Home > Uncategorized > Problems with Pareto optimality

Problems with Pareto optimality

from Gary Flomenhoft, “The triumph of Pareto”, real-world economics review, issue no. 80, 26 June 2017, pp. 14-31.

There are several serious problems with the use of Pareto Optimality as the central goal of economics. One of the primary implications of “Pareto Optimality” is that it accepts the current distribution of wealth as a given. If any income distribution can lead to an “optimal” outcome, there is no need to be concerned about just distribution. Mainstream economists generally make no distinction between earned or unearned income, and when they do, it is typically to recommend lower taxes on the latter, a policy that has been adopted in the USA. Mainstream economists rarely question the legitimacy of the source of wealth. Fairness or origin of the current distribution is a problem left to politicians and society. It is not considered a legitimate question for economics. As Steven Hackett points out, “Slavery was widely seen in the North as being unethical from a deontological perspective, but a policy alternative of ending slavery would make slave owners worse off than under the status quo, and thus would have failed the Pareto efficiency criterion” (Hackett, 2001: 26).  

While Pareto developed his theory of Optimality, he also described the idea of “indifference curves” in conjunction with Edgeworth, which captures each person’s preferences for different combinations of various goods.  It established the idea of ordinal rather than cardinal welfare, and eliminated comparisons of utility between people. According to Pareto and current neo-classical orthodoxy, each person can only decide how well off they are “in their own estimation”. This avoids any consideration of justice in the current social conditions. In the words of Daly, “The extreme individualism of economics insists that people are so qualitatively different in their hermetical isolation one from another that it makes no sense to say that a leg amputation hurts Smith more than a pin prick hurts Jones” (Daly and Farley, 2010: 306).

Economics was originally based on classical utilitarianism, which followed the philosophy of “the greatest good for the greatest number”, and thus was very concerned with issues of distribution. Maximizing the total utility of society was the goal, and it was well understood that extra income provided more utility for a poor person than for a rich one.

Following Pareto, this was abandoned in favor of ordinal measures of welfare. Interpersonal comparisons of utility are still generally considered outside the bounds of neo-classical welfare economics.

Utility curves of an individual assume diminishing marginal utility: the more of something a person has, the less utility an additional unit provides. Figure 1 below depicts the difference in utility from receiving $100 for a person with $1000 compared to the same person with $0. Is it really so far-fetched to believe that two human beings might have similar utility curves, especially when satisfying basic physiological needs? If this curve represented two people, rather than one person at different times, then the wealthier person obviously gets less utility from $100 than the poorer person. Economists can only accept Pareto efficiency as a central goal of economics by largely rejecting the notion of diminishing marginal utility.

Therefore Pareto Optimality is self-contradictory. 

Figure 1 Interpersonal comparison of Utility

 

 Source: http://mrski-apecon-2008.wikispaces.com/Sun%27s+Page.

One of the primary implications of Pareto optimality is that economists cannot pass judgment on the desirability of different distributions of wealth and income. “Potential Pareto optimality” relaxes this criterion by declaring one option superior to another if the winners could potentially compensate the losers through transfer payments, even if no compensation actually takes place (Kaldor-Hicks criteria). Actual compensation is left to society to take care of and is out of the realm of economics.

Economists’ obsession with Pareto optimality has led them to virtually ignore the welfare implications of upward and downward redistribution. If redistribution of the pie is considered off-limits, then the only option left for improving welfare is a bigger pie, typically measured by higher GDP. Also, since the measure of welfare is entirely subjective, how could one determine who feels better or worse? It’s much safer to assume that a rising tide lifts all boats, and don’t worry about the people with no boats. It is universally believed that we can grow our way out of poverty. Does reality support the myth? Prior to 1967 the poverty rate appeared to decline as GDP increased. However, as shown in Figure 2, since 1968 there has been no relationship between long term GDP growth and poverty alleviation as is commonly believed.

 Figure 2 Poverty rate vs GDP

Source: Author from US Census Bureau data, 2014.

 Even if growth did contribute to poverty alleviation it is questionable if it is a viable option any longer due to the limits of planetary growth. It would require an estimated 4.5 planets to extend current levels of US consumption of resources and emission of pollutants to all 7 billion people on the earth (Ewing et al., 2010).

