I think the plot is most often referred to as a Ternary plot

This reminds me of the horror that the Kolm Triangle would strike in the hearts of undergraduate economics students. The KT is the analogue of the famous Edgeworth Box for an economy with a public good.

Ternary plots plotting vote shares are sometimes called Nagayama triangles. See http://eprints.lse.ac.uk/4273/1/Is_Duverger's_Law_based_on_a_mistake_(LSERO).pdf for some examples.

I wish you'd read my post before making comments! The reason why it takes a bit of time to read this chart is precisely because it is NOT a ternary plot! I thought this post was about ternary plots, then I realize this is a scatter plot with two axes, while a ternary plot has three axes.

Kaiser, it seems to me that apart the triangle deformation and the misleading top axis label directions, a two axes scatterplot is the same thing as a ternary diagram.

http://i.imgur.com/tYWFy.png
In a ternary diagram, all the points along a line parallel to one side have the same percentage.
Look at the three points from top left to bottom right: they all have Romney 45%. Look at the three points from bottom left to top right: they all have Santorum 30%.
Look at the projections of Abortion point: it looks having 1/4 Romney and and 2/3 Santorum...

Antonio: thanks for the note! I see the light. The ternary plot and the scatter plot are different even though the pattern of the dots appears to be similar. See my additional comment above.

A bit confused this. If it is a ternary plot then going up the vertical line will absolutely produce the share of "other candidates". I think you need to read up on ternary plots.
Her is a simple introduction

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