New Year, New Voting System?
by Ukamaka Ezimora
JAN. 15, 2021 | 6:14 PM
What’s your new years’ resolution? State legislatures’ resolution is to start 2021 with focus on election procedures.
The predominant philosophy around voting within the United States (and the Western world) is plurality voting, the ‘one person’, ‘one vote’ methodology. Controversial elections such as last term’s and this terms’ have left voters on both sides feeling like their voice wasn’t heard. Though some see plurality as the common-sense approach, many people see it as the source of much unfairness in election results. As these concerns compound with the coronavirus pandemic and upheaval over racial inequality, the United States must seek to address its problems by empowering people to have a stake in the electoral process. This can be accomplished through reform. 2020 has the opportunity to stimulate massive improvements in the American electoral system. The most common issue with plurality voting is the matter of vote splitting, in which multiple candidates run on similar platforms and each gets a share of (thereby "splitting") the same electorate. When this happens, a candidate disliked by the majority can still win a race since the vote against them is split.
Within the US, the most common form of vote splitting is the spoiler impact, in which a third candidate draws a significant share of the votes from either the Democrat or the Republican that would have otherwise won. The 1992 triumph of Charge Clinton over George H.W. Bush was the result of (Republican) vote splitting by the spoiler candidate Ross Perot. The 2000 triumph of George W. Bush over Al Gut was the result of (Democrat) vote splitting by spoiler candidate Ralph Nader.
Vote splitting can be successfully avoided by changing the voting strategy. There are different approaches to this conclusion, each with its pros and cons. Many of them depend on the use of ranked ballots. Ranked choice voting allows voters the option to rank candidates in order of preference: one, two, three, and so forth. If your vote cannot help your top choice win, your vote counts for your next choice. Once voting is conducted in this way, there are various approaches to decide which candidate wins.
PluralityThe candidate with the most first-place votes wins the election. The simplest, and most familiar, is the Plurality Method. This is the conventional one person, one vote method we use today in most elections. In this case, the winner is the candidate that gets the most votes. To do this with the survey data: I gave a vote to only the top-ranked superhero in each survey entry (the one with a ranking of 1) and added up the totals.
Borda CountEach place on a preference ballot is assigned points. The candidate with the most points wins. This method was developed by 18th century mathematician Jean-Charles de Borda and is used today to decide the MLB MVP of the year and the ranking of the NCAA college teams. In this method, the voter ranks each candidate numerically and the winner is decided by adding points given to each candidate according to their ranking. Last place receives one point, next to last place receives two points, and so on. Thus, if there are N candidates, then first-place receives N points. Now, multiply the point value for each place by the number of voters at the top of the column to find the points each candidate wins in a column. Lastly, total up all the points for each candidate. To do this with the survey data: I gave points to each candidate in reverse proportion to their ranking based on the total number of options. So a ranking of 1 gives that candidate 12 points and a ranking of 2 gives 11 points...etcetera. If a candidate is not ranked, they get zero points. The superhero with the most points wins.
CondorcetThe candidate who would beat every other candidate in a head-to-head majority vote is the winner. This method was developed by the Marquis of Condorcet, Marie Jean Antoine Nicolas de Caritat. Condorcet was an 18th century French philosopher and mathematician and a rival of Borda. Today, Condorcet voting is used by the Wikimedia foundation and the Linux community for most internal elections. In Condorcet voting, the winner is decided by determining the candidate that would beat every other candidate in a hypothetical head-to-head match. To do this with the survey data: I used the rankings given in the survey to determine the winner by considering every possible pair of superheroes. For example, if Batman is paired against Superman I would count both the number of people who have ranked Batman better (that is, with a lower number) than Superman, and the number who have ranked Superman better than Batman. If Batman is preferred by more people then he is the winner of that pairing. I repeated this procedure for every possible pairing. The superhero with the most victories is the winner. If there is no clear winner, the Condorcet method ends up in a draw.
ApprovalThe voters decide whether they approve or disapprove of candidates in an election. The candidate with the most approval votes is the winner. This method was developed by Cornell University mathematician Robert J. Weber in the 1970s. Today it is relatively uncommon outside of professional organizations, but the United Nations uses it to elect its Secretary General. In approval voting, voters simply approve or disapprove as many candidates as they want. The winner is whichever candidate gets the most positive votes. To do this with the survey data: I found the average ranking for each survey entry. Any ranking below the average would count as an approval and anything above would be a disapproval. For example, if a survey entry ranks four superheroes (the average would be 2.5) the rankings 1 and 2 would be approvals while 3 and 4 would be disapproval. If I have an entry with five superheroes ranked (average 3) rankings 1 and 2 would be approvals, while rankings 4 and 5 would be disapproval. Ranking 3 would not count at all. After doing this for every survey entry, you count the total number of approvals, and the candidate with the highest number wins.
A survey (512 participants) was conducted by my professor, Alejandro Gutierrez, who asked students to rank their favorite superheroes from 1-12, with 1 being the best.
Each column is a single voter’s “ballot” or survey entry. Every row shows the frequency of which that superhero received that rank. This "ballot data" has been processed through the four voting methods described above.
What do the results show?
In this presidential race (Batman took that term quite literally) Iron Man always won. Though this result wasn’t intentional, and was purely due to the nature of the data (everyone loves Iron Man), it goes to show that no voting system is perfect. Read about the flaws of each here. Though voting reform could make a difference is who’s in government, this mock election showed the alternate reality wherein which it made absolutely no change. Making a change in government is a mix of efforts. If you want to make a difference, you may need to seek change in not only the system, but the people. So educate yourself about the changes being made in your city, because as shown above, sometimes it’s not the big things, but the little things that count.
Press Play. If the window is too small, click the red link to resize.
On a scale of 1-12 (1 being the highest), cast your rankings.
Based on what you learned about the voting types above, guess who you think will win. Select that candidate with the yellow dropdown.
Click a button to simulate that voting method.
To go more into depth about voting paradoxes, how to compare voting methods, general voting theory, and other voting methods that weren’t covered, read more from these sources: