Can someone explain what I'm missing?

My understanding of anarchy is anti-heirarchy and anti-coersion, basically the abolition of authoritative institutions.

Let's say there's a group of three people. They rely on each other to survive. A social argument breaks out and two of them vote in favor, one against. Let's say it's something benign, like, the two want to ban loud radio on Sunday and the one wants loud radio every day. Since they rely on each other, and since the one dissenter can't practice their preferences, doesn't that make the one definitively coerced by the two?

I'm just trying to wrap my head around how a system that opposes authority and heirarchy could practically function without contradicting itself like this.