A Mathematical Approach to Moderacy

Neha Mukherjee, the editor for smerconish.com, is a rising sophomore at Brown University. She is a Pre-Medical student concentrating in Political Science and has a profound interest in journalism. A recent graduate of the Episcopal Academy, she was born and raised in the Philadelphia suburbs.

Neha Mukherjee, the editor for smerconish.com, is a rising sophomore at Brown University. She is a Pre-Medical student concentrating in Political Science and has a profound interest in journalism. A recent graduate of the Episcopal Academy, she was born and raised in the Philadelphia suburbs.

President Trump continues to push extremely conservative reform. Democratic candidates seem to be shifting to target a more progressive, liberal base. Yet, a recent Gallup Poll stated that 42% of Americans deem themselves to be Independents, not aligned with either political party.  A disconnect? I think so.

The separation between our ideology as citizens and the candidates that we elect could be found in our voting method.

It is difficult to assure that a voting method is always “fair.” According to Social Choice Theory, there is no one definition of “fairness.” Each electorate has different needs in their leader and thus, the idea of “fairness” is difficult to quantify. Anytime we set out to vote, whether it be a school election, a corporate affair, or the presidential race there is always a third party involved in deciding and executing a voting method, whether it be a school, business, or government. If an unjust voting method is chosen by this third party, that is essentially the same has having a rigged election and rejecting the concept of “fairness.”

Some voting methods also give way to prioritizing strategy over ideology. For example in our current method, what is known as “the third party dilemma” causes people to strategically vote for someone they feel may realistically win, rather than someone with whom they share similar beliefs. These types of issues all play into our inability to elect a candidate that best matches the ideology of the majority

We currently operate under the ever contested electoral college, in which states are afforded electoral votes. These electoral votes are based on a plurality voting method within each state. Plurality voting consists of casting a singular vote on one day for one’s most prefered candidate. But often, plurality voting, leaves voters susceptible to placing strategy over ideology and could be a prime reason, more “moderate” candidates have not been chosen in previous election cycles.  

This leaves us to question the way that we vote. Throughout history, other countries have utilized a variety of other methods. For example, France uses a runoff method, in which voters vote twice. Their first time voting is among all of the available candidates. When they go to the polls to vote a second time, only the top two candidates from the last vote are available options. This eliminates the “third party dilemma,” as people can freely cast their first vote for whoever they truly like most and their second vote can go towards a candidate that can realistically win. This is not to say that the US should adopt this exact method; America has long struggles with voter turnout and we may not be at a place to require a multistage voting method.

Yet, it may be worth examining other types of voting methods to find one that will elect candidates that best serve the current needs of the country. Some alternative ways of voting include ranked choice voting methods, where instead of casting a single vote for a candidate, voters are asked to provide a list, ranking their preference of the candidates. The following examples show different voting methods that could be considered for use in the United States.

Instant Runoff Method  

Instant Runoff is a preferential voting system in which a ranking of all candidates is submitted in one trip to the polls. The top two candidates are selected based on the highest numbers of first place votes. Then a second round is performed with just these two candidates and the winner is chosen based on whoever has the higher number of first place votes.

In the scenario below, the electorate consist of 25 people. A,B,C, and D are different candidates. The numbers represent the number of people who had that voting preference (ie: 10 people had the ranking of A (1),C(2),D (3), and then B (4)). Since candidate A receives 10 first place votes and candidate B receives 8 first place votes they move onto the next round where candidate B would ultimately win because he or she has 13 first place votes as opposed to candidate A who has 12. More people were tolerant of B and he or she ultimately wins the elections as they higher rankings overall in comparison to A.

Figure 1. Instant Runoff Matrix, Winner: Candidate B

Figure 1. Instant Runoff Matrix, Winner: Candidate B

Hare Method

The Hare Method, essentially the “most preferred method”, employs  ranked choice voting where candidates with the highest number of first place votes move onto the next round. The candidate with the least amount of first place votes is eliminated and a new matrix is created. This continues until two candidates are left and the candidate with the most first place votes wins.

Figure 2. Hare Matrix, Winner: D

Figure 2. Hare Matrix, Winner: D

Reverse Hare Method

The Reverse Hare Method is known as the “least hated” voting method, in that it selects for the candidate that has the least amount of last place votes. Essentially candidates are eliminated if they have the greatest amount of last place votes, until a winner is chosen. This method assures that while the candidate chosen may not be the most beloved, he or she is definitely not the most hated. A method, like this could fare well in the US if we hope to reduce polarization in coming election cycles. With this method we could have seen a more neutral candidate come out of the 2016 election, instead of a candidate that is strongly loved by some and profusely hated by others.

Figure 3. Reverse Hare Matrix, Winner: Candidate C

Figure 3. Reverse Hare Matrix, Winner: Candidate C

Borda Count Method  

The Borda Count Method is another ranked voting method in which points are attributed to first, second, and third place. A candidate receives a certain number of points for each ranking that they are selected for. These point totals are then added up and the candidate with the highest point total wins. In the case below, 1st place is given 3 points, second place is given 2 points, and 3rd place is given one point. In order to win this election system, a candidate does not necessarily have to have the most first place votes. It is more critical to have a larger number of people who rank you somewhere in the top three, than to have only first place votes and a number of last place votes.  Again, this method may favor moderacy more than our current voting method.

Figure 4. Borda Count Matrix, Winner: Candidate A

Figure 4. Borda Count Matrix, Winner: Candidate A

The exploration of these various approaches should not suggest that we must immediately change our current voting method, but rather that we should not blindly follow a design that does not serve the current needs of the nation. It is possible that if one of these methods were used, it would be more realistic for a third party candidate to run and succeed in securing the presidency. The Instant Runoff, Hare, Reverse Hare, and Borda Count approaches each have methods in place to promote moderacy; this ensures that more people are “ok” with the selected candidate, in contrast to methods where people either love or hate the elected official, as we saw in our last election cycle. In striving to fix the polarized state of the country, it is critical that we look at the origins of our problem: the way that we choose candidates to begin with. It is up to us as citizens to question the status quo and challenge our leaders to utilize methods that we feel will most benefit the country. This will allow us to tackle the roots of the issue and hopefully elect a candidate that more of the electorate can support in years to come.