  1. originalsandwichman
    July 31, 2017 at 7:51 pm

    I like “the road to Hell is paved with Pareto improvements…”

    http://econospeak.blogspot.ca/2016/04/is-road-to-hell-paved-with-pareto.html

  2. August 1, 2017 at 1:34 am

    “According to Pareto…each person can only decide how well off they are ‘in their own estimation’.”

    There are two major problems with this assumption: 1) rich people tend to suffer a great deal from Money Illusion, and 2) their rationalizations of their shared situation are typically flawed by one or more fallacies of composition.

    They fantasize about what they might do with another big tax-cut windfall, while failing to realize that when ALL rich people get the same money gift, it deprives ALL of them of the big increase in purchasing power they’d otherwise experience if only they, themselves, alone had received the gift.

    But because all of them are receiving the same gift, none of them experiences an improvement in hiser ranking within the hierarchy of all disposable incomes RELATIVE TO EACH OTHER. Because this is true, and because we have a market economy which auctions all scarce desirables to the highest bidders, all those extra dollars inevitably get burned up in an economically meaningless inflation event.

    The ultimate truth is that even steeply progressive marginal income tax rates would not impose any material sacrifice or any loss of purchasing power whatsoever on the Upper Class. They would still end up with the highest disposable incomes in the land, and in a market economy, that’s all you need to claim the scarcest luxuries and assets that the economy brings to market.

    The assumptions upon which Pareto’s rationalizations were based are so flawed, they really should be retired to the dustbin of history.

  3. C-R D
    August 1, 2017 at 4:53 pm

    Pareto wanted to counteract the criticisms addressed to Walras’ attempt to measure individual satisfaction by putting satisfaction or utility (U) in ordinal space. Then how does one measure delta U when mathematical operations are not defined in ordinal spaces?
    I think that until we reject the notion of utility,all derived economic conclusions will appear convoluted.

    • August 1, 2017 at 5:52 pm

      Re: your last line. Yes and absolutely!

      I refer more technically minded readers to Jonathan Barzilai brilliant essay entitled “On Ordinal, Cardinal, and Expected Utility” http://scientificmetrics.com/downloads/publications/Barzilai_Ordinal_Cardinal_Expected_Utility.pdf See also: http://scientificmetrics.com/downloads/publications/Barzilai_RWER_June%202014.pdf His arguments refer to the mathematics.

      Mine do also, but basically for non-mathematical reasons: namely, the fact that ‘utility’ is undefined and thus is neither operational nor measurable. I emphasize the reality that material benefits from consumption, as distinct from satisfaction or dissatisfaction with what one is consuming, are empirical (i.e.,cardinal) measures; and, finally, that scalar values of non-material benefits like ‘satisfaction’ or ‘dissatisfaction’ should be associated with whether or not one has met basic needs in ways a person would like to. [I agree with Professor Barzilai completely that the normal operations of simple arithmetic, and those of the calculus, cannot be applied to the notion of subjective utility in currently mainstream economics.]

      More to the point, the very idea of Pareto optimality does not permit society to decide which income distributions within society provide for economic stability while also permitting the population within economies –not merely consumers with the ability to pay– to realize their material and other needs across the spectra of human needs: biological, psychological, and social.

  4. C-R D
    August 1, 2017 at 8:30 pm

    The Barzilai’s paper and more are taken up in microeconomics. Even non technically minded readers can see the problem with utility in the following two papers.

    https://mpra.ub.uni-muenchen.de/id/eprint/78716
    https://mpra.ub.uni-muenchen.de/id/eprint/80408

    • August 2, 2017 at 7:05 pm

      Thank you for these references to your work. I had not seen either. I find them to be quite technical, however, no doubt because I struggle with math.

