Would a different style of voting have changed the 2016 election? We tested 5 alternatives.

We all know who won the presidential election according to the Electoral College: Donald Trump. And we all know who won the presidential election by popular vote: Hillary Clinton.

But who would have won if the US used instant runoff voting, a kind of ranked voting system utilized in Australia, Ireland, and San Francisco, and which Maine just voted to adopt for all its elections?

To find out, I teamed up with David Shor, a senior data scientist at Civis Analytics, a Democratic data and polling firm formed by veterans of the 2012 Obama campaign (like Shor). He added a ranking option to a Civis online poll of 1,084 registered voters who report having voted in 2016, conducted on November 15 and 16. The results were then weighted to reflect the election outcome and Civis’s best guess as to the demographics of the 2016 electorate.

Instant runoff voting works by eliminating the worst-performing candidate and distributing their votes to the others, using the rankings their voters provided. For example, the first candidate eliminated in Civis’s poll was Darrell Castle, the nominee of the far-right Constitution Party. So each respondent who put Castle first saw their votes go to their second-place candidate. This process is repeated until one candidate has a majority. It goes like this:

Javier Zarracina/Vox

The result, after supporters of Castle, Jill Stein, Evan McMullin, and Gary Johnson see their votes distributed, is a narrow Clinton victory — just as would’ve happened if the US used a traditional, first-past-the-post popular vote system to elect the president.

Other voting systems also show Clinton wins — but not all of them

But there are other ranked voting systems too. Many experts don’t like instant-runoff voting because there’s a chance that it won’t elect the candidate who’d win against every other candidate in a one-on-one race. That candidate is known as a “Condorcet winner,” after the 18th-century French mathematician Marquis de Condorcet.

As it turns out, the 2016 election has a Condorcet winner, according to the Civis poll. It’s Hillary Clinton, who bests each other candidate in a one-on-one race:

Vox / Javier Zarracina

Some ranked voting systems would change the result of the election, however. One common method, used for determining the winner of the Heisman Trophy and the MLB MVP awardee, is the Borda count, devised by another 18th-century French mathematician, Jean-Charles de Borda. The Borda count gives a set number of points for each ranking a candidate gets. For example, in a six-candidate race, the first-ranked candidate would get six points, and the last-ranked one would get one. All the points from each person's ballot are added up, and the person with the most points wins.

This is a somewhat ham-handed way to compute results, and it gives some very weird results; like instant-runoff voting, it doesn't always elect the candidate who'd beat all the others. In the 2016 election, it would’ve resulted in Gary Johnson winning the presidency: Trump would get the second-highest number of points, then Clinton very closely after, then Stein.

Lastly, some voting experts have argued that neither rankings nor first-past-the-post voting methods are ideal, and instead favor what’s known as “approval voting.” In that system, voters just put a check mark next to each candidate they’d be okay having as president. So someone who supported Bernie Sanders in the Democratic primary could put a check next to both Hillary Clinton and Jill Stein, but not next to Gary Johnson or Donald Trump. The candidate with the most checks wins.

Civis asked respondents if they “strongly approved,” “somewhat approved,” “somewhat disapproved,” or “strongly disapproved” of each of the six candidates included in the poll. It then added up the percentage strongly or somewhat approving of each candidate, and compared them. The result was a Clinton victory:

Vox / Javier Zarracina

A more complicated alternative to approval voting is “range voting,” where instead of merely putting a check or not, voters rate each candidate on a scale of, say, one to five. The ratings are then added up and the candidate with the most is the victor. You can think of this as voting the same way you rate songs in iTunes: giving five stars to your favorite candidate, then maybe three to one you agree with on some issues but not others, and so on.

You can use the Civis data to simulate range voting as well. The strongly/somewhat approve/disapprove question functions as a rating on a scale of 1 to 4, with 1 being strongly disapprove and 4 being strongly approve. The data suggests that if you evaluate the results this way, Trump emerges as the winner, with Clinton shortly behind him.