How would the dynamics of negativity change if every downvote required an input field for justification. Even if someone made their justification something stupid or simplistic, it places their reputation on the line, transparently onto the blockchain.

Hatred will exist, regardless of platform. The only danger I can see is in 'incentivizing hateful behavior'.

While I respect the arguments in favor of some sort of 'downvote reward structure', I agree with @dantheman's assessment that it could incentivize hateful behavior.