There are two dimensions to improving lives. The first has to do with income transfer from rich to poor, the second with raising real Median wages. Those initiatives are not at odds with each other but they are separate.
There is so much talk about income inequality and stagnating median income in ways that suggest the speaker thinks they are the same thing. They are not.
Most people agree that the rich should help the poor. There can be arguments about who is rich, who is poor and how much help they should provide. Those are important arguments.
For instance, I believe it's absurd for someone in the top 49th percentile to help someone who is in the bottom 49th percentile. Someone making $60k shouldn't have to give $500 to someone making $55k. There has to be a middle ground of 30%, 50% or even 80% of people who are neither expected to help others or expect to be helped. (At least formally through income transfer in the form of taxation and welfare. Obviously everyone helps and needs help just to get through the day.)
Should only people making $200k help only those making less than $10k? Or should even households making $100k help households making less than $35k? The first choice would leave about 87% in the middle class who neither got nor gave help. Do you make more than $10k a year? Don't expect any help. Do you make less than $200k? Don't worry about being taxed to help the poor. The second (tax above $100k and subsidize below $35k) would leave about 43% in the middle class who neither got nor gave help.
In the last 100 years, the top marginal tax rate has ranged from a low of 28% to a high of 94%. Even within the same country, the consensus about what constitutes a fair rate of taxation varies over time.
[You can find data on median income and what percentage of Americans make more or less than certain amounts here.]
You can argue about the cutoff point for who pays additional tax for the poor and who is poor enough to benefit from that tax. Ultimately, though, voters will decide what is fair. There is no magic formula for that.
By definition, though, you can never raise the average wage through income transfer. In theory you can raise the median wage through income redistribution but that strikes me as funky; it essentially means that you would tax enough people in the top 49th percentile at high enough rates to lift the income of everyone in the 50th percentile on down.
To define someone making the median income as poor is odd. It's like defining a 5'10" man as short. Income transfer is compassionate, practical and yet does nothing to raise median income. For that you need a completely different set of policies.
Raising Median Income
The usual suspects to raise median income? Investments in infrastructure and education, research and development, childcare and healthcare. These all help to raise incomes. These are essential. We're not doing enough of them or even doing them enough. That said, the biggest boost to an economy is moving into a new one.
In the century after the US was founded, median wages rose as we created an industrial economy that gradually supplanted the agricultural economy. Last century, median wages rose as we created an information economy and workers moved from factories into cubicles. This century, median wages will rise as we create an entrepreneurial economy. The median wage in Santa Clara County - home to companies like Google, Intel, HP, and Apple - is $107k, nearly double the $58k for the US. This will become a norm as more regions adopt and adapt the entrepreneurial culture that defines Silicon Valley. And there is so much more we can do to popularize entrepreneurship. Redefining work to become more entrepreneurial will do as much to raise productivity and wages as any previous change.
The question of how to alleviate poverty through income transfer is an important one and needs to be defined in a way that voters think is fair. The question of how we move into a new economy to create more for everyone is even more important. How a community answers the first one defines how they pursue fairness. How a community answers the second one defines how they will pursue progress.