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Social Choice: A Closer Look At The Math Behind The Way We Vote

By Katie Campbell
Published: Wednesday, November 4, 2020 - 12:56pm

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An early voting center in north Phoenix on Oct. 22, 2020.
Sky Schaudt/KJZZ
An early voting center in north Phoenix on Oct. 22, 2020.

The country is still waiting and waiting and waiting some more for final results in last night’s elections.

No one ever said democracy is perfect, but some people are certainly wondering whether our current system is really as effective as it could be.

Andy Jennings is a mathematician who has spent a lot of time looking at the numbers behind the way we vote — specifically voting systems he says could be more effective than what we’re seeing play out this morning.

“So, if you want a group of people to make a decision — and it could be a political decision like we’re talking about now, but it could also be like a group of six or seven people deciding which restaurant to go to for dinner. Everyone has their preferences. How do you take the preferences of the people and submit them somehow, write them down, and then, choose the best restaurant for the group to go to,” he said.

“So, it’s the problem that the mathematicians and the economists call social choice —  how does a group make a decision?” Jennings said. “And there’s a lot to say about social choice. There’s a lot of mathematics involved. There’s psychology. There’s economics. There’s game theory. There’s a lot of different subjects involved. It does, it completely applies to politics and elections and voting and the way we vote in huge groups when we make these political decisions.”

There are races where your choice may be between A or B, or even C, like in the presidential race this year, which included Libertarian Jo Jorgensen. But there are also races where you choose two or three candidates, as it was with the Arizona Corporation Commission.

Consider the crowded primary races of the last two presidential cycles, though. Voters were asked to narrow wide fields down to just one candidate per party for the General Election. Mathematician Andy Jennings says social choice asks the question: Is that right?

“How do you even ask the people what their preferences are? Is it the right thing to ask for each person to vote for one?” he says.

“You may have heard of other voting systems where people are allowed to rank multiple choices,” he adds. “They can rank their first choice and then their second choice and their third choice. And in some places, in stops there - you can only rank three choices on the ballot when you’re actually voting.

“And in some places, it goes further — you can rank four, five, six, seven. You can rank all your choices, and that’s the actual ballot that you turn in. So, it’s a different way to vote. It’s a different way to express your preferences. It’s a different way to actually have the opportunity to say who you like second-best and who you like third-best.”

Then, there are many ways to choose the winner out of those preferences. And, as with so much in politics, that has led to long-standing debates around how best to do that.

As with any system, that’s the real trouble. But considering the trouble we’re seeing today and in past elections, some state and local governments have been willing to try something different.

Maine actually used the ranked-choice voting model in this election, including in the presidential race. And that decision is now playing a key role in one of the most competitive U.S. Senate races in the country: the contest between Republican Sen. Susan Collins and Democratic challenger Sara Gideon, as well as two independent candidates.

A winner will only be named outright if they receive 50% plus one of the total votes. If no one does, the lowest-ranked candidate will be dropped and another round of ranked-choice will take place until a candidate reaches that simple majority threshold.

“And there are other municipalities and states around the country that have tried ranked voting in the past,” Jennings says. “There’s also growing support for these graded-choice systems. The simplest one is called approval voting, so you just look down the list of candidates and you give each one, kind of, approve or disapprove.”

That system would actually be compatible with our existing voting machines, he says.

“So, if we program these machines to, say, let people vote for president — there’s four candidates, and let them vote for up to four candidates — then these machines could count an approval-voting ballot. It would just say ‘vote for all that you approve’ instead of ‘vote for one.’”

Now, that may be hard to execute on a nationwide scale. But Jennings says it’s worth considering alternative models that may give voters more choices.

“We’ve had this voting system for hundreds of years, where a third candidate can act as a spoiler and can ruin the election. And so, you can totally see why third and fourth candidates are excluded from the debates or excluded from the discourse or excluded from being able to participate,” he says. “But if we had a better system and that spoiler effect wasn’t such a problem, then we could have better debates, we could have more voices, we could have more choices in the whole process.”

For now, the country is left waiting — and some voters may be left wanting.

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