Raising minimum wage to 1/2 of median income would do four things.
It would make work pay. A full time minimum wage job would no longer be a life sentence of poverty. This would enfranchise and include those workers into society. They would become more valuable employees, just as they are valued by receiving a fair, living wage.
It would stimulate the economy. The big jump in income for minimum wage earners would translate to higher wages for everyone at the lower end of the pay scale, and to huge increases in consumer spending, which accounts for 60% of our economy.
Tying minimum wage to median income would help it keep pace with the economy, without continuous battling in congress.
It would help reduce the huge disparity in wealth, and create an economy of prosperity for everyone.