Ranked Choice Voting

[Cap]

What most people called Ranked Choice Voting is what election method theorists call Instant Runoff Voting. It is but one of many methods in which voters rank their choices of the candidates. Unfortunately, it has some severely problematic behaviors, and there are much better ways to do ranked voting.

IRV starts with a good intuition. If the election goes 40-30-30, the 40% shouldn’t necessarily win. Democracy isn’t “biggest group rules,” it’s “majority rules.”

So what do you do if nobody has a majority? The obvious solution: narrow down the field of candidates until somebody does. And how do we narrow it down? Let’s eliminate the guy with the fewest first place votes. Not exactly majoritarian, but you can’t make majoritarian decisions until the field is narrowed down, so whaddayagunnado?

There’s a better class of methods called pairwise methods. Instead of narrowing the multi-way race down to two, it looks at all two-way races simultaneously. There are only so many ways the candidates can pair off, and for any pair of candidates you can determine how they fare head-to-head.

If any candidate wins all their head-to-head races, that’s called a Condorcet Winner and wins the election in any pairwise method worth discussing. (A pairwise method that satisfies this criterion is called a Condorcet method.) If there is no Condorcet Winner, you have a situation called cyclical preferences and there are various methods for breaking the cycles.

Let’s look a a couple of simple example elections to contrast the behavior of IRV and Condorcet methods.


Example 1

There are three candidates for election: a Conservative, a Moderate, and a Liberal. Voter preferences are as follows:

40% C > M > L
15% M > C > L
05% M > L > C
40% L > M > C

First, let’s consider how this election goes under IRV. In the first round C and L each get 40 while M gets 20, so M is eliminated. In the second round, C beats L 55-45. C wins.

Note that liberal voters have a tactical dilemma. If everyone votes sincerely, C wins. But if enough liberal voters put M on top of their ballots, then M can make it to the second round and win the election. So what are liberal voters to do: give their top votes to the one they like the best, or to the one that can win? This is exactly the kind of dilemma we’re looking to RCV to get us away from. IRV just doesn’t do the trick.

How does this same election go in a pairwise method?

M beats C 60-40.
M beats L 60-40.
C beats L 55-45.

M is a Condorcet Winner. M wins.

Comparatively simple and sane, wouldn’t you say?


Example 2

The government is going to buy one of three things: A, B, or C. They decide to hold a vote to decide which. The voter preferences are:

40% A > B > C
35% B > C > A
25% C > A > B

What will happen when we vote? C gets fewest top votes and is eliminated. Then A beats B 65-35. A is what we will buy.

But wait! There’s a twist! Before the vote, the government comes into some money and we decide we’re going to buy two of the three things. So instead of having an election to decide which of the three to buy, we’ll have one to decide which to exclude.

The voters reverse their preferences. The ones they most wanted to buy are the ones they least want to exclude and vice versa. So the ballots are:

40% C > B > A
35% A > C > B
25% B > A > C

B is eliminated first. Then A beats C 60-40. A is what we’ll exclude.

We reversed the order of preferences on every ballot and got the same winner. That’s pretty messed up.

A typical pairwise method will have this one as A>B>C before reversal and C>B>A after reversal.

Note that this example is a case of cyclical preferences, which are inherently challenging for democracy. Still, a method where you can reverse all the ballots and get the same result seems particularly messed up.


I used to know a dozen examples of pathological behavior in IRV, but it has been a very long time since I have studied this stuff.

[Kryptonic]

Good stuff Cap... I've watched a few things about ranked choice and thanks for clarifying it and IRV. Our political system definitely has some improvements to do in how we elect officials.

One thing I did see was how in some states, the candidates were more likely to work together on political ads because they wanted to be bundled together. Was shocking to see to political opponents actually working together... Who'd think?

https://www.washingtonpost.com/election ... n-results/

[Mori Chu]

Thanks Cap, super interesting post. I get that IRV isn't perfect and would be fine with any sort of RCV system that helps break up the two-party system and all the dumb incentive structures that come with it.

[Nodack]

Because what we have now is failing.