Speak Up:Mock Ranked-choice Voting Election Delivers Surprise

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Walker, Douangmany Cage and Hanneke Elected In Simulation

The Indy’s mock election for Councilor-At-Large using ranked-choice voting illustrates both the richness and the intricacy of the voting method that Amherst will use in future local elections pending approval by the state legislature.

The first lesson learned was that determining a winner of a ranked-choice voting (RCV) election involves a series of computational steps that are not practical to perform manually on a large scale.  Fortunately, the turnout for the mock election was light, with 44 ranked votes cast, and the task of calculating winners could be accomplished using a simple spreadsheet.

To begin, we need to understand the RCV algorithm.  The Councilor-At-Large election must recognize three winners based on the votes cast.  The Amherst Ranked-Choice Voting Commission examined five different methods for handling multiple-winner contests and recommended an approach with the highfalutin name of Weighted Inclusive Gregory Method or WIGM.  The Northampton Ranked-Choice Voting Committee has also settled on using WIGM, reportedly because it is the only method supported by the Dominion voting machines that the city owns.

I won’t dive too deeply into the weeds, but the process starts with determining the threshold number of votes that a candidate must achieve to win.  In the case of the 3-seat Councilor-At-Large contest, this number is equal to 25% of the total votes + 1.  In our 44-vote mock election, the threshold is 12 votes.

Let’s look at how the election played out.

Voters assigned rankings to the six candidates, though they could choose not to assign a ranking to one or more candidates.  Results showed that a certain amount of bullet voting was done.  17 voters ranked all six candidates; 2 ranked five candidates; 14 ranked four candidates; 10 ranked three candidates; and 1 voter ranked only two candidates.

The mock election ballot was set up as an RCV ballot and not a traditional plurality voting ballot, but for comparison’s sake let’s suppose that we can measure the candidates’ performance in a plurality election by counting votes received in ranks one, two and three.  Here are the counts.

CandidateFirst-place votesSecond-place votesThird-place votesTotal Votes
Robert E. Greeney25916
Viraphanh Douangmany Cage1418032
Andrew J. Steinberg3429
Mandi Jo Hanneke4318
Ellisha M. Walker2081139
Vincent J. O’Connor162027

The top three plurality vote-getters would have been Ellisha Walker, Vira Douangmany Cage and Vince O’Connor.

Turning to the ranked-choice method, the WIGM process required four rounds to determine three winners.

Ellisha Walker and Vira Douangmany Cage were immediately elected, because their first-place vote totals exceeded the threshold of 12. In WIGM, surplus votes above the threshold are apportioned to the remaining candidates according to winners’ votes’ second-place rankings.

The mathematics of the WIGM method involves fractional votes.  After surplus votes were transferred the totals were

CandidateTotal votes after Round 1
Robert E. Greeney2.72727
Andrew J. Steinberg3.00000
Mandi Jo Hanneke4.18182
Vincent J. O’Connor2.09091

Since none of the remaining candidates have achieved 12 votes, the candidate with the lowest vote total is eliminated, and his votes are apportioned to the remaining candidates according to the rankings in these votes.  After Vince O’Connor’s votes were transferred the totals were

CandidateTotal votes after Round 2
Robert E. Greeney4.81818
Andrew J. Steinberg3.00000
Mandi Jo Hanneke4.18182

There is still no candidate with 12 votes, so we need another round.  This time Andy Steinberg has the lowest vote total, so he is eliminated, and his votes transferred to the remaining two candidates, like so

CandidateTotal votes after Round 3
Robert E. Greeney4.81818
Mandi Jo Hanneke7.18182

At this point neither candidate has reached the winning threshold so we must exclude Bob Greeney who has the lowest number of votes.  This leaves only Mandi Jo Hanneke standing, so she is declared winner of the third Councilor-At-Large seat.

Interestingly, we see that RCV produced a different third-place winner (Mandi Jo Hanneke) than our projected plurality third-place winner (Vince O’Connor).  One of the benefits of RCV, according to fairvote.org, is that in multi-winner contests it “allows diverse groups of voters to elect candidates of choice.”

Vince O’Connor supporters may not appreciate this aspect of the algorithm, but Mandi Jo Hanneke can be viewed as belonging to a faction that felt strongly that she and Andy Steinberg should represent them on the Town Council.  RCV allowed this faction to have one of its Councilor-At-Large candidates triumph in the mock election.  Vince O’Connor, by virtue of having only one first-place vote, was eliminated from the RCV race early on.

My thanks go out to the Amherst Ranked-Choice Voting Commission for their comprehensive 53-page report and to James Gilmour for his indispensable white paper describing in detail how WIGM was applied to the local government elections in Scotland in 2007.  And thanks to you readers who took the time to participate in this demonstration of ranked-choice voting in action.

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3 thoughts on “Speak Up:Mock Ranked-choice Voting Election Delivers Surprise

  1. Thanks, Rob, for pointing out Arrow’s Theorem, which essentially states that no ranked-choice voting system can be perfectly fair and representative 100% of the time.

    Perhaps RCV advocates can take heart in Nobel Prize winner Kenneth Arrow’s remark that “Most systems are not going to work badly all of the time. All I proved is that all can work badly at times.”

  2. That’s a good summary, Jeff. It’s reminiscent of an aphorism often attributed to Abraham Lincoln (at least apocryphally, from the years before the U.S. Civil War), but more reliably to the 16th century poet John Lydgate:

    “You can please some of the people all of the time, you can please all of the people some of the time, but you can’t please all of the people all of the time.”

    Ironically – especially in the context of recent events surrounding missing ballots and disqualified signatures – it seems that Lincoln’s version substituted the verb “fool” for the the verb “please”!

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