It also means due to personal whim. I don't think it was this either. Pai has reasons for his choice. Many, of course, disagree with these reasons or think they are bad reasons but they are reasons nonetheless. It wasn't an arbitrary decision.

It's "arbitrary" because Pai, on multiple occasions, indicated he will not take the comments into effect. Even after the reports of the faked comments, the calls to delay the vote by some senators, the faked DDoS attack, he still went through with it. There's also allegation he violated the FCC's process. He was determined to ram this through no matter what. That's arbitrary.

No, that just means it's not a democracy. One can listen to a bunch of comments, disagree with them, and choose to do the opposite of what they say without being arbitrary.

His determination actually demonstrates the lack of arbitrariness. Arbitrary choices are held lightly and easily changed. This was the opposite.

That's capricious, not arbitrary. If Pai wanted this to go by the book, he would have pushed the vote out until the investigations into the fraudulent comments was completed, at the least. Someone who was determined to see this go through, but not in an arbitrary fashion, would have waited until the various issues with the process were resolved, and then held the vote. Pai was determined to hold this vote no matter what, that's arbitrary.

Capricious means "given to sudden and unaccountable changes of mood or behavior."

AFAIK at no point during the process did Pai change much at all. He made it clear what he was going to do from the beginning and stuck to it the whole way through.

Here is the definition of arbitrary:

"The term arbitrary describes a course of action or a decision that is not based on reason or judgment but on personal will or discretion without regard to rules or standards."

Most of Pai's arguments are half-truths or out right lies. There have been several instances where his claims were fact checked against the data and proved to be false.

Furthermore: "In many instances, the term implies an element of bad faith, and it may be used synonymously with tyrannical or despotic."

I think there's a good case that Pai's actions and statements could be shown to be despotic.