Friendship and happiness generation

Hap­piness and util­ity are differ­ent things, with hap­piness (mea­sured in he­dons) gen­er­ally refer­ring to the de­sir­a­bil­ity of an agent be­ing in its cur­rent men­tal state, while util­ity (mea­sured in utils) refers to the de­sir­a­bil­ity, from the point of view of some agent, of the con­figu­ra­tion of the uni­verse.

Naively, one could model car­ing about an­other per­son as hav­ing a por­tion of your util­ity func­tion al­lo­cated to mimick­ing their util­ity (me.util­ity(uni­verse) = car­ing_fac­tor*friend.util­ity(uni­verse) + me.util­ity(uni­verse ex­clud­ing value of friend’s util­ity func­tion)) or their hap­piness (me.util­ity(uni­verse) = car­ing_fac­tor*friend.hap­piness + me.util­ity(uni­verse ex­clud­ing friend’s hap­piness)). How­ever, I think these are bad mod­els of how car­ing for peo­ple ac­tu­ally works in hu­mans.

I’ve no­ticed that I of­ten gladly give up small amounts of he­dons so that some­one I care about can gain a similar amount of he­dons. Ex­trap­o­lat­ing this, one might con­clude that I care about plenty of other peo­ple nearly as much as I care about my­self. How­ever, I would be much less likely to give up a large amount of he­dons for some­one I care about un­less the ra­tio of he­dons that they could gain over the he­dons I would have to give up is also fairly large.

While try­ing to figure out why this is, I re­al­ized that when­ever I think I’m sac­ri­fic­ing he­dons for some­one, I usu­ally don’t ac­tu­ally lose any he­dons be­cause I en­joy the feel­ing as­so­ci­ated with know­ing that I helped a friend. I ex­pect that this re­ac­tion is fairly com­mon. This im­plies that by do­ing small fa­vors for each other, friends can gen­er­ate hap­piness for both of them even when the amount of he­dons sac­ri­ficed by one (not count­ing the friend-helping bonus) is similar to the amount of he­dons gained by the other. How­ever, this hap­piness bonus for helping a friend is bounded, and grows sub­lin­early with re­spect to the amount of good done to the friend. In terms of evolu­tion­ary psy­chol­ogy, this makes sense: seek­ing out cheap ways to sig­nal loy­alty sounds like a de­cent strat­egy for get­ting and keep­ing al­lies.

I don’t think that this tells the whole story. If a friend had enough at stake, I would sac­ri­fice much more for them than could be re­im­bursed with the hap­piness bonus for helping a friend (plus hap­piness penalty that I would oth­er­wise ab­sorb for the feel­ing of know­ing I had aban­doned a friend), be­cause I do ac­tu­ally care about peo­ple. Again, I would ex­pect that most other peo­ple would act this way as well. But it seems likely that most fa­vors that peo­ple do for each other are pri­mar­ily mo­ti­vated by pur­su­ing per­sonal hap­piness that they can get from know­ing that they’ve helped a friend, rather than di­rectly car­ing about how happy their friends are.