Hmm. So the classic case for the minimum wage and/or unions is the employer/employee relationship, and how unequal it is. If you work for somebody with 10 employees, you count for a 10% of their employees, but they're 100% of your employment.
Thus, they have a massive advantage over you at the negotiating table. Unions help balance this out by increasing your negotiating power by allowing you and your fellows to negotiate as a group, while minimum wage balances it out by short circuiting the entire contest and ensuring that no matter how high their negotiating power, they can't push you below a minimum.
I was trying to think of another way to balance out this relationship, and the best I could thin of was "Everybody refuses to work more than 8 hours for any given employer and just pursues 5 different jobs., thereby reducing the amount of employment any given employer provides to just 20%, instead of 100%."
Unfortunately, this also reduces the amount of work any given employee provides to a 5th what it otherwise would be, which kinda cancels out the benefits. And thats before you factor in the costs and difficulties of the approach.
Given how terrible an answer that is, should tell you how big a problem this fundamental inequality is... :/