How do redundancies work in aircraft systems?
Triple-redundant systems have four independent members, so if one fails, a two-to-one vote of the remaining three is still possible.

One system    = No redundancy.
Two systems   = Simple redundancy.
Three systems = Double redundancy.
Four systems  = Triple redundancy.


However, often the term "triple redundant" is used when the system has only three members. And if all three disagree, two of them must be faulty already, so this is a case of multiple failures.

In case of Airbus, besides the three main FCS computers two backup systems are available to help isolate the faulty one. Inside, each has two channels which run software written by a different team, run on a processor different to the one in the other channel and which are supplied by two different suppliers.  This helps to reduce systematic errors, when all together would fail because of a common malfunction.



Airbus flight control system diagram (picture source). Only the first system of each is expanded; the boxes for system 2 and 3 look the same on the inside. Input is from the side sticks, and output goes to the hydraulic valves at the control surfaces. The voting happens first in the comparator step (between the two channels) and again in the filters (between the single systems).