Edward Tufte, the elder-statesman of data visualization, is famously not a fan of the pie chart:
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. Edward Tufte
The purpose of a pie chart and its alternatives is to allow the viewer to quickly assess the ratio of different parts to each other, and to the whole. Tufte contends that the pie chart arrangement undermines this function. Instead, he argues that data should be arranged along a visual dimension to assist the viewer's comprehension of the data.
The leading contrary view comes from a study by Spence and Lewandowsky. They demontrate experimentally that viewers are not impeded by the structure of the pie chart as much as Tufte asserts. More recently, Stephen Few has led a response to this criticism. The academic arguments continue to go back and forth.
Visualizing the ratio between three quantities is interesting because it side-steps one of the more difficult controversies about non-adjacent values. In all of the visualizations above except for the bar, each quantity is adjacent to each other quantity, allowing the ratios of parts and whole to be considered.
The relative simplicity of visualizing a triple affords us some aesthetic leeway. With the force of academic argument, there will of course be some who consider these visualizations mere toys or trinkets, not appropriate for serious data visualization. Perhaps they are... but they are rather lovely trinkets, I think. The aesthetic virtues of visualization plays too small a role in the argument, and the maxim that a difference is not a difference unless it makes a difference is particularly apposite for visualizing triples.
-- Alec McEachran, December 7, 2015