To solve a problem, we have to ask the right question. For example, is our goal to increase the minimum wage or to reduce poverty? If our goal is to reduce poverty, the next question would be: what is the best way to reduce poverty?
By taking this approach, we would more clearly see increasing the minimum wage is a tool to achieve our goal of reducing poverty. And we would be more open to alternatives, which in combination with a minimum wage would better enable us to achieve our goal such goal.