Some time back I saw this beauty and had to snap a picture of if for petty scrutiny later (like this and this). It is a printed graphic illustrating the relative proportions of 5 major wireless providers' customers, particularly how a potential merger of two smaller providers would compare in that regard. And it has some problems.
Five numbers represented in a confusing and unnecessarily complex fashion.
At first glance I thought Verizon's magnitude was a small sliver compared to the others, which is unfortunately the exact opposite of the intent. Verizon is the biggest player in this data set but the chart's first impression makes it appear as a minuscule marginal player. Nested area charts are at least better when they are unfilled so misunderstandings due to occlusion are reduced.
Nested radial charts that are filled have problems of occlusion and are misleading. Coloring only the stroke sort of helps.
Supposing you are Ok with the problem of occlusion, or at least overcome it, why break this up into two separate graphics? This is an illustration of a handful of numbers, why pull apart a nested radial chart and turn it into a nested radial chart and a pie chart?
Here's a clumsy reinsertion of the parts into a single graphic where the proportions are still hard to compare, but less so. It's at least a reduction of complexity with no loss of data. But still, a nested radial chart with a pie slice? It turns out, humans are waaay worse at at visually discerning the relative areas of circles than we are at comparing the relative height of columns (on the same plain).
Five numbers shown as more readily-comparable columns in one chart. Also, I put dumb newsprint texture behind the chart in a halfhearted whim of fairness. 'Fine, I'll isolate the variables,' he growled reluctantly.
So here it is as a boring old column chart. It avoids the miscue of Verizon looking like a small portion of the whole, the relative heights of the columns are easier to compare than the relative areas of bubbles, and the hypothetical merger column of Metro PCS and T-Mobile are in a stacked column living in with the rest of the data for easier visual comparison. Does my labeling look awful? Sure! But check out those sweet sweet columns!