Jews and Nazis: a version of dust specks vs torture

This is based on a dis­cus­sion in #less­wrong a few months back, and I am not sure how to re­solve it.

Setup: sup­pose the world is pop­u­lated by two groups of peo­ple, one just wants to be left alone (la­beled Jews), the other group hates the first one with pas­sion and want them dead (la­beled Nazis). The sec­ond group is oth­er­wise just as “good” as the first one (loves their rel­a­tives, their coun­try and is known to be in gen­eral quite ra­tio­nal). They just can’t help but hate the other guys (this con­di­tion is to fore­stall the ob­jec­tions like “Nazis ought to change their ter­mi­nal val­ues”). Maybe the shape of Jewish noses just creeps the hell out of them, or some­thing. Let’s just as­sume, for the sake of ar­gu­ment, that there is no chang­ing that ha­tred.

Is it ra­tio­nal to ex­ter­mi­nate the Jews to im­prove the Nazi’s qual­ity of life? Well, this seems like a silly ques­tion. Of course not! Now, what if there are many more Nazis than Jews? Is there a num­ber large enough where ex­ter­mi­nat­ing Jews would be a net pos­i­tive util­ity for the world? Umm… Not sure… I’d like to think that prob­a­bly not, hu­man life is sa­cred! What if some day their so­ciety in­vents im­mor­tal­ity, then ev­ery death is like an ex­tremely large (in­finite?) nega­tive util­ity!

Fine then, not ex­ter­mi­nat­ing. Just send them all to con­cen­tra­tion camps, where they will suffer in mis­ery and prob­a­bly have a shorter lifes­pan than they would oth­er­wise. This is not an ideal solu­tions from the Nazi point of view, but it makes them feel a lit­tle bit bet­ter. And now the util­ities are un­ques­tion­ably com­pa­rable, so if there are billions of Nazis and only a hand­ful of Jews, the over­all suffer­ing de­creases when the Jews are sent to the camps.

This logic is com­pletely analo­gous to that in the dust specks vs tor­ture dis­cus­sions, only my “lit­tle XML la­bels”, to quote Eliezer, make it more emo­tion­ally charged. Thus, if you are a util­i­tar­ian anti-specker, you ought to de­cide that, bar­ring chang­ing Nazi’s ter­mi­nal value of hat­ing Jews, the ra­tio­nal be­hav­ior is to herd the Jews into con­cen­tra­tion camps, or pos­si­bly even ex­ter­mi­nate them, pro­vided there are enough Nazi’s in the world who benefit from it.

This is quite a re­pug­nant con­clu­sion, and I don’t see a way of fix­ing it the way the origi­nal one is fixed (to para­phrase Eliezer, “only lives worth cel­e­brat­ing are worth cre­at­ing”).

EDIT: Thanks to CronoDAS for point­ing out that this is known as the 1000 Sadists prob­lem. Once I had this term, I found that luke­prog has men­tioned it on his old blog.