And following some links from there leads to this 2003 Eliezer posting to an AGI mailing list in which he explains the mirror opinion.
I can't say I completely understood the argument, but it seemed that the real reason EY deprecates AIXI is that he fears that it would defect in the PD, even when playing against a mirror image - because it wouldn't recognize the symmetry.
Probably the two most obvious problems with AIXI (apart from the uncomputability business) are that it:
Would be inclined to grab control of its own reward function - and make sure nobody got in the way of it doing that;
Doesn't know it has a brain or a body - and so might easily eat its own brains accidentally.
I discuss these problems in more detail in my essay on the topic. Teaching it that it has a brain may not be rocket science.
Link: physicsandcake.wordpress.com/2011/01/22/pavlovs-ai-what-did-it-mean/
Suzanne Gildert basically argues that any AGI that can considerably self-improve would simply alter its reward function directly. I'm not sure how she arrives at the conclusion that such an AGI would likely switch itself off. Even if an abstract general intelligence would tend to alter its reward function, wouldn't it do so indefinitely rather than switching itself off?
If it wants to maximize its reward by increasing a numerical value, why wouldn't it consume the universe doing so? Maybe she had something in mind along the lines of an argument by Katja Grace:
Link: meteuphoric.wordpress.com/2010/02/06/cheap-goals-not-explosive/
I am not sure if that argument would apply here. I suppose the AI might hit diminishing returns but could again alter its reward function to prevent that, though what would be the incentive for doing so?
ETA:
I left a comment over there:
ETA #2:
What else I wrote: