> "Reducing inequality" is very different from democracy, and would probably lead to reduced economic efficiency, as it necessarily reduces the incentives for efficient production.

They are absolutely bound together. Ensuring that every person has the same power in the political process means that everyone has the time and energy to pay attention and be educated on what's going on the world, and that nobody has so much wealth that they can use it to buy influence. The trend towards more inequality while the working class has less and less political power is painfully obvious, especially in the United States.