I think it’s a mistake to conceive the huge disparities of wealth and income we’re seeing at the moment as a question of equality against inequality. It’s easy to arouse people’s outrage at inequality, particularly when it’s gross, but it’s less easy to motivate them to do something about it. In part, that’s because the way to counter inequality is, obviously, with equality — and the unfortunate fact is that we can’t agree on what equality would require and how we’d recognize it if we saw it.
It’s more useful to see these disparities as growing to constitute a threat to the very system that gives rise to them. For reasons I’ve glanced at in my original comment, the effect of greater automation and accelerated productivity will be to worsen the imbalance. Even as the benefits of increased productivity are concentrated at the rich end of the social structure, it’s disadvantages will be felt at the (much more populous) poor end, in the form of fewer, worse paid jobs.
That in turn will mean less demand, less economic activity and falling prices, leading eventually to economic crisis. We can avoid this only by making sure that the effects of automation don’t simply translate into a lot more money for the superrich, but they’re more evenly distributed throughout the global economy.