One reason reason is that it seems like it might be helpful with friendliness proofs, particularly the part where you have to prove the AI's goal will remain stable over millions of self-modifications (the harder, and all too frequently ignored, side of the problem). Basically, it takes dilemma's which might otherwise tempt an AI to self-modify, and shows that it need not have to.
I think with CDT you can prove an AI won't need to modify its goal system on action-determined problem, while with TDT you can prove the same for the broader class of decision-determined problems. This leaves many issues, but its a step in the right direction.
Disclaimer: The above post should not be taken to speak for Eliezer Yudkowsky, SIAI, or anyone other than me. I am not in any way a member of SIAI or any other similar organization. There is a good chance that I am talking out of my arse.
to prove the AI's goal will remain stable over millions of self-modifications (the harder, and all too frequently ignored, side of the problem)
What's the easier side?
I don't know if this is a little too afar field for even a Discussion post, but people seemed to enjoy my previous articles (Girl Scouts financial filings, video game console insurance, philosophy of identity/abortion, & prediction market fees), so...
I recently wrote up an idea that has been bouncing around my head ever since I watched Death Note years ago - can we quantify Light Yagami's mistakes? Which mistake was the greatest? How could one do better? We can shed some light on the matter by examining DN with... basic information theory.
Presented for LessWrong's consideration: Death Note & Anonymity.