Assistant professor Kebra Ward helps students with some of the math involved in the different voting systems.
NORTH ADAMS, Mass. — Massachusetts College of Liberal Arts students recently learned the pitfalls of plurality voting and got a crash course in ranked voting.
Members of the Quantitative Understanding Across the Curriculum Committee looked to open students' eyes with the help of a little math — and some candy — to demonstrate that not only are their different methods of voting in an election but some, they believe, are vastly fairer.
"We want people to know there are different ways to vote and I think a lot of people think you just fill out a ballot, say what you want to say, and that is it you are done," assistant physics professor Kebra Ward said. "There are other ways to do it."
Erin Kiley, an assistant mathematics professor, said ranked choice voting, in which voters rank candidates instead of just casting one vote, is used in Australia, in local elections in Amherst, and for state and congressional elections in Maine among others.
She said other communities throughout the country have shown an interest in different voting systems and that the "ball is rolling."
"Now seems to be the right time to talk about ranked-choice voting," Kiley said. "There has been so much buzz around it and this is a mathematical topic and we thought we should pull together a workshop."
Samantha Pettey, an assistant professor of political science and public policy, first gave the group of 26 students an overview of electoral laws and the consequences of having single-member districts with plurality voting — the current voting statewide system in which the candidate with the most votes is the winner.
"When you have single-member districts with plurality ... you don't need a majority to win ... you could easily win with 21 percent," she said. "Whoever has the most votes wins ... this type of voting can lead to a two-party system."
Kiley handed out workbooks so students could work out how the different voting systems function.
"In math, we think of an election as a kind of decision-making process ... it is just a way of using math out in the wild," Kiley said. "With plurality voting, the candidate with the most votes is declared the winner but that type of method might leave out critical information about how each voter ranks the entire list of candidates."
Students were given a table with 21 preference ballots each with rankings of letters A, B, C and D. Using the plurality system, students tallied up all the first-place ranked letters and found that the letter A received the most votes with eight first-placed rankings. B came in second with seven first-place ranked votes.
Kiley then introduced a "fairness criterion" that she said is used to test an election system to see if it is fair and actually reflects the will of the voters.
The group first learned about the "majority winner criterion" that Kiley explained is if any candidate receives a majority of first-place votes the election system should declare that candidate the winner.
A majority vote is 50 percent of the number plus one rounded down to the nearest whole number. This means in the mock election, a candidate would need 11 votes to hold the majority.
Kiley said if A is the winner but only has eight votes, this would not be a majority, therefore, plurality voting fails this criterion.
"If most people want someone in a system that is fair that candidate would be declared the winner," she said.
Kiley went on to Criterion 2: The "majority loser criterion" in which if any candidate receives a majority of last-place votes then the election system should not declare that candidate the winner.
Students tallied up the last-place votes and were surprised to find that candidate A was the majority loser.
"Does that unsettle us a little bit? The majority of people ranked A as last, but A won the election anyway," Kiley said. "So the plurality system does not satisfy the majority loser criterion."
Kiley went on to describe another downside of plurality voting — the "spoiler effect." She said when two or more candidates are ideologically similar they can divide voters in a plurality system.
She also referred to this as the "Ralph Nader Effect."
"In the 2000 presidential election in Florida, George Bush had 537 more votes than Al Gore. Nader had 97,421 votes in Florida," she said. "People feel a lot of these votes would have gone to Gore if Nader was not in the election ... that is why they call it a spoiler candidate: they spoil everything."
In criterion 3, the "independence of irrelevant alternatives," if a non-winning candidate is removed from the ballot it should not change the winner of the election.
Kiley asked the students to turn again to their ballots and noted that B and C were often ranked near each other. Kiley asked that the students remove C.
The students found that removing C again changes the results of the election in a plurality system and B is the winner instead of A.
With a deeper knowledge of the mathematics behind plurality voting, the group looked at a ranked voting system.
"Let's use more information from the preferential table than just the first row. We have this whole table let's use it," she said. "So ranked-choice method refers to any method that uses more than just the first row."
Kiley said the most popular ranked-voting system is the instant runoff system.
"If they win the majority of first-place votes then the election is done, that candidate is declared the winner. If there is no one that won the majority of first-place votes you eliminate the candidate with the smallest number of first-place votes," she said. "You recount the first-place votes and follow those steps until a winner is decided."
Students went through rounds eliminating majority losers until they came upon a majority winner, which in this case was candidate B.
Kiley said instant runoff satisfies the majority winner and the majority loser criterion but not the Independence of Irrelevant Alternatives Criterion.
She said preference tables also allow head-to-head comparisons of candidates and explained another fairness criterion, the Condorcet Criterion, which states if a candidate wins in every head-to-head comparison with other candidates then that candidate should be the winner.
The Copeland's Method election system scores candidates on head-to-head comparisons. Candidates are given one point for a win and a half a point for a tie. The candidate with the highest score is the winner.
Kiley said although this satisfies Criterion 4, a tie in this system is possible. She added that Copeland's method meets all the criterion except the Independence of Irrelevant Alternatives.
The Arrows Impossibility Theorem, which she summarized as elections with three or more distinct alternatives that can satisfy all criteria simultaneously.
"There will always be a tradeoff between certain fairness criterion," she said. "The system voters chose to use depends on what they value in terms of fairness criteria. ... If you want to expand the possibilities of fairness criterion in an election the simple thing would be to switch to a ranked-choice ballot."
She added there are more than just four fairness criteria.
Meghan Molinari of Voter Choice Massachusetts demonstrated the possibilities in election systems where students voted for their favorite candy after a taste test of course.
In a plurality system, Butterfinger was the clear victor, however, after switching to a ranked system, Nestle Crunch Bar came out on top.
Assistant professor Samantha Pettey goes over electoral law before delving into different voting systems.
Molinari gave the students a brief overview of the groups bipartisan efforts to place a ranked voting system in Massachusetts.
"This will have a huge impact that will have a ripple effect not only in Massachusetts but throughout the rest of the country because all eyes are kind of on us," she said. "We are the next state closest to passing ranked choice voting. We have a huge population and if we can do it any state can do it."
Some of the students already knew about ranked voting.
"I have learned about this before in high school, but I came here because I wanted to be more informed," student Paul Davila said.
Some other students heard about ranked voting for the first time and were already converts.
"I think that it is definitely an interesting way I didn't know about," student Samantha Harrington said. "I think that it would get more people's voices heard."
Molinari also pointed students to a table set up in the Bowman Hall classroom where they could register to vote.
"Hopefully one day we will have ranked voting, but it is better to go out and cast a vote in the system that we have than not at all," she said.
The MCLA faculty agreed.
"Make sure you get out there and vote in November," Ward said. "You have a voice and you should use it no matter what it is."
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