When you have a private/permissioned ethereum consortium, you are somehow trusting the members of the network.
How do you prevent a single user for tampering part of or the full chain, given that it is faster to get transactions approved?
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In such setups, you'll be most probably using a Proof of Authority (PoA) consensus algorithm. PoW doesn't make sense in such small setups (not safe + wasting energy).
For instance, when using geth's clique algorithm, you'll have a number of authorities in the network, which are allowed to seal a block. As long as at least 2/3 of these authorities are honest, you'll be fine.