Actual represents the actual distribution of wealth. Estimated is what people think the distribution of wealth is. I agree with Noah that the methodology that generated the “ideal” numbers is a bit odd so I’ll ignore it.
Both Noah and Ariely & Norton focus on what this shows us about the top twenty percent, but I don’t think that’s news. We already know from polling that the median voter supports “soak the rich” tax policies far beyond what the right people who run the Democratic Party are prepared to propose. What’s interesting here is the extent to which the public vastly overestimates the prosperity of lower-income Americans. The public thinks the 4th quintile has more money than the median quintile actually has. And the public thinks the 5th quintile has vastly more wealth than it really has.
You can easily see how this could have a giant distorting effect on our politics. Poor Americans are simply much, much, much needier than people realize and this is naturally going to lead to an undue slighting of their interests.