Edward Tufte gives the pie chart a more succinct and decisive treatment in "The Visual Display of Quantitative Information":
A table is nearly always better than a dumb pie chart; the
only worse design than a pie chart is several of them, for
then the viewer is asked to compare quantities located in
spatial disarray both within and between charts [...] Given
their low density and failure to order numbers along a
visual dimension, pie charts should never be used.
Tufte is simply wrong here. A pie chart implicitly conveys an additional piece of information which a series-style chart like a table or bar chart does not: that the information presented represents some meaningful total. A table listing percentages can achieve the same result, as can a single bar, but both require closer inspection. For a small number of variables, and particularly where there is a large disparity between the values, a pie chart is better. Unfortunately, many people break this contract with the viewer and present a pie chart solely to show the ratios, in which case I would agree that it is poor presentation.
Showing the ratios is fine: your meaningful total is their total.
For instance, showing revenue breakdown while trying to explain that some department pulls more than the rest. Here, without normalization (via pie charts, percentages, stacked bars) it becomes more difficult to compare the ratios. This perfectly mirrors the idea of sufficient statistics for a particular inference.
I'll also argue that pie charts are still terrible ways to display "data of bounded measure". The primary arguments are (a) people are quite terrible at doing accurate comparisons with area or, worse, arglength and (b) it tends to destroy the consistency of you labels since there's not a clear preferred ordering in a pie chart.
In this case, I'd say that stacked bar charts or empirical empirical CDFs do a much better job displaying bounded data, and, if you can suffer removing the bound, then simple bar charts or dot plots do it best.
I'd be amazed to hear of a time that a pie chart is actually optimal. I think perhaps the best argument going forward is if ratios are sufficient for your story even with the labeling obscured (it just adds noise). Here, the ambiguity of the ordering on a pie chart might provide exactly the right vehicle.
I still wouldn't know whether it should be computed by arclength or area, though.
I think perhaps the best argument going forward is if ratios are sufficient for your story even with the labeling obscured (it just adds noise). Here, the ambiguity of the ordering on a pie chart might provide exactly the right vehicle.
The use case you describe is actually quite common. If I have eight products and want to see at a glance which are contributing the most to my bottom line, a pie chart is perfect. The two conditions are met:
1) I'm looking at a meaningful total (all of my products)
2) I'm only interested in the ratios among them
To clarify, showing ratios is fine in a pie chart as long as the pie represents a meaningful total. If I just showed my top 3 products rather than all of them (or at least all of them in some explicit category), then using a pie chart would be inappropriate because there is no meaningful total; a bar chart or table would better in that case.
I still respectfully disagree that there is almost any purpose at all for using a pie chart. We're just, as humans, not terribly good at making visual comparisons on angular scales.
I think you may have missed his point, I had an opportunity to go to Tufte's talk and his issue is their mixing of of area and lack of numbers. He points out that you can take any pie chart, convert it to a stacked bar chart of one 'bar' and put the numbers along the stack axis on one side and qty labels along the stack axis on the other side and convey more information, more accurately, and in less space. Pie charts are big wide open wedges of color and no additional information so they were inferior.
What Tufte is missing is that a pie chart does immediately convey one additional piece of information that a bar chart can't without closer inspection: that the individual wedges add up to some meaningful whole. With a bar chart, you need some kind of explicit labeling to indicate that the bar represents a total, whereas with a pie chart it's implicit. It's inherent from the topology: as a circle, the pie chart is closed, implying that there is no additional data and that only the ratios are important. A series such as a bar chart or table is not closed, carrying the implication that it might simply have been truncated for reasons of space or clarity. A series-style chart also may or may not be presenting absolute values rather than ratios, and further inspection is needed by the viewer to distinguish which is the case.
I get what you are saying, basically that the 'pie' itself is a sum of units. However, I expect that Tufte would tell you to include that information more succinctly (or densely). I actually re-did the graphic in Corel Draw to show this but darned if there is a way to upload here, so I've put it in a google 'drawing' : https://docs.google.com/drawings/d/11hLh7DarPLrRHwVOQAC6Semn... which may or may not come through.
The top bar, which bounds the bars with the axis label 100% conveys the same 'from a whole' concept that the pie does in less space. Its also commutive across all three bars :-)
I think you're overstating the value of a pie chart's to ability to communicate that the parts make up a whole.
I agree with the OP and Tufte: something else is nearly always better than a pie.
Not too fan boy Apple too much but it is one of the few that uses pie charts effectively. But it is normally with only 2 or 3 pieces and usually to reinforce the difference in share.
I'll point out that less information can in fact be a good thing. A min-max-normalized line chart is not always better than an unnormalized one, though people often assume so, and adding the numbers or other easy means of comparison to imprecise or insignificant data only serves to distract.
For example, consider the voting pie charts earlier. Is it really helpful to notice that independents pick "other" a whole 1% more often than republicans? Because with a bar or labeled chart, you will pay attention to that.
See jgrahamc's post above for a great alternative: a set of bar charts color-coded into subsets. Much more effective than a big pie chart. Many other "part-of-a-whole" charts improve on pie charts as well.
