used quite a bit to find and display Pareto frontiers) Halcyonhazard 18:43, 3 February 2007 (UTC)

[edit] not Pareto efficient

Could you describe a situation that is not Pareto efficient? Surely if you reallocate resources somebody will allways be made worse off. I am just a beginner at economics can somebody put me right?

You are tight if all goods have positive value to all consumers, and all goods are consumed. A simple example of a non-Pareto efficient situation would be one where I want a piece of food, but I just leave it there to rot. It would be better for me to eat it, while no one is made worse off, since no one else was going to eat it. Hopefully that helps. Smmurphy(Talk) 17:52, 25 May 2007 (UTC)

[edit] As a solution concept in GT

Would it be useful to put in an equilibrium solution concept infobox into this article? I'm not sure what would go in some of the fields, and maybe it isn't helpful. {{infobox equilibrium| name= Pareto efficient (Pareto optimum) outcome| subsetof = List of equilibrium concepts that this equilibrium concept is a subset of| supersetof = Nash equilibrium| intersectwith = List of equilibrium concepts that overlap with this one, but that are neither subsets nor supersets| independentof = List of equilibrium concepts that do not overlap with this one| discoverer = The person who first defined the equilibrium concept| usedfor = If the concept is used for particular purposes, list them here| example = A game that provides an interesting example}} Smmurphy(Talk) 17:45, 18 March 2007 (UTC)

[edit] New section: Pareto efficiency: a formal representation

The new article section Pareto efficiency#Pareto efficiency: a formal representation now has 2 subsections with the same names as before from the preceding Edit: Pareto efficiency#Pareto frontier & Pareto efficiency#Relationship to marginal rate of substitution. There is a gain in continuity for grouping the 2 together in formal representation & subject matter. There is also continuity in what comes before them, since earlier sections to do not mention or rely on the new subsections or use a mathematical representation. Those with the necessary math or econ background to follow these 2 sections should not be deterred by such placement. But if they are, there is no reason to make them "eat their spinach." Those without such background are less likely to to be deterred from reading the other sections. The subsections still need to be edited for clarity and context. --Thomasmeeks 21:36, 23 September 2007 (UTC)

[edit] weak and Strong Pareto Optimal

I've rephrased the WPO and SPO in the intro,as they (IMHO) were misleading. It seemed to indicate 2 other forms forms of Pareto Optimality, other that restating one and introducing the weaker form. I took as reference Equilibrium: Theory and Applications By Bryan Ellickson.

Please correct if need be.

Pbrandao 20:55, 1 October 2007 (UTC)

Weak and strong got mixed up, because the source uses the terms "strongly Pareto dominated" and "weakly Pareto dominated". A Pareto optimum is strong, because it is not weakly dominated by any other allocation, whereas a weak Pareto optimum is not strongly dominated by any other allocation. I fixed it anyway. Geometry guy 14:35, 27 October 2007 (UTC)

Right now, it doesn't make sense to me. It says: Strong Pareto Optimum is "a movement from one allocation to another that can make at least one individual better off" and a "Weak Pareto Optimum (WPO) satisfies a less stringent requirement, in which a new allocation is only considered to be a Pareto improvement if it is strictly preferred by all individuals". Surely being strictly preferred by all individuals is a more stringent outcome than being strictly preferred by one individual? Or am I misunderstanding what strictly preferred means? I like this explanation "Pareto efficiency means that no one can be made better off without someone becoming worse off". This is strong pareto efficiency presumably? --Billtubbs 22:38, 1 November 2007 (UTC)

I agree that right now it does not make any sense. I think the weak and strong designations are mixed up. 14 November 2007


This article may be too technical for a general audience.
Please help improve this article by providing more context and better explanations of technical details to make it more accessible, without removing technical details.
Distinction between weak and strong too abstract for the lay reader. 69.140.152.55 (talk) 09:39, 22 March 2008 (UTC)

