"Do we have the authority to impose arbitrary rules on our neighbors..."
I have very clearly said we have authority over ourselves, and in agreement. I have never intimated any other thing. I have instead pointed out that governments claim authority they do not have. HOA's included.
I also vehemently disagree that democracy isn't tyranny of the majority of voters - which is never a majority of the population, in living memory. Just because three of my neighbors tell me to cut my grass doesn't mean I have to - unless I have contractually agreed to abide by majority decisions regarding the length of my grass - which a lot of people do when they buy property in HOA's, to their regret.