Suppose I played a chess game with 60 minutes on both side. I play blindfolded while my opponent does not. Assuming that my rating is 2000 fide, what rating would my opponent have to be so that the expected score is a draw? Is this dependent on a person's rating? This question might be hard to answer. I am interested to know if anyone has any insight from their experience playing blindfolded.
I think it is ridiculous to assume that someone's normal rating would in any way be indicative of their blindfold rating. Your understanding of chess and ability to play with the chess pieces in front of you has little to do with your ability to hold all of the information in your head.
The only assumptions you can make are:
A) a person isn't going to be better at blindfold chess than they are at regular chess
B) someone with a higher rating in regular chess is more likely to be better at blindfold chess than a lower rated player.
My suspicion is that your blind strength increases in some relation to your sighted strength as well as your experience with blindfolded play, but I very much doubt that there's a specific (or even vague) formula. For instance, this article (actually a review of Blindfold Chess by Eliot Hearst and John Knott) mentions that "Some of the strongest blindfold chess masters claim that the strength of their blindfold play is similar to that of their sighted play."
Answering this question "definitively" would likely require a dedicated study on the topic (an idea also mentioned in that review), pitting players of varying strengths against one another multiple times, alternately blindfolded and not, and comparing all the results. It would be a very interesting study, I think!