No, I'm confused too. It isn't logical that SPO is a subset of WPO if everyone must strictly prefer the outcome for it to be a WPO and people only have to weakly prefer it for it to be a SPO. If this is the case, an SPO is not a WPO (if something must be strictly preferred then it can't be weakly preferred), but a WPO could be an SPO. Perhaps I'm also misunderstanding what "strictly preferred" means (maybe economists are redefining math terms?). This last comment that the "distinction between weak and strong [is] too abstract for the lay reader" is a bit condescending considering the comments in this section. Surely it's not too abstract. It just looks like someone has gotten things switched around in their definitions. —Preceding unsigned comment added by 216.189.162.121 (talk) 07:22, 8 April 2008 (UTC)

The confusion here seems to stem from the difference between a Pareto improvement and a Pareto optimum; a Pareto optimum is a situation in which no further Pareto improvements can be made. However, to qualify as a WPO situation, a new allocation need only be considered a Pareto improvement if it benefits all individuals. In an SPO situation, a new allocation can be considered a Pareto improvement if it benefits all involved or if it benefits at least one individual involved and does not make any individual involved worse off. If there is a possible new allocation strictly preferred by all individuals, the allocation is not Pareto optimal at all; if there is a possible new allocation strictly preferred by at least one and weakly preferred by the rest, the allocation is weak Pareto optimal but not strong Pareto optimal; and if there are no possible new allocations strictly preferred by at least one and weakly preferred by the rest, the situation is strong Pareto optimal and weak Pareto optimal (since there cannot be any new allocations that are strongly preferred by all individuals).
206.180.156.197 (talk) 21:50, 16 May 2008 (UTC)

[edit] "Formal representation" section: templates for clean-up & references added

Why?

  1. There are no page-specific references (or references of any kind) cited for this section.
  2. The exposition of the first subsection is opaque & does not correspond to that in the References for the article. There is no verbal translation of the math notation employed.
  3. The figure is non-standard in presenting (without comment) Pareto effic. as a minimization rather than maximization condition. --Thomasmeeks 14:58, 14 November 2007 (UTC)
Though I'm not an expert in this particular area, I think the choice is quite reasonable in view of mathematics generally and optimization problems in particular. --Ezrakilty 23:46, 30 March 2008 (UTC)

I did some work to clarify the math of the first sub-section, on the Pareto frontier. More could be done. --Ezrakilty 23:46, 30 March 2008 (UTC)

[edit] Question

I removed this question from Daspranab from the original article, since it belonged here on the talk page instead: "Does Pareto Optimality presumes watertight compartmentalization among individuals? Else, SPO and WPO would not mean the same thing?" Halcyonhazard (talk) 15:40, 21 February 2008 (UTC)

[edit] Criticism cleanup

The criticism section is awful. I've seen several complaints about this section in the above discussion, so I'm just gonna go ahead and delete the worst of it.

Let's go through it one by one:

Pareto efficiency does not require an equitable distribution of wealth. An economy in which the wealthy hold the vast majority of resources can be Pareto efficient. This possibility is inherent in the definition of Pareto efficiency; by requiring that an allocation leave no participant worse off, Pareto efficiency tends to favor outcomes that do not depart radically from the status quo. It is also argued that Pareto efficiency does not always result in the socially optimal, in terms of efficiency and equity, distribution of resources; thus, necessitating redistribution programs.[1]

Pareto efficiency refers to markets. In a communist utopia, a Pareto efficiency won't exist (well, it will, but that won't concern the communist New Class). This isn't a criticism of Pareto efficiency, this is a criticism of capitalism. It doesn't belong here. (I'd actually contend that a lack of Pareto efficiency is nearly chief among the deficiencies of communism, but I digress.)

