I carry no backup. My reasoning:
3 possible failures:
1) transmitter fails, computer still working.
If this is the case, the computer will alert me rather loudly that it can't
get a pressure reading (0 psi). At this point, I know that before it lost connection,
I still had enough air to safely make an ascent, safety stop, and reach the top with
more than 500 psi. So I simply call the dive.
2) receiver fails (we're talking catastrophic failure). This is extremely unlikely, but
in theory could happen. At this point, I have to make a safe ascent without a depth
gauge or timer. Most likely I am with a buddy and can easily inform him of the
situation, and simply call the dive, and use him as a reference for ascent speed, and
safety stop.
3) buddy fails AND computer fails. This one sucks... But I dive recreational limits
anyways.. so I do my best to do a slow ascent. I probably will miss the safety stop,
but odds of DCI are still pretty low.
In any case, I don't do cave diving. I don't need to carry a backup for any possible failure point. Nobody I know that has a hosed AI computer carries two of them. So really it's just
people whining about the transmitter (envy?). That failure mode is #1, and is trivial to deal with. (yes you might lose one dive... but we're talking a VERY rare failure anyways).