On Friday, we discussed voting systems. We’ll continue this on Monday. First, we discussed the voting system in the United States, hitting on some topics such as the electoral college system and drawing district lines. Then, we developed the following axioms for voting fairness. These are essentially the building blocks that any fair voting system must satisfy.

  1. (Majority Criterion) If one candidate is preferred by an absolute majority, then that candidate should win.
  2. (Mutual Majority Criterion) If an absolute majority prefer every member in one group over every member in another group, then a member of the preferred group should win.
  3. (Later-No-Harm Criterion) If every voter’s preference of $X$ or $Y$ remains unchanged, then the overall group’s preference of $X$ or $Y$ remains unchanged.
  4. (Condorcet Criterion) If a candidate would win a head-to-head battle against every other candidate, then that candidate should win.

There are other things we could add to this, such as a “dictator criterion,” i.e., that no person has any more power than any other person.

Voting Systems

We discussed a few voting systems. The details can be found on Wikipedia, and so for each of the ones we considered I am simply going to post a link. We’ll discuss these more on Monday.

The first system we discussed was plurality (first-past-the-post). Plurality fails to satisfy the mutual majority or Condorcet criteria.

The second system we discussed was the Borda count method. We considered an example where this method fails the later-no-harm criterion. Actually, interestingly, one can come up with examples to show that it fails all 4 of our fairness criteria.

We then considered the method known as instant runoff. This method has been shown to satisfy all of our criteria except the Condorcet criterion.


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