# What's the opposite of a Pareto improvement called?

Wikipedia defines a Pareto Improvement, "given a certain initial allocation of goods among a set of individuals" as:

a change to a different allocation that makes at least one individual or preference criterion better off without making any other individual or preference criterion worse off

Given this definition, then, the opposite of a Pareto Improvement should be:

a change to a different allocation that makes at least one individual or preference criterion worse off without making any other individual or preference criterion better off.

What's the correct way to refer to this? Does it have a name?

• Wouldn’t the opposite be a change that leads to a situation in which at least one individual is able to be made better off? Like a movement towards an allocation such that there exists a pareto-superior allocation. I dont think the opposite as you state would be meaningful as, with well-behaved preferences (monotonicity, strict quasi-concave utility function, etc.) any allocation other than the unique interior solution would satisfy this (so long as the budget constraint is binding) Nov 5 '19 at 5:11
• Why would the 2nd def (yours) be interesting? It seems to me you can obtain if from the first by changing the sign of the function.
– Fizz
Nov 5 '19 at 7:35
• @Brennan I understand your first point about the allocation s.t. ∃ a pareto-superior allocation. I think that's the same as what I'm saying. I don't understand your second point about well-behaved preferences so you'll need to explain (or link to something that does) that if you want me to respond. Nov 6 '19 at 19:03
• @Fizz It's interesting to me because I often want to use it in conversation. Saying e.g. "negative Pareto Improvement" doesn't seem to work well. Nov 6 '19 at 19:05

I usually use the phrase "Pareto worsening". It is not really widespread, in fact I am not sure I have ever heard anyone else use it. However now I googled it and people seem to use it in connection with Hart's 1975 paper wherein he shows that the opening of some new markets can make every agent worse off. Hart himself did not call this Pareto worsening, but other scholars do. An example is on page 230 of volume II of General Equilibrium, Growth, and Trade. Here is the same phrase used in Information and Securities: A Note on Pareto Dominance and the Second Best.

• This is basically what I was looking for. Thank you! Nov 6 '19 at 19:18

The strict logic opposite of course is simply any change where at least one person is worse off but not sure we need a name for that. The conceptual opposite to Pareto improvement can as you say be a change where no one is better off and at least one person is worse of.

Existing Antonyms to "improvement"

As for what to call it, the Thersaurus does indeed suggests the primary antonym of "improvement" is "worsening", which would justify "Pareto worsening" but to me it is an unsatisfying pairing.

Some less perfect antonyms that work for me would give us:

• Pareto impairment
• Pareto decrease

Or a range of other choices.

New coining from the etymology of "improvement"

If we look into the etymology, the "-prove" comes very satisfactorily from old french for "profit" and "im-" is an intensifier (though confusingly "en-", "em-", "in-" and "im-" prefixes have multiple and often contradictory meanings). From which, if I were to make a new coining, we could use:

• Pareto deprovement

I would choose "impairment"

I think on balance I would go with "improvement" and "impairment" because they are readily understandable and fit well together.

• Thanks for the thoughtful answer! Nov 6 '19 at 19:18

The negation would be "there does not exist at least one person that is better off, or, there exists someone that is worse off." That is the improper use of police power. Indeed, this could be a stylized definition of racism if you defined racism as the theft of life or property from one group to another based on the color of their skin or other social classification. The opposite of Pareto optimization would be something like institutionalized racism.

A person commented it did not answer the question. That isn't true, but I will expand on the discussion.

The negation of the definition of Pareto optimality is above. Either a reallocation has happened but no one is better off, or at least one person is worse off.

For the former to happen, there would have to be a use of police power. If everyone is indifferent then there is no reason for reallocation to happen. Although no one cares, it isn't rational for changes to happen as it is an equilibrium.

An example of this is where a bunch of people are sitting around a table and no one cares where they sit. The only way reallocation of chairs will happen is if someone with power says "okay, everyone shift right one chair, for no reason, just because I have the power to do make everyone do it."

The second case has at least one person worse off. No one would rationally make themselves worse off. That also requires police power.

The problem is that English lacks a good term for theft of goods through police power except in the case of racism.

Note that the definition of racism is not bigotry or prejudice. Bigotry is the strong personal aversion by a person against a group, possibly racial or ethnic but it could be on other dimensions such as religion or politics. Neurological studies of bigotry show that it processes in the area of emotion connected to smell, disgust and emotion and links the group to danger to food. That is bigotry.

Prejudice is simply the fast judgment of a person by observable characteristics and may not be related to race.

Racism is the theft of property or life from one group to another through the use of police power, whether formal as in Title One of the Housing Act of 1947 also known as the Negro Removal Act or informal as when the Klan was permitted to kill or seize property without governmental recourse by the victims. It is the use of police power through acquiesence.

The only requirement of the negation of the Pareto principle is indifference OR at least one person loses.

That could also describe crime as it says nothing about at least one person being worse off.

I don't agree with your negation. It does not follow from de Morgan's laws.

Finally, it could happen due to taxation and reallocation. Those would not be crimes either, moral or otherwise, but we lack a term for it. Libertarians view it as theft for this reason. Most people consider it morally neutral because there if there is no intent to specifically do harm to any group for the benefit of others.

I should point out that we usually lack words for things other than optimums and points of inflection. If you look at $$y=-x^2$$ there is an extreme value and we call it a maximum. We do not have a name for the other uncountably many points.

EDIT Based on your comment, where someone is worse off and no one is better off is called waste. However, for the reallocation to happen on purpose it would mandate irrationality to happen. I do not mean irrationality as a psychologist would mean it. For example, a schizophrenic may have psychotic preferences but they still act rationally on those preferences.

Let me give you an example. Let us assume that I hate you and you have apples that have rotted. You do not care because you can turn them into applesauce and you are indifferent between fresh apples and applesauce. I, on the other hand, hate applesauce.

I offer to trade your rotten apples, which you are indifferent for, for my good apple making me worse off. Although I am indifferent to trade a good apple for a good apple, I am not indifferent to getting a rotten apple.

So I would be acting in an individually irrational manner. There is no word for this but the term of art would be to act in an irrational manner.

• His "negation" indeed doesn't follow from de Morgan's laws. I don't understand what the 90%-part of your answer theorizing racism has to do with the question though.
– Fizz
Nov 6 '19 at 1:14
• @Fizz his question was on nomenclature. As a side effect of other work I have been doing the last couple of years, I have been noting areas where English lacks a way to discuss things with a word. It started when I needed to describe a statistical issue where statistical distributions lack a second moment. I discovered that macroeconomic and finance distributions lack a first moment. I settled on askedastic for distributions without a variance. Nov 6 '19 at 2:57
• @Fizz We have a word for racism and the system of transfers it creates, but not for things such as religious groups or other power groups. We can discuss taxation and resource reallocation but we cannot discuss it with a single word and a system as communism, capitalism and socialism is so broad that they are not really close. Nov 6 '19 at 2:59
• @Fizz and Dave Harris re: the point about de Morgan's laws: I intentionally picked the "reflection over the axis" interpretation of "opposite" rather than the set-theoretic negation because that's the sense I want to use in conversation-- where the possibility of no change is not included. If I wanted the strict set-theoretic complement I would have said that in the question. "Opposite" doesn't have to be interpreted in that way. Nov 6 '19 at 19:16