Voting systems in the Utah caucuses

In the caucuses in Utah County, many precincts use a voting system called "Instant Runoff Voting" (IRV) or "alternative vote" or "preferential voting."

This system is a fairly standard, reasonable method for selecting one winner from a field of many candidates. The problem is with electing multiple winners (for example delegates to the state convention).

The IRV system can be used to select multiple winners, and it is a good system for doing this, when used correctly. But there are several ways to do this incorrectly.

Many of my mathematical colleagues noticed at the last caucuses that the bad ways were used in their districts, presumably because the bad methods are slightly easier to implement and no one had thought about their problems in advance.

In fact, all voting methods have the potential to produce some paradoxical or counter-intuitive results, but bad ways of using the IRV for selecting multiple winners are much more likely to produce unfair or paradoxical results than the correct way.

It is important to be aware of these problem, so that you can help prevent or correct the problem in your precinct. I have found my precinct to be very open to accepting my ideas about fair voting rules. I encourage you to talk to your precinct about making sure that the bad multiple-winner methods discussed below are not used.

How Instant runoff (preferential) voting works

Here is a quick explanation and example of the IRV and what the right and wrong ways to select multiple winners with one ballot using IRV.

Single-Winner IRV

The IRV method for a single winner is as follows:
  1. Voters write the candidates in order of preference.
  2. If any candidate is the first choice for more than 50% of voters, they win.
  3. otherwise, the candidate who has the fewest first-preference votes is eliminated and the ballots that had him/her first are redistributed to their next preference.
  4. If any remaining candidate has more than 50% of the vote, they now win, otherwise, repeat steps 3-4.

Example: a single-winner race

Assume that there are 5 candidates A-E and 10 voters. The voters list their preferences and the results are as follows:
# of votesPreference order
No one has a majority, so candidate A is eliminated, and A's ballots are redistributed to B, who now has 3. Still no one has a majority so one of candidates C and D are eliminated (by coin flip, since they are tied for last)--say C--and C's votes can't go to A, who is out, so they go to B, who wins.

Multiple-Winner Races

IRV can work very well for multiple-winner races, but it can be very unfair when implemented incorrectly. The difference between the right way and the wrong ways may seem minor, but they lead to very different results. The correct way to elect multiple winners with this same system is to select each winner, one at a time, and start over with the original ballots after each winner is chosen (but eliminating the previous winners).

The Utah County GOP Caucus training video states. ``Filling the second seat is a new election, with a new tally sheet.'' This may seem like a little thing, but it makes a big difference in the final outcome. If you fail to treat the second seat like a new election, you will likely have some weird results.

For the previous example with a two-winner contest, the first runoff gives B as one winner, exactly as before. For the second runoff, return all the candidates to the pool who were previously eliminated.

Since B has already won the first seat, then B is eliminated, so ballots that had B first now go to A. This gives 3 votes to A, 2 to C and D, and 3 to E. Eliminate C or D (by coin flip, since they are tied for last)--say C. So C's votes go to A, who now has 5--still not a majority. D has fewest, so is eliminated, and D's votes go to A, who wins.

So the winners in this method are A and B, which seems reasonable, since A and B seem to rank above most of the others most of the time. Some wrong ways to do a multiple-winner election:

Wrong way #1: Starting from the beginning, just eliminate those with the fewest first-place votes until you have two candidates. This method eliminates A, then C and D.

So B and E are elected, despite the fact that E is ranked last by 70% of voters and A is everyone's first or second choice.

Wrong way #2: After finishing the runoff for the first seat, eliminate that winner and keep on eliminating without returning those previously eliminated, until another winner is chosen. This method eliminates A, then C, and B is the first winner.

B is now removed and B's votes go to D (since A and C are out), this makes B and D the winners, despite the fact that A is everyone's first or second choice and 80% of voters prefer A and C both more than D.

Voting systems are subtle. Do them right.

Elections are essential to a free society, and the voting systems we use have a big impact on the outcomes of our elections. Minor changes to a voting system can have big effects on the final results; so, it is important to ensure that a good system is used and the system is implemented correctly.

Appendix: other Utah County voting systems

In the Utah county caucuses in 2016 each precinct chose from one of the following voting systems:

  1. Plurality
  2. Multiple-round runoff
  3. Instant runoff, also called preferential voting.


Under the plurality system, the candidate with the most votes wins, even if they do not have a majority, and even if most voters have a strong preference against the candidate.

The plurality voting system has the advantage of being fast and easy to implement, but it will often elect a candidate that most of the voters dislike. The more candidates that run, the weirder the results of a plurality election are likely to be.

As an example, in 1992 the presidential election was split three ways: between Bill Clinton, George H. W. Bush, and Ross Perot. Clinton won the election with 43% of the vote, Bush had 38%, and Perot had 19%.

Given what we know of Perot supporters, it seems very possible that if the candidate with the fewest votes (Perot) had been eliminated and a runoff election held between Bush and Clinton, Bush could have been the majority winner. So was the plurality system really fair? Did it reflect the will of the people?

Multiple runoff system

The multiple-round runoff system involves eliminating the least popular candidates and having a runoff among the most popular candidates. Sometimes additional runoff votes must be held until only one candidate receives more than 50% of the vote. This system is much less likely to give a result that voters feel is unfair, but it takes a long time to hold and a lot of work to count the ballots.

Instant Runoff Voting (IRV)

Instant Runoff Voting (IRV) has the advantage of giving a result similar to the multiple-runoff system, and it is usually considered more fair than the plurality method. It takes a little more time than the plurailty system but a lot less time than the multiple-runoff system. It only requires one ballot and the main cost is in the additional counting. IRV is used in Australian national elections, and in several US cities and states. Overall this seems like a good compromise---more fair than plurality and easier to implement than multiple runoff.

The main problem with IRV is that many people implement it incorrectly, and the incorrect implementation is very unfair. The difference between the right way and the wrong ways may seem minor, but these little differences lead to very different results.

Copyright © 2016. Tyler Jarvis.