Rob Richie misleads on Approval Voting at Dartmouth

In a recent spate of Twitter posts, FairVote executive director Rob Richie criticized Approval Voting, citing specific elections at Dartmouth University.
On Dartmouth, see low winning %'s in its 2 uses.. Winner [of the 2012 Student Assembly election] had <33% & may have won due to tactical voting.
Richie implies that the "low" 33% approval rating is a flaw. He would predictably tout his favored Instant Runoff Voting (IRV) system for its guarantee of a 50%+1 "majority winner". Let me now demonstrate the fallacy of Richie's argument.

Consider the following hypothetical voter preferences, unrelated to the Dartmouth election. The letters represent candidates ordered by preference. The bold red letters are "approved" candidates whom that faction of voters would support in an Approval Voting election.

 % of voterstheir ranking 
35%W | Y > Z > X
 17%XY | Z > W
 32%Y | Z > X > W
 16%Z | X > Y > W

For example, the first row says that 35% of the voters favor W first, Y second, Z third, and X fourth. They would approve only W in an Approval Voting election.

With Rob Richie's favored IRV system we eliminate Z, then Y. Then X wins with a 65% to 35% landslide majority against W.

With Approval Voting, Y wins with 49% approval—not a majority. The full results are:
Y 49%, W 35%, X 17%, Z 16%
Given Y's 49% approval rating, Richie would argue that Approval Voting failed to elect a "majority winner". He would contend that IRV produced a clear "majority winner".

But wait!
  • Only 17% of voters approve of X, which is far lower than Y's 49% approval. Richie complains that Approval Voting elects someone with only 49% approval—but his IRV system elects someone with only 17% approval.
  • X isn't really a "majority winner" after all! Note that Y is preferred to X by a huge 67% majority of the voters (35% + 32%). And Y is the first choice of 32% of the voters, compared to only 17% for X. Y is thus the true majority winner, not X. So Approval Voting, not IRV, elects the true majority winner here.
When I explained this to Richie, he replied:
Hmm. I'd say your math breaks down because of not understanding psychology. Thus, failing to grasp Dartmouth
He cited no evidence as to how psychology could refute the above concrete math. Given Richie's historical behaviors, this is not surprising. In my experience, Richie and his FairVote colleagues are not a reliable source of information on electoral systems.

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