Loss aversion is not what you think it is

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• Phras­ing this in terms of util­ity func­tions is mis­lead­ing. I sug­gest think­ing in terms of a Schel­ling Point strat­egy, as David Fried­man de­scribes in his ac­count of why prop­erty rights ex­ist. Most util­ity func­tions will gen­er­ate strate­gies such as this un­der many con­di­tions.

• Could you ex­plain the ra­tio­nal jus­tifi­ca­tion for loss aver­sion ? (If pos­si­ble, write a top-level post on this.)

• As Pa­trick said, loss aver­sion is pre­sent on the scales small enough for the DMU to not mat­ter. Slightly more math­e­mat­i­cally, when, given the util­ity func­tion x->U(x), the gain vs loss util­ity ra­tio for the same change in the ar­gu­ment is small: Δx << U’(x)/​U”(x). It does not in­val­i­date the au­thor’s point though, that there ex­ists a phe­nomenon that is bet­ter de­scribed as the util­ity hys­tere­sis: one ends up with less util­ity af­ter gain­ing 2x and then los­ing x than af­ter just gain­ing x.

• The val­idity of the au­thor’s point seems to de­pend on what is the best way to in­ter­pret the phrase “losses hurt more than equiv­a­lent gains”. Two ways that you could in­ter­pret it in which it would be a con­se­quence of loss aver­sion but not of DMU:

• “Hav­ing your wealth de­crease from X to Y de­creases your satis­fac­tion more than hav­ing your wealth in­crease from Y to X in­creases it.”

• “The pain of a small loss is sig­nifi­cantly more than the plea­sure of a small gain.”

It seems to me that most of the quotes at the end, if you in­ter­pret them char­i­ta­bly, mean some­thing like the above. So the post seems like a nit­pick to me. It’s great to ex­plain the differ­ence be­tween loss aver­sion and DMU for peo­ple who don’t nec­es­sar­ily know about them, but it’s not clear to me that it means that the quoted peo­ple were ac­tu­ally wrong about some­thing.

I would also dis­agree with point #3, e.g. the last sen­tence of the Economist quote seems valid as an in­tu­itive ex­pla­na­tion of loss aver­sion but not of DMU.

• In short, the au­thor is wrong. Diminish­ing marginal util­ity only re­ally ap­plies when the stakes are on the or­der of the agent’s to­tal wealth, whereas the loss aver­sion asym­me­try holds true for rel­a­tively small sums.

• See e.g. a nice pa­per by Matthew Rabin which quan­tifies the ex­tent to which dimin­sh­ing marginal util­ity is too weak an effect to ex­plain ac­tu­ally-ob­served risk aver­sion, by prov­ing state­ments like this: “If you would turn down a 50:50 gam­ble be­tween gain­ing \$101 and los­ing \$100 on ac­count of diminish­ing marginal util­ity, then you would also turn down a 50:50 gam­ble be­tween gain­ing all the money in the world and los­ing \$10,000.”

• DMU is only ra­tio­nal when ap­plied to the larger sums. It’s pretty be­liev­able that much of what’s called loss aver­sion is a bro­ken heuris­tic in hu­man brains, which mis-im­ple­ments DMU by pick­ing way-too-small refer­ence classes. IMO, hy­per­bolic dis­count­ing is a re­lated evolved heuris­tic which con­flates value dis­count­ing and fu­ture un­cer­tainty.

• That makes a lot of sense to me. Aver­sion to small losses makes a ton of sense as a blan­ket rule, when the gam­ble is: lose: don’t eat to­day win: eat dou­ble to­day don’t play: eat today

Our an­ces­tors prob­a­bly faced this gam­ble since long be­fore hu­mans were even hu­mans. Un­der those sta­ble con­di­tions, a heuris­tic ac­count­ing for scale would have been need­lessly ex­pen­sive.

• I don’t think you read the au­thor right. He is not say­ing that loss aver­sion is ex­plained by diminish­ing marginal util­ity, he’s say­ing pre­cisely the con­trary.

• I mean...he quotes Kah­ne­man; claiming the guy doesn’t know the im­pli­ca­tions of his own the­ory.

Losses hurt more than gains even at scales where DMU pre­dicts that they should not. (be­cause your DMU curve is ap­prox­i­mately flat for small losses and gains) Loss aver­sion is the psy­cholog­i­cal re­sult which ex­plains this effect.

This is the au­thor’s con­clu­sion: “So, please, don’t go around claiming that be­hav­ioral economists are in­cor­po­rat­ing some brilli­ant newfound in­sight that peo­ple hate losses more than they like gains. We’ve known about this in price the­ory since Alfred Mar­shall’s 1890 Prin­ci­ples of Eco­nomics.”

Sorry nope. Alfred Marhall’s Prin­ci­ples would have made the wrong pre­dic­tion.

• I don’t think you read the au­thor at all. The whole post is about struc­tural qual­i­ta­tive differ­ences be­tween “peo­ple hate losses more than they like gains” (DMU) and loss aver­sion. He is not say­ing DMU ex­plain loss aver­sion. He is not say­ing Alfred Mar­shall’s Prin­ci­ples would have made the right pre­dic­tion. What he is say­ing is that loss aver­sion is much less in­tu­itive than the pop sci­ence ver­sion of loss aver­sion.

• I read him, he is just in­cor­rect. “Peo­ple hate losses more than they hate gains” is not ex­plained by DMU. They dis­like losses to an ex­tent far greater than pre­dicted by DMU, and more im­por­tantly, this dis­like is largely scale in­var­i­ant.

If you go read pa­pers like the origi­nal K&T, you’ll see that their data set is just a bunch of state­ments that are pre­dicted to be equally preferrable un­der DMU (be­cause marginal util­ity doesn’t change much for small changes in wealth). What changes the prefer­ence is sim­ply whether K&T phrase the ques­tion in terms of a loss or a gain.

So...un­sur­pris­ingly, Kah­ne­man is ac­cu­rately de­scribing the the­ory that won him the No­bel prize.

• The au­thor ex­plain very clearly what the differ­ences are be­tween “peo­ple hate losses more than they like gains” and loss aver­sion. Loss aver­sion is peo­ple hat­ing los­ing \$1 while hav­ing \$2 more than they like gain­ing \$1 while hav­ing \$1, even though it both case this the differ­ence be­tween hav­ing \$1 and \$2.