Pareto improvements are rarer than they seem

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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.

  1. This feels like it gen­er­al­izes far be­yond ques­tions of Pareto effi­ciency, but I’m not sure how to frame it. Some­thing like game the­ory is more com­pet­i­tive than it ap­pears. Even when no two play­ers value the same re­source, even when all play­ers gen­uinely want all other play­ers to do well, play­ers still have an in­cen­tive to sab­o­tage each other.

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