Choosing the Lesser Evil: Helping Students Understand Voting Systems Session S035 Tower Court B, 10:20 – 11:10 am Curtis Mitchell Kirkwood Community College Cedar Rapids, IA curtis.mitchell@kirkwood.edu

Talk Outline A bonus quote from this election cycle The “standard approach” to voting theory Tactical voting in ranked-choice systems – concepts, terminology, and discussions Tactical voting in other systems Why teach this material? Questions

Johnson Says He’s a Condorcet Candidate (not in so many words) While Johnson is getting less than 10% of the voters in the most recent four-way national polls, he said if matched head-to-head against the candidates, he'd do much better. "I would love to see a poll head-to-head, Johnson versus Clinton, Johnson versus Trump," he said. "I think that would really be revealing. I think I would be the President of the United States in that poll.“ (CNN Politics, “Gary Johnson stands by being skeptical of elected officials, foreign leaders,” October 4, 2016.)

The Typical Approach Introduce preference ballots Cover voting systems: Plurality/first-past-the-post Single (sometimes) and sequential runoffs Borda count Condorcet voting Brief mention of approval voting (sometimes) Fairness criteria and Arrow’s Impossibility Theorem

Tactical Voting Our definition: a tactical vote is a vote that does not reflect that voter’s true preferences, but is intended to produce an outcome they prefer. Other terms: insincere voting, sophisticated voting, manipulation. An effective tactical vote depends on information about other voters’ preferences. Definition excludes other reasons to cast a vote e.g. to obtain funding for a party, or to protest or send a message.

Example #1 Who would win the election under plurality? % of voters 15% 25% 20% 1st Choice A B C 2nd Choice 3rd Choice Who would win the election under plurality? How could A’s supporters vote tactically to obtain an outcome they prefer? What do you think is the “right” thing for A’s supporters to do in this situation? Would using a different voting system remove the incentive for A’s supporters to vote tactically?

Example #2 % of voters 31% 9% 15% 20% 25% 1st Choice A B C 2nd Choice 3rd Choice How is this preference schedule changed from the previous one? Who would win this election using sequential runoffs? Borda count? Pairwise comparisons? Who has potential incentives to vote tactically here?

Strategy #1: Compromise A voter insincerely ranks an alternative higher with the goal of causing it to win. Extremely common in plurality (and Borda count). All commonly studied voting systems (except dictatorship) can have situations where compromising will lead to a more desired outcome.

Example #3 # of voters 4 3 2 1st Choice A B C 2nd Choice D 3rd Choice 4th Choice E 5th Choice Who wins this election if Borda count (or pairwise comparisons) is used? How can A’s supporters vote tactically (under either system) to obtain a result they prefer?

Strategy #2: Burying A voter insincerely ranks an alternative lower with the goal of causing it to lose. Borda count and, to a lesser extent, pairwise comparisons are vulnerable to burying. Burying is not effective in runoff methods (or plurality).

Example #3 redux # of voters 4 3 2 1st Choice A B E 2nd Choice C D 3rd Choice 4th Choice 5th Choice What happens if A’s supporters and B’s supporters both use the burying tactic? Borda count: A 27, B 25, C 30, D 26, E 27 Pairwise comparisons: A 1, B 2, C 3, D 1, E 3

2002 French Presidential Election Candidate 1st Round 2nd Round Chirac 5,665,855 19.88% 25,537,956 82.21% Le Pen 4,804,713 16.86% 5,525,032 17.79% Jospin 4,610,113 16.18% Bayrou 1,949,170 6.84% Laguiller 1,630,045 5.72% Chevènement 1,518,528 5.33% Mamère 1,495,724 5.25% Besancenot 1,210,562 4.25% Saint-Josse 1,204,689 4.23% Madelin 1,113,484 3.91% Hue 960,480 3.37% Mégret 667,026 2.34% …

Strategy #3: Push-Over A voter insincerely ranks an alternative higher, but not in hopes of getting it elected. Also called “mischief voting.” Primarily occurs in runoff systems (and runoff-like systems like U.S. primary elections).

Example #4 Suppose that in an election with 3 candidates, A, B, and C: 35% of voters prefer A, but also approve of B (and really don’t want C to win). 25% of voters prefer B, but also approve of A (and also really don’t want C to win). 40% of voters prefer C (and don’t like either A or B). What would be the outcome using approval voting? How can voters preferring A or B vote tactically? What happens if they all do this?

Approval Voting Our definition of tactical voting does not apply, since the method doesn’t use ranked lists. If we assume that each voter has an “inner” ranked list and sets an approval cutoff somewhere on the list, then a tactical element to voting is inevitable. Studies are somewhat mixed on whether voters actually do this.

Can we avoid tactical voting? A voting system is called manipulable if there is any arrangement of ballots for which a voter can obtain a better outcome by voting insincerely. A voting system in which voters never obtain a better outcome by voting insincerely is called non-manipulable (or sometimes strategy-free or strategy-proof). Discussion: is it worthwhile to look for voting methods that are non-manipulable, or “less manipulable?” Why or why not?

The Gibbard-Satterthwaite Theorem The only non-manipulable voting systems are: Dictatorships, and Non-deterministic systems (meaning that the same ballots won’t always yield the same outcome). A sample non-deterministic voting system is random ballot.

Measuring manipulability Probabilistic analysis Simulations Empirical data Computational complexity analysis

Why Teach Tactical Voting? More relatable than fairness criteria More obvious real-world applicability Helps lead in to the “what-if” reasoning involved in some fairness criteria Including this material has led to (n is small, though): Better class discussions of voting theory Better performance on voting theory tests (even if tactical voting questions are excluded) More students rating “elections” as their favorite course topic

Questions? For more information: Session S035 Tower Court B, 10:20 – 11:10 am Curtis Mitchell For more information: Email: curtis.mitchell@kirkwood.edu Phone: 319-398-7745 List of sources provided with the packet