A Reasonable Approximation

Pareto improvements are rarer than they seem

this is surely not an original insight, but I haven't seen it before

A Pareto improvement is where you make one party better off and no parties worse off.

Suppose Adam has a rare baseball card. He assigns no intrinsic value to baseball cards. Adam likes Beth, and somewhat values her happiness. Beth collects baseball cards, and would happily pay $100 for Adam's card.

If Adam just gives Beth his baseball card, is that a Pareto improvement? Naively, yes: he loses the card that he doesn't care about, and gains her happiness; she gains the card. Both are better off.

But I claim not, because if Adam has the card, he can sell it to Beth for $100. He would much prefer doing that over just giving her the card. But if Beth has the card, he can't do that. He assigns no intrinsic value to the card, but he can still value it as a trading chip.

Now suppose Adam has the baseball card but Beth also has a copy of that card. Then Beth has less desire for Adam's card, so this situation also isn't a Pareto improvement over the original. By giving something to Beth, we've made Adam's situation worse, even though Adam likes Beth and values her happiness.

And I think situations like this are common. The ability to give someone something they want, is a form of power; and power is instrumentally useful. And the less someone wants, the less able you are to give them something they want¹.

For a closer-to-reality example, the reddit comment that sparked this post said:

bringing Platform 3 back into use at Liverpool Street Underground Station was denied because the platform would not be accessible. Neither of the platforms currently in use for that line is accessible, so allowing Platform 3 to be used would be a Pareto improvement

The model here is that there are two parties, people who can access the platforms at Liverpool St and those who can't. If Platform 3 is brought back into use, the first group gains something and the second group loses nothing.

But I think that if Platform 3 is brought back into use, the second group loses some power. They lose the power to say "we'll let you bring back Platform 3 if you give us…". Maybe Platform 3 can be made accessible for $1 million. Then they can say "we'll let you bring it back if you make it accessible", but they can't do that if it's already back in use.

And they lose some power to say "if you ignore us, we'll make things difficult for you". Maybe it would take \$1 trillion to make Platform 3 accessible. If Platform 3 remains out of use, people are more likely to spend \$1 million to make their building projects accessible, because they've seen what happens if they don't. Conversely, if Platform 3 comes back, people are more likely to exaggerate future costs of accessibility. "If I say it costs \$1 million, I'll have to pay. If I say it costs \$10 million, maybe I won't."

I haven't researched the situation in question, and I expect that the actual power dynamics in play don't look quite like that. But I think the point stands.

(My original reply said: "If it's easier to turn an unused inaccessible platform into a used accessible platform, than to turn a used inaccessible platform into a used accessible platform - I don't know if that's the case, but it sounds plausible - then opening the platform isn't a Pareto improvement." That still seems true to me, but it's not what I'm talking about here. There are lots of reasons why something might not be a Pareto improvement.)

This doesn't mean Pareto improvements don't exist. But I think a lot of things that look like them are not.

Update 2018-02-02: some good comments on reddit and LessWrong. Following those, I have two things in particular to add.

First, that I like /u/AntiTwister's summary: "If you have the power to prevent another party from gaining utility, then you lose utility by giving up that power even if you are allies. There is opportunity cost in abstaining from using your power as a bargaining chip to increase your own utility."

Second, that there is a related (weaker) concept called Kaldor-Hicks efficiency. I think that a lot of the things that look-like-but-aren't Pareto improvements, are still Kaldor-Hicks improvements - meaning that the utility lost by the losing parties is still less than the utility gained by the winners. In theory, that means that the winners could compensate the losers by giving them some money, to reach a Pareto improvement over the original state. But various political and practical issues can (and often do) get in the way of that.

Posted on 27 January 2018

Tagged: game theory; economics