Re: the claim that groups of pie charts are especially awful, I have a counterexample. How would you express this more clearly without a series of pie charts?

 Like this: http://imgur.com/rGvFWThe example you give falls into the 'multiple pie chart' nightmare where it's hard to compare the percentages across charts. At the same time I can easily see how far from a majority each group is and also the pattern in abstaining from the question.
 The problem with using stacked bars in political situations is that the 50% threshold is critical. Without reading the numbers, it's much harder to tell with stacked bars whether a close vote (or poll) is at 48% or 52%.
 You don't need to go back to a pie chart for that. On the chart above that I created there is a clear 50% line in the middle. If necessary, it could be darkened to make the mid point more obvious.
 But that is still not an accurate view, since the number of independents, democrats, and republicans aren't the same.
 That doesn't mean it's inaccurate, that means it's emphasizing the comparison between relative numbers rather than absolute numbers. If it was the way you wanted, then the percentages would be difficult to compare.
 Not really. The chart type that incorporates that information is called a mosaic chart, and is one of my favorites.
 Couldn't you encode the sizing with the size of the pie? ie, if Independents are the smallest group, they should be a smaller circle. In this manner, area allows for accurate comparison (it could be that more Republicans disapprove of direct voting than Independents approve for example).
 You could do that, but then you compound the problem of comparing the size of slices with an additional size of circle comparison. Humans aren't good at comparing size between these kind of shapes. We're much better at comparing rectangular shapes. You'd be much better off splitting the visualization into two bar charts - one for the % of group calculation and one for the total count of people calculation.
 Out of curiosity, what did you use to make that?
 Apple Numbers
 Honestly, I can't understand in which way your charts is more readable than pie charts.I frequently use combination of graphic, histogram and bar chart with one pie chart.Graphics - for chronological data, pie chart - for absolute values.

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