# I Want to Review FDT; Are my Criticisms Legitimate?

I’m go­ing to write a re­view of func­tional de­ci­sion the­ory, I’ll use the two pa­pers.
It’s go­ing to be around as long as the pa­pers them­selves, cou­pled with school work, I’m not sure when I’ll finish writ­ing.
Be­fore I start it, I want to be sure my crit­i­cisms are le­gi­t­i­mate; is any­one will­ing to go over my crit­i­cisms with me?

My main points of crit­i­cism are:
Func­tional de­ci­sion the­ory is ac­tu­ally al­gorith­mic de­ci­sion the­ory. It has an al­gorith­mic view of de­ci­sion the­o­ries. It re­lies on al­gorith­mic equiv­alence and not func­tional equiv­alence.
Quick sort, merge sort, heap sort, in­ser­tion sort, se­lec­tion sort, bub­ble sort, etc are mu­tu­ally al­gorith­mi­cally dis­similar, but are all func­tion­ally equiv­a­lent.

If two de­ci­sion al­gorithms are func­tion­ally equiv­a­lent, but al­gorith­mi­cally dis­similar, you’d want a de­ci­sion the­ory that recog­nises this.

Causal de­pen­dence is a sub­set of al­gorith­mic de­pen­dence which is a sub­set of func­tional de­pen­dence.

So, I spec­ify what an ac­tual func­tional de­ci­sion the­ory would look like.

I then go on to show that even func­tional de­pen­dence is “im­pov­er­ished”.

Imag­ine a greedy al­gorithm that gets 95% of prob­lems cor­rect.

Let’s call this greedy al­gorithm f’.
Let’s call a cor­rect al­gorithm f.

f and f’ are func­tion­ally cor­re­lated, but not func­tion­ally equiv­a­lent.

FDT does not recog­nise this.

If f is your de­ci­sion al­gorithm, and f’ is your pre­dic­tor’s de­ci­sion al­gorithm, then FDT doesn’t recom­mend one box­ing on New­comb’s prob­lem.

EDT can deal with func­tional cor­re­la­tions.

EDT doesn’t dis­t­in­guish func­tional cor­re­la­tions from spu­ri­ous cor­re­la­tions, while FDT doesn’t recog­nise func­tional cor­re­la­tions.

I use this to spec­ify EFDT (ev­i­den­tial func­tional de­ci­sion the­ory), which con­sid­ers P(f(π) = f’(π)) in­stead of P(f = f’).

I spec­ify the re­quire­ments for a full Im­ple­men­ta­tion of FDT and EFDT.

I’ll pub­lish the first draft of the pa­per here af­ter I’m done.

The pa­per would be long, be­cause I spec­ify a frame­work for eval­u­at­ing de­ci­sion the­o­ries in the pa­per.

Us­ing this frame­work I show that EFDT > FDT > ADT > CDT.
I also show that EFDT > EDT.
This frame­work is ba­si­cally a hi­er­ar­chy of de­ci­sion the­o­ries.

A > B means that the set of prob­lems that B cor­rectly de­cides is a sub­set of the set of prob­lems that A cor­rectly de­cides.

The de­pen­dence hi­er­ar­chy is why CDT < ADT < FDT.

EFDT > FDT be­cause EFDT can recog­nise func­tional cor­re­la­tions.

EFDT > EDT be­cause EFDT can dis­t­in­guish func­tional cor­re­la­tions from spu­ri­ous cor­re­la­tions.

I plan to write the pa­per as best as I can, and if I think it’s good enough, I’ll try sub­mit­ting it.

• You could also sim­ply con­tinue work­ing on the re­view: you are clearly mo­ti­vated to ex­plore these is­sues deeper so why not start flesh­ing out the pa­per?

Note that I said “con­tinue” rather than start. The bar­rier is of­ten not the ideas them­selves but get­ting it writ­ten in some­thing ap­proach­ing a com­plete pa­per. this is still the is­sue for me and I have 50+ peer re­viewed pa­pers in the past 20 years (al­though not in this field).

• I will then.

• I sug­gest you check with Nate what ex­actly he thinks, but my opinion is:

If two de­ci­sion al­gorithms are func­tion­ally equiv­a­lent, but al­gorith­mi­cally dis­similar, you’d want a de­ci­sion the­ory that recog­nises this.

I think Nate agrees with this, and any lack of func­tional equiv­alence is due to not be­ing able to fully spec­ify that yet.

f and f’ are func­tion­ally cor­re­lated, but not func­tion­ally equiv­a­lent. FDT does not recog­nise this.

Can’t this be mod­el­led as un­cer­tainty over func­tional equiv­alence? (or over in­put-out­put maps)?

• Can’t this be mod­el­led as un­cer­tainty over func­tional equiv­alence? (or over in­put-out­put maps)?

Hm, that’s an in­ter­est­ing point. Is what we care about just the brute in­put-out­put map? If we’re faced with a black-box pre­dic­tor, then yes, all that mat­ters is the cor­re­la­tion even if we don’t know the method. But I don’t think any sort of rep­re­sen­ta­tion of com­pu­ta­tions as in­put-out­put maps ac­tu­ally helps ac­count for how we should learn about or pre­dict this cor­re­la­tion—we learn and pre­dict the pre­dic­tor in a way that seems like up­dat­ing a dis­tri­bu­tion over com­pu­ta­tions. Nor does it seem to help in the case of try­ing to un­der­stand to what ex­tend two agents are log­i­cally de­pen­dent on one an­other. So I think the com­pu­ta­tional rep­re­sen­ta­tion is go­ing to be more fruit­ful.