Two-boxing, smoking and chewing gum in Medical Newcomb problems

I am cur­rently learn­ing about the ba­sics of de­ci­sion the­ory, most of which is com­mon knowl­edge on LW. I have a ques­tion, re­lated to why EDT is said not to work.

Con­sider the fol­low­ing New­comblike prob­lem: A study shows that most peo­ple who two-box in New­comblike prob­lems as the fol­low­ing have a cer­tain gene (and one-box­ers don’t have the gene). Now, Omega could put you into some­thing like New­comb’s origi­nal prob­lem, but in­stead of hav­ing run a simu­la­tion of you, Omega has only looked at your DNA: If you don’t have the “two-box­ing gene”, Omega puts $1M into box B, oth­er­wise box B is empty. And there is $1K in box A, as usual. Would you one-box (take only box B) or two-box (take box A and B)? Here’s a causal di­a­gram for the prob­lem:



Since Omega does not do much other than trans­lat­ing your genes into money un­der a box, it does not seem to hurt to leave it out:


I pre­sume that most LWers would one-box. (And as I un­der­stand it, not only CDT but also TDT would two-box, am I wrong?)

Now, how does this prob­lem differ from the smok­ing le­sion or Yud­kowsky’s (2010, p.67) chew­ing gum prob­lem? Chew­ing Gum (or smok­ing) seems to be like tak­ing box A to get at least/​ad­di­tional $1K, the two-box­ing gene is like the CGTA gene, the ill­ness it­self (the ab­scess or lung can­cer) is like not hav­ing $1M in box B. Here’s an­other causal di­a­gram, this time for the chew­ing gum prob­lem:

As far as I can tell, the differ­ence be­tween the two prob­lems is some ad­di­tional, un­stated in­tu­ition in the clas­sic med­i­cal New­comb prob­lems. Maybe, the ad­di­tional as­sump­tion is that the ac­tual ev­i­dence lies in the “tickle”, or that know­ing and think­ing about the study re­sults causes some com­pli­ca­tions. In EDT terms: The in­tu­ition is that nei­ther smok­ing nor chew­ing gum gives the agent ad­di­tional in­for­ma­tion.