Since people here are also advising always follow the RA, without exception, it might be appropriate to point again to my paper, which ATC Watcher referenced, in which I note that
* the TCAS algorithm is known to resolve all conflicts between two aircraft (Lynch, Lygeros, MIT 1997)
* It is still not known whether the TCAS algorithm resolves all conflicts between three aircraft
and I have offered (since 2002) a PhD to anyone who can definitively answer the question whether the TCAS algorithm resolves all conflicts between three aircraft.
I also pointed out that, in the Überlingen collision, the Russian commander believed they were in a possible three-aircraft conflict (I wondered about that in a paper I put on the WWW in August 2002, and it was confirmed by the report in 2004). Further, in the decision situation they were given, it was rational to choose to descend (I also went to some pains to point out that saying "it was rational" and supposing that that was the reason he continued to command a descent are not the same thing at all).
Capt Pit Bull suggests that following the RA is appropriate some X percentage of the time, and maybe inappropriate some other percentage (100-X). (He chose X = 0.1, but I presume he was illustrating his point, rather than suggesting a real value for X.) One of the main issues with TCAS, for me, is that no one knows what the value of X is.
What if it turns out to be 50?
PBL