And who decides when people don't have a choice? If someone offered her a job at 10 cents an hour would she take it? Of course not, ergo she has a choice. The problem with minimum wage is it assumes a certain amount of income is fair and another amount is not, across the board. Is digging a ditch in the hot sun for 5 dollars an hour the same as flipping hamburgers? Shouldn't the ditch digger get 6 dollars an hour? What if I offer you a job in my bicycle repair shop for 3 dollars an hour because it's all I can afford to pay you, but you want to take the job because you primary goal is to learn how to fix bicycles? According to the government, you are not allowed to work for me. My point is, when the government gets involved more people have fewer choices, no one is any better off, and more people end up unemployed.
I'd suggest you read Henry Mayhew's The London Poor. It was written in the 1800s, so I believe it's non-copyrighted and should be available free online.
Capitalism, market forces, etc. are powerful engines capable of truly astounding things. We owe most of our modern world to the miracle of capitalism. But there is a dark side to it, which must be mitigated. That's where minimum wage comes in.
If you know how to splice genes, run a complex piece of equipment, cut cancers out of people, create pastries (sic), formulate computer models for movements in the stock market or have one of a thousand other sophisticated skill sets, then the bidding for your services/expertise goes no place but up. On the other hand, if you have a non-sophisticated skill set, even if you are willing to work hard, then the bidding for your services points downward.
If we, as a nation, devolve into a two-tier economic systems, then we'll be in for a rocky road ahead. It'll be like some South American countries where the rich fly in sushi chefs for parties behind high walls manned by armed guards.