      Now let me introduce a value–in-use for two goods x and y, a well-defined value-in-use that makes these goods equivalent as substitutes for each other when used to obtain this specific and cardinally measurable value-in-use, say an intake of calories, or proteins, or vitamins or minerals. Let an exigency level [Exy –namely a vital level of consumption — be, for instance, 80 units of protein daily. Let x provide 8 such units and y provide 16 such units. This means that there exists an Exigency Constraint of the form Exy – ax -by = 0 which, for proteins is 80 – 8x – 16y, from which we can derive y = 5 – .5x in Cartesian positive (xy) space. This Exy Constraint shows all of the baskets that are just sufficient to realize a person’s protein replenishment needs for maintaining health. That is, a person must be able to obtain at least one of these baskets if health is to be maintained. If the period for analysis is drawn out to a month or a year rather than merely a day, then clearly protein deficiencies lead to various deficiencies leading to diseases and possibly death. Thus, for one day it may not matter if an exigency level is realized; but, that said, the lengthier the period under analysis, the more essential realizing the Exigency constrain becomes.

      Given the nominal prices of x and y, we can now move into nominal budgetary space to create the range of budgets just needed that will permit a person to purchase any basket along the Exy constraint. If it should happen to be that the prices of x and y are equally $2.00, then every Exigency budget Bxy -pxx -pyy = 0 lies on the line from (0, $10.00) to ($20.00,0) defining the set of all combinations of x and y just sufficient to meet protein requirements. The defined range of budgetary minimums just sufficient to meet requirements lie on the line y = -1/2x + $10.00. Clearly, if either the nominal price of x or y, or the nominal prices of both, were to change, so also would this set of budgetary requirements for any basket just sufficient to meet needs.

      I add that, for any set of prices of x and y, y = px/py*y is the pure exchange, er, optimum for any single budget decided upon by the person. This is an ‘indifference’ optimum in the sense that if a person has no preferences between goods x and y, and also that no exigencies that must be met, then the exchange optimum requires that pxx = pyy in every basket (x,y) bought with any budget Bxy: which means that the same amounts be spent on x and y all of the time if only pure exchange occurs.

      Now, does how the budget is actually spent reflect preferences between x and y?

      I’ll leave you with that question, CR. My wife has just informed me that we’re going camping, and she must be obeyed. {I have no way to get back to you when off in the bush.}

      Ta, for now.

  5. August 2, 2017 at 12:56 am

    There is nothing wrong with pareto optimality as one criteria or metric (except it may not be the best one–nowadays people use entropy , j galbraith uses a form of that, and there are
    better ones in my view) ). Pareto himself had what i call quasi-fascist poltics, like mosca, spengler, etc.. Pareto optimaility says absolutely nothing about inequality.

    John Roemer of UC Davis and later Yale pointed this out—one can have a Pareto optimal economy with a Gini =1. or a pareto optimal economy with a Gini=0. . Thats a polticial decision. Even Krugman has mentioned that. (basically about why NAFTA sortuh failed.)

    One problem with pareto optimality from a practical view is it assumes GET–ie you can compute it and get there. ‘are we there yet?'(my typical question when i am on a car trip).

  6. August 2, 2017 at 7:16 am

    All good reasons to not just reject but end the use of Pareto’s little mythology. In energy and environmental modeling, we had a much simpler reason, however, the word optimal. We always replied to modelers using optimization models by saying, “Fart the wrong direction and the optimal is done.” Crude, right? But it always worked.

  7. Blissex
    August 2, 2017 at 12:40 pm

    The point that is being made with «“Pareto Optimality” is that it accepts the current distribution of wealth as a given.» can be summarize explicitly in a simple way:

    * Only changes to a state can be “Pareto optimal”.
    * A state cannot be called “Pareto optimal”.

    And this comes from the very definition of “Pareto optimality”.
    Not even a state that to which no “Pareto optimal” changes can be made can be called “Pareto optimal” because that simply does not make sense, as the very definition relates changes in A to changes in B.

  8. August 3, 2017 at 3:29 am

    All optimizations must begin with specific assumptions/desires/expectations and end by moving toward specific assumptions/desires/expectations. These are all the result of human judgments about what’s good and worth pursuing. Judgments that are based on many cultural assumptions, which economists, and in fact most social scientists never consider or question. This is all good so long as everyone knows other starting and ending points are available and just as worth pursing, even if we don’t agree with or like them. Neoliberal individual capitalism is the starting point Pareto chose. He could have chosen socialist community, Communist solidarity, or Fascist power maximization. He chose neoliberal individualism. Why?

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