Inequality and Direct Democracy

One may assume that if we were all able to vote on every issue the vast majority, with low incomes, would claim the wealth held by the rich for themselves. They would vote for a vast redistribution.
Switzerland is the pre-eminent example of a direct democracy and this graph (data from the UN) shows that the top 20% of wealthy Swiss have 5.7 times more assets than the poorest 20%. They are in the middle of the range of countries with far more inequality than Japan (3.4) and far less than Singapore (9.7).
For more on inequality I'd recommend this TED talk by Richard Wilkinson. He highlights the multiplicity of social benefits, for the poor and rich, evident in more equal societies.