Remove slashed validators from active authority set for rest of era

[acatangiu]

There is existing work disabling validators to account for parachain consensus. Conclusion for Beefy was that plain disabling does not work in bridges case, because the other chain that does not care. The only thing that works is removing beefy keys. As of the current design, disabling will only prevent block authorship, backing and triggering of disputes. Everything else stays unaffected: Approval voting, grandpa, beefy.

For BEEFY we can either have:

1. BEEFY slashing means kicking out of the validator set or
2. Have a strong enough notion of disabling that means that the BEEFY key is left out of the list of BEEFY keys for the remaining sessions in this era.

We probably don't want to have disabling that we suspect might reach a significant fraction of validators with the wrong bug trigger 2 though, as we also need to be worried about BEEFY liveness. A liveness of safety violation in BEEFY can brick bridges on chains without governance like Ethereum.

On the other hand validators who are completely slashed can attack BEEFY for free. So having either 1 or 2 beng the result of a large slash but not apply to things with small slashes, like raising disputes.

With random sampling, BEEFY security relies on cryptoeconomics like backing security. When we have BEEFY with BLS and SNARKS, then disabling or slashing need not affect BEEFY and we can all sleep easier.

Originally posted by @AlistairStewart in https://github.com/paritytech/polkadot-sdk/issues/1961#issuecomment-1836022433

[eskimor]

One question is also with regards to Beefy liveness, whether we need a separate system for Beefy disabling than the rest or is it "ok" if Beefy keys are dropped, because a validator voted invalid on a valid candidate?

We are limiting the disabled validators to 1/3 of the network and the plan is to re-enable lowest offenders once we would overstep that limit. But even if disabling a full third were ok for Beefy - we would then need to re-instantiate the keys of those lowest offenders.

[AlistairStewart]

If we did remove disabled validator's keys, we wouldn't make the threshold 2/3 of the total validiator set size, but 2/3 of the keys we have in the list. But it still means that if we disbable 1/3 of validators who are honest, then we need no more than 2/9 of the validator set to be dishonest then. Or make our already bad parameters worse.

It would be better to keep keys for validators who we have disabled, might be honest, and we didn't slash much.

[eskimor]

So something like:

1. Disabling does not affect Beefy.
2. 100% slash -> Beefy key gone.

Should do the trick then.