An interesting, non-governmental, solution?
One way our society tries to address income inequality is through non-profit work, dedicated to improving various aspects of people’s lives. Check out this TED talk (below), by Dan Pallotta, the organizer of the AIDS Ride and 3-day Breast Cancer events (through his company, Pallotta Teamworks), summarizing 5 ways we handicap the non-profit sector, and what we could do to change that, thereby providing a market mechanism for redistributing income and handling problems that may be better handled in this way than by government (see this TV interview for the last two points).
Over the course of 9 years, Team Pollota events raised $556M in gross contributions ($305M net = 55%) from about 182,000 people participating in the events. That means that each person raised an average of $3,055, with $1676 going to beneficiary organizations.