The Math of Ranked Choice Voting

Prop 1, Ranked Choice Voting, will be on the ballot this November. What is it? What impact will it have? Should Idaho support it?

The Ranked Choice Voting website explains what it is:

“Ranked choice voting (RCV) is an election method in which voters rank candidates for an office in order of their preference (first choice, second choice, third choice, and so on). Ranking candidates is different from simply selecting one candidate or what is known as plurality voting. If a candidate receives more than half of the first choices, that candidate wins, just like in any other election. However, if there is no majority winner after counting the first choices, the race is decided by an instant runoff. The candidate with the fewest votes is eliminated, and voters who ranked that candidate as their first choice will have their votes count for their next choice. This process continues until a majority winner, a candidate with more than half of the vote, wins.”

How it Works

As I contemplate this proposal, I realize it impacts General Elections differently than Primary Elections. This is because the candidates and voters are different.

General Elections

Let’s start with the General Election.

First, we will notice that there will be more than one round of voting. If there are multiple candidates, and no one candidate receives 50% of the vote; under RCV a new round of voting will be triggered with the candidate with the least amount of vote eliminated. If the second round of voting also does not result in a majority vote, a third round is triggered with one eliminated. This process keeps going until the final candidate receives the majority vote.

Sounds harmless, doesn’t it? Until we do the Math.

Let’s do the Math

For ease of understanding, let’s assume that four candidates are running, candidates A, B, C, and D. Let us also assume that the votes received are as follows:

This distribution is typical according to the demographic of our State.

Note that the counts are in percentage. Also, note that there is not a majority winner, so a second round of voting is automatically triggered.

How would the votes in the second round look like? Candidates A, B, and C will keep their original supporters. The supporters of Candidate D will shift their support to other candidates. Before we proceed further, let’s be honest here. This is Idaho, a Red State. In most cases, the lead voter, Candidate A, is likely to be affiliated with a certain political party–a Republican. The other candidates? Perhaps not. The second round will look like this:

With the underdog effect, the supporters of Candidate D will tend to shift their votes to Candidate C, then to B, and a small amount to Candidate A. Ironically, the distribution will likely be the reverse of the ranked-choice order, as illustrated above.

Still without a majority winner, a third round of voting is triggered. The third round and final round in this example will likely look like this:

Similar to the previous rounds, the supporters of Candidate C will favor the underdog. A statistical explanation would be something like this. Candidate C has 25 votes. The majority of them favor the underdog in a reverse ranked-choice distribution. Or Candidate A has 1 rank point, and Candidate B has 2 rank points.

1 Rank point + 2 Rank points = 3 Total Rank points

Distribution for Candidate A: (1 / 3) x 25 votes = 9

Similarly, Candidate B’s distribution is (2 / 3) x 25 votes = 16

Did you notice that the eventual winner is Candidate B, who is not the original highest vote-getter? It happens like this all the time.

Last year, August 19, 2023, Sarah Palin visited Idaho. I was in attendance at that meeting. She told Idaho that because of Ranked Choice Voting, she lost the election, even though she was the overwhelming leader in the early rounds.

Ranked Choice Voting intends to elect the second or third highest vote-getters. Not the first. Frankly, if the supporters of RCV want to elect the most popular candidate, they should leave the voting system the way it is, without changing anything.

Primary Elections

In the Primary Elections, the situation is a bit more complicated in Idaho. In other States, registered voters of each party vote in their respective Primaries. So, the Republicans vote in their Republican Primaries, and the Democrats vote in their Democratic Primaries. In the last Primary Election (in my home State of Idaho), I was offered the choice to vote in either the Republican or Democratic Primaries. Still, the voter base is more homogenous, and I believe the proper candidates won. Nonetheless, I can see that a fractured District would end up supporting the wrong candidate if Prop 1 passed.

What we can expect from RCV?

I did the Math. It is not difficult to illustrate that the original leading candidate would end up losing the election. I did other scenarios with different percentages of votes. The result is the same. The original candidate with the highest number of votes loses the election.

The promoters of Ranked Choice Voting are aware of this. It is for this reason that they are promoting it. Not for democracy, but the subversion of it.

This is not all. With RCV, we can expect to see more candidates jumping in. While this may sound good to you, many of the lower ranked candidates will use this to influence the political system. I intend to write a follow-up article to elaborate on what the Founding Fathers intended our election system to be. My next article will serve to illustrate the philosophical flaws of Ranked Choice Voting. See you in about a week.