The center squeeze: a deep dive under several voting methods

  • Kurt Wright (Republican): 32.9%
  • Andy Montroll (Democrat): 23.0%
  • Bob Kiss (Progressive and current incumbent): 28.8%
  • Dan Smith (Independent): 14.5%
  • James Simpson (Green): 0.4%
  • Write-ins: 0.4%
  • Kurt Wright (Republican): 36.7%
  • Andy Montroll (Democrat): 28.4%
  • Bob Kiss (Progressive): 33.2%
  • Exhausted ballots: 1.7%
  • Kurt Wright (Republican): 45.2%
  • Bob Kiss (Progressive): 48.0%
  • Exhausted ballots: 6.7%

The Center Squeeze

Voters and three candidates are distributed along a left-to-right axis. The candidate at the center of public opinion gets eliminated first under IRV due to being the first choice of the fewest voters.
The center squeeze, as illustrated by the Center for Election Science

Strategic Voting in IRV’s center squeeze

Plurality

  • Kurt Wright (Republican): 32.9%
  • Andy Montroll (Democrat): 23.0%
  • Bob Kiss (Progressive): 28.8%
  • Dan Smith (Independent): 14.5%
  • James Simpson (Green): 0.4%
  • Write-ins: 0.4%
  • An even worse candidate would have been elected
  • Many votes would have been completely wasted on non-viable candidates like Dan Smith
  • Dan Smith would have seen less support due to strategic voters deserting him

Plurality + Runoff

Approval

  • Wright: 36.7% #1, 12.7% #2
  • Kiss: 33.2% #1, 20.3% #2
  • Montroll: 27.4% #1, 39.6% #2
  • < 24.8%: Wright wins, Kiss finishes second
  • 24.8%-30.7%: Wright wins, Montroll finishes second
  • 30.7%-45.7%: Montroll wins, Wright finishes second
  • > 45.7%: Montroll wins, Kiss finishes second

Approval + Runoff

  • Montroll has an easier time winning: Since he’d win the runoff, it’s only necessary for 24.8%, instead of 30.7%, of voters with a second choice to vote for that second choice in order for Montroll to win under the simple model above.
  • Wright never wins. Even if Montroll misses the runoff, Kiss will still beat Wright so the worst-case outcome will be avoided.
  • Everyone would get an equal vote in the runoff. Without a runoff, the handful of voters who vote in a strategically foolish manner (e.g. only voting for Dan Smith) are throwing their votes away, and the runoff mitigates this issue.

STAR

Condorcet

What if Montroll shouldn’t win?

  • The Condorcet definition: The best candidate is the one who would defeat anyone else head-to-head (when such a candidate exists).
  • The utilitarian definition: The best candidate is the one whose utility, summed over all voters (presumably after being normalized somehow), is the highest.
  • All voters who expressed a second choice thought their second choice (among the top three) was 60% as good as their first choice. (They have utilities like {Kiss: 10, Montroll: 6, Wright: 0}). In this case, Montroll should win.
  • Voters are far more concerned about helping their first choice win than preventing their last choice from winning. They have utilities like {Kiss: 10, Montroll: 1, Wright: 0}. In this case, Wright should win.
  • Kiss>Montroll>Wright voters and Montroll>Kiss>Wright voters have utilities like {Kiss: 100, Montroll: 90, Wright: 0} and {Kiss: 90, Montroll: 100, Wright: 0}, but Wright voters (who expressed a second choice) have utilities like {Kiss: 0, Montroll: 1, Wright: 100}. In this case, Kiss should win.
  • Approval voting: Suppose everyone only votes for their second choice if that second choice is at least half as good as their first choice (i.e. if they have utilities like {A: 10, B: X, C: 0}, where X ≥ 5); this is the correct strategy if they believe all three candidates are equally viable. If everyone thinks their second choice is only 40% as good as their first choice ({A: 10, B: 4, C: 0} utilities), Montroll would be the utility-maximizing candidate — but everyone would bullet vote so Wright would win.
  • Approval + Runoff is incapable of ever electing Wright no matter how little voters care about their second choices compared to their first choices.
  • STAR: If everyone thinks their second choice is 20% as good as their first choice, Wright is the utility-maximizing candidate but Kiss will win in the runoff if everyone casts an honest (and, in this case, strategically sound) 5–1–0 ballot.

Conclusion

--

--

--

I am an advocate of better voting methods which eliminate the spoiler effect, make third parties viable, and yield proportional representation.

Love podcasts or audiobooks? Learn on the go with our new app.

Recommended from Medium

Slabtown Road over U.S. 30 to remain closed through mid-summer

Right On Cue, Republicans Are Screaming About the Debt — Again

Voting In a Time of Corona: My Dystopic Wisconsin Election Story

Selfie of a woman wearing a hat, glasses, and cloth mask

Lisa Bari, MBA, MPH — She Went Straight to the Source

independent voices

Be Careful What You Wish For Re: John Bolton

On the Sterilized Façade of Political Elitism

The Iran Deal’s Fundamental Flaw is Revealing Itself in Iraq

Get the Medium app

A button that says 'Download on the App Store', and if clicked it will lead you to the iOS App store
A button that says 'Get it on, Google Play', and if clicked it will lead you to the Google Play store
Marcus Ogren

Marcus Ogren

I am an advocate of better voting methods which eliminate the spoiler effect, make third parties viable, and yield proportional representation.

More from Medium

Byzantine Fault Tolerance

Vulkan Swapchain

GCN with TigerGraph and PyG

Computational 2D Geometry Part 3: Vector and Point