No, neither of those is false. There is no stated LW moderation policy, which as far as I'm concerned is equivalent to having no moderation policy. And given the lack of policy, moderation power is necessarily exercised arbitrarily. This does not imply that your judgement is bad, nor does it imply that other moderators' judgement is good.
If there is some official LW moderation or comment policy, I'd appreciate being pointed to it. But again, I've been active here since the beginning and I'm not aware of one, so it might as well not exist.
And given the lack of policy, moderation power is necessarily exercised arbitrarily.
As I understand it, the word "arbitrary" refers to lack of relevant or systematic explanation or reason for something. I'm not sure what meaning you intend, the word is confusing the way you use it in this context. (Suppose hypothetically that the policy I stated above was more prominently stated previously.)
In light of recent (and potential) events, I wanted to start a discussion here about a certain method of handling conflicts on this site's discussion threads, and hopefully form a consensus on when to use the measure described in the title. Even if the discussion has no impact on site policy ("executive veto"), I hope administrators will at least clarify when such a measure will be used, and for what reason.
I also don't want to taint or "anchor" the discussion by offering hypothetical situations or arguments for one position or another. Rather, I simply want to ask: Under what conditions should a specific poster, "Alice" be prohibited from replying directly to the arguments in a post/comment made by another poster, "Bob"? (Note: this is referring specifically to replies to ideas and arguments Bob has advanced, not general comments about Bob the person, which should probably go under much closer scrutiny because of the risk of incivility.)
Please offer your ideas and thoughts here on when this measure should be used.