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This week, I read a post by Nicholas Hamilton about ternary plots that made me think, how this geometric diagram has many different application in science fields. Couple weeks ago, I was reading a book by Donald Saari, who uses ternary charts massively to project election outcomes in different electoral settings.

Perhaps, most common, ternary diagrams are used for projecting 3-parties elections; the same idea can be generalised for more parties, though it gets more complex. When we study elections with this geometric figure, each point of the triangle intuitively represents 3 coordinates (say A, B, C, because I’m creative today) that correspond to the percentage of votes each political organisation obtained. From this, we may speculate the composition of the legislative body. Here I use colors to make it fancier.

The whole point of the book is not about election outcome visualisation, but that the election outcome may be depend on the formula used to aggregate votes and the number of seats available. For instance, if we have a constituency of M=5 seats, the possible outcomes are:

If party “A” has 60% of the popular preference, party “B” 20%, and “C” other 20%, then a system using d’Hondt to distribute seats proportionally among the parties will give: A(3), B(1), C(1).

Rather than thinking on edges, we can draw regions to make more clear how electoral formulas cause small, but different shapes, which in the long run may affect the number of parties and coordination among party supporters, to mention few adverse reactions.