We continued to look at voting systems, with a botched attempt at explaining the Instant Runoff Method. (The example will work now. It’s relatively straightforward once figured out … no thanks to the Wikipedia article.)

See the chart of this page for a detailed matrix of which voting systems satisfy a multitude of criteria.

Why Plurality Satisfies Later-No-Harm

I found this a bit interesting. Namely, our analysis in class of the plurality method (and in fact, how we see it function in society) noted that it’s entirely possible to have three candidates in an election as follows.

  • Blue (40% of votes)
  • Red (30% of votes)
  • Green (30% of votes)

In such a situation, let’s say that the Red and Green parties are very similar but that both are very different from the Blue party. What happens if the Green party candidate is removed? Well, technically speaking, we’d have to have a new election if we were counting based on Plurality, since it isn’t a preference system. So, technically speaking, plurality can’t fail the later-no-harm criterion since the preference doesn’t change while tabulating the votes. Arguably, holding a new election with the Green party candidate removed DOES ESSENTIALLY THE SAME THING, but it’s technically a new election. That’s interesting, since we can see this at work, for instance, when smaller parties gain power in U.S. elections. Those smaller parties are often blamed for skimming off votes from one of the larger parties, leading to that larger party failing to gain enough votes overall.

Instant Runoff Voting Example

After some searching, I found this example on YouTube:

We’ll reconsider our example of votes in Tennessee on Wednesday. I’ll assign another homework then related to voting systems.


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