Nobel prize winning economist Amartya Sen has elaborated the mathematical basis for this criticism, pointing out that under relatively plausible starting conditions, systems of social choice will converge to Pareto efficient, but inequitable, distributions.[2] A simple example is the distribution of a pie among three people who each want as much of the pie as they can get. The most equitable distribution would assign one third to each person. However the assignment of, say, a half section to each of two individuals and none to the third is also Pareto optimal despite not being equitable, because none of the recipients is left worse off than before (when none had pie); there are many other such distributions (any where the entire pie is distributed). An example of a Pareto inefficient distribution of the pie would be allocation of a quarter of the pie to each of the three, with the remainder discarded, as welfare can be increased without reducing the welfare of any individual (e.g. just give the quarter pie to someone). The origin of the pie is conceived as immaterial in these examples, i.e. the pie was "free." In such cases, in which a "windfall" that none of the potential distributees actually produced is to be allocated (e.g., land, inherited wealth, a portion of the broadcast spectrum, or some other resource), the criterion of Pareto efficiency does not determine a unique optimal allocation.

This "free" pie thing is incredibly contrived—land doesn't come from nowhere, inherited wealth is doled out according to the wishes of the deceased, and broadcast spectrums are typically auctioned off to the highest bidder by the FCC or similar agency (basically, who can best capitalize it is willing to pay the most for it). There's not a single a real-world example I can immediately think of that can fit this, and it's simply to awkward to be a serious criticism. For some unlikely edge case Pareto efficiency doesn't apply? Please.

This second paragraph might belong somewhere else, but it's not really criticism of Pareto efficiency, but, like the first example, a case where Pareto efficiency isn't the best option. You wouldn't criticize a car because it can't drive underwater, why would you criticize Pareto efficiency for something it was never intended to solve?

The third paragraph I'm leaving, despite that it appears to be original research. While the issue of local maxima may be small or negligible here, this is potentially the first legitimate criticism in this section.

The last paragraph may be the worst of all:

Despite its drawbacks (or perhaps precisely because of these drawbacks),

This is just bad writing.

Pareto-efficient improvements to real-world economic systems are extremely rare, and considered "the holy grail" of economic improvements.

This is absurd—Pareto-efficient improvements are the basis of entrepreneurism, and incredibly common. Someone creates a new product, or more efficiently produces an existing product. This creates a boom of wealth for everyone: entrepreneurs gain a large amount of wealth in the form of money, while customers collectively gain a large amount of wealth in product. This happens every single day.

They can be thought of as "free money" in some sense- someone's lot is improved without taking anything from anyone else.

No, it can't be—there's no such thing as a free lunch. Pareto efficiency improvements happen when individuals work hard and that effort pays off for them and society. The economy isn't a zero-sum game, and regularly expands and contracts. None of this is free though, it's earned.

One of the other benefits of such improvements is that they do not require the social planner to define a "social welfare function," a (necessarily arbitrary) weighting system which reflects the priorities given to the welfare of each individual in society.

This is irrelevent even if the rest of the paragraph weren't being deleted.

If you feel you can clean these up enough to be re-included, be my guest. For now, they're just gonna have to sit it out in Wikipedia's history.--71.234.44.178 (talk) 05:34, 11 May 2008 (UTC)

I want to second your editing of this section and agree wholeheartedly with your arguments. I had considered performing a similar edit, but because I'm not as trained in the softer side of econ and politics (my research is in computer science and have done work with game theory and mechanism design in resource allocation), I just wasn't sure if these views were held in certain political science or econ circles. Halcyonhazard (talk) 04:08, 12 May 2008 (UTC)
Although I disagree with some of your (71.234.44.178) criticisms (the pie metaphor was a useful way to visualize the concept), I agree that the section was problematic and you may have been right to remove it. After all, "Pareto efficiency" is just a formal criterion one can use to evaluate a situation, and not really a normative ideal (or so I think; I'm not an economist), so a section of social "Criticisms" seemed out of place. Indeed, the section was too narrowly focused on one interpretation or use of Pareto efficiency in economics, and ignored other possible uses, such as in game theory. Ezrakilty (talk) 19:43, 12 May 2008 (UTC)