No subject

enough details of proofs so that he/she
can judge on that basis alone, whether it is likely that the proofs 
in the paper are correct. 
In this situation it is helpful for the referee if he/she can also take
into account how carefully that particular author tends to check
his/her math. proofs (of course, if they don't know the author, they 
should give the benefit of the doubt).
It is a fact of life, that different authors tend to check their proofs
with quite different amounts of care.

Unfortunately it is NECESSARY for a referee to make a guess about 
the correctness of proofs in a theory paper. On the basis of 
the statements of the theorems and their consequences alone,
incorrect theoretical paper often appear to be more exciting 
(and therefore more "acceptable") than correct ones.
Hence I am bit afraid that a "blind reviewing" policy provides
an incentive for submitting exciting but only half-finished 
theoretical papers, and that NIPS ends up publishing more incorrect theory-papers.

I would like to add, that in the well-known (often very selective)
conferences in theoretical computer science the submissions are NOT
anonymous, and this seems to work satisfactory. 
There, the main precaution for avoiding biased decisions lies in 
a careful selection  of referees and program committee members 
(trying to get researchers who are known for the quality of their own
work;  but still enforcing a substantial amount of rotation). 
The results of these policies are certainly not perfect, but quite good.

Wolfgang Maass