The only federal elections are for the President, Senators, and Representatives. This is not a direct democracy.

based on random choice or personal whim, rather than any reason or system.

"his mealtimes were entirely arbitrary"

synonyms: capricious, whimsical, random, chance, unpredictable;

(of power or a ruling body) unrestrained and autocratic in the use of authority.

"arbitrary rule by King and bishops has been made impossible"

synonyms: autocratic, dictatorial, autarchic, undemocratic, despotic, tyrannical, authoritarian, high-handed;

mathematics. (of a constant or other quantity) of unspecified value.

This is false both in mathematics and in everyday language.

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

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.

"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.