Game Theory and the 2016 US Presidential Election

Game Theory and the 2016 US Presidential Election

“The United States is the only country that elects a politically powerful president via an electoral college and the only one in which a candidate can become president without having obtained the highest number of votes in the sole or final round of popular voting” – George C. Edwards, 2011

The 2016 US election was a strange one for many reason, but what I’m going to focus on is how Donald Trump was able to become the 45^th President of the United States despite losing the popular vote to Hilary Clinton, as well as the game theory behind voting for a third party candidate.

Winning Without the Popular Vote

Ideally an election should represent what the people want. In the US we have a one-person one-vote principle that allows every citizen to have a say in the election process. We will see that even if every citizen in the US were to vote, our current system still allows a candidate to win without receiving the majority of the popular vote.  

Lets start out by going through the election process in the US for those of you who may be unfamiliar with it. 

-       Each citizens casts their individual vote (this is called the popular vote)

-       Votes are tallied for each state.

-       Each state plus Washington D.C is given a certain number of electoral votes roughly based on their population (for example California has 55 electoral votes while Wyoming only has 3).

-       Every state (excluding Maine and Nebraska) implements a winner-take-all system where a candidate either receives all of a states electoral votes or none of them.  

-       There are 538 total electoral votes, so if a candidate receives at least 270 of those votes, they have the majority and win the election.

In the history of the United States there have been 58 elections. Out of these 58 elections, 6 of them have run into problems with the system, and 5 of them have resulted in a winner that did not win the popular vote. How can this happen? Well, lets try to apply this voting process to a simpler example.

Today we’re going to have an election where we vote for our first Game Theory president! Yaba-daba-doo!!!!

We’ll have two candidates, Jack and Haley. We’ll also have 4 states that hold different numbers of electoral votes based on their population. These are the states along with their population and number of electoral votes. 

House (Carolina, Michael Lawrence, William) = 3 electoral votes

Classroom (Madison, Greg, Molli, Katie, Nevin, Riley, Zach, Gavin) = 8 electoral votes

Suite (Andrew, Matt, Cam, Patrick, Mac) = 5 electoral votes

Back (Sonny Jim) = 1 electoral vote

For those of you who don't know, this is Sonny Jim. He lives in the Back and we're gonna take over the world someday. 

We’ll implement our one-person one-votes principle, and have a winner-take-all structure when counting the electoral votes.

Here are the results to our election.

Because the majority of the house voted for Jack, he receives all 3 of the House’s electoral votes.

Haley won the vote in the classroom by a landslide, so she receives all 8 of the Classroom’s electoral votes.

Jack won the Suite vote so that’s another 5 electoral votes for him.

And finally Jack was able to win over Sonny Jim and receive the last electoral vote from the Back. This is Sonny Jim. We’re taking over the world.

When we add up all of the electoral votes we see that Jack will be our new game theory president because he received 9 of the 17 electoral votes. This should seem strange because it was actually Haley who won the popular vote 11-6. We can see this same problem occur in US elections, where it is actually possible for a candidate to win even if they only receive 22% of the popular vote in a 2-candidate race since margin of victory in each state doesn't matter. 

For this reason, candidates change their campaign strategy when they know that they can win the electoral vote by doing things like capturing swing states when they really don’t care about the population as a whole. So in our example, if these results were just projections and

, how might Jack or Haley strategize their campaign? Do certain voters have more of an impact than others? Feel free to comment any thoughts you might have. Also, this is Sonny Jim. We’re taking over the world.

Third Party Voting

Another thing that was strange about this election was that both of the candidates kinda sucked. Nobody wanted to vote for Hilary or Trump, so many people decided to vote for a third party candidate. There are arguments for and against third party voting. Some say that it is essentially a waste of a vote, while others believe that it is a way to make their party to take their issues seriously. People don’t want their party to assume they automatically have their vote. The idea is that if the Democrats saw that voters from their own party voted for a third-party candidate because they felt strongly about a certain issue, then the Democratic nominee would be more likely to address that issue in the next election. However these third party voters would be taking a risk because while they want to make a statement, they would still rather see their party win. If we were able to accurately predict an the outcome of an election, we would be able to conduct a strategy in which we could make a statement to our own party while they still win the election.

Lets think about how this could work.

Say there’s a large group of republicans who care deeply about gun control. They still would rather see their republican candidate win than lose, but if they vote for a third party candidate because their more agreeable views on gun control then it would send a message to their party that that issue needs to be taken more seriously. So the best possible outcome for this group of republicans is to maximize their number of third party votes while their candidate still wins the election but by the smallest margin possible.

Lets consider a potential issue. What if this entire group of republicans voting third party resulted in their candidate losing the election? In this situation there would be no pure strategy among this group of republicans. In other words they can’t all vote third party because they would lose the election, but they can’t all not vote third party because then they wouldn’t be making a statement about their views on gun control. We could tell a certain proportion of the group to vote third party while the rest voted for the republican candidate, but what if communication wasn’t that easy? What if we needed to make one statement about a strategy that every person in the group would implement when they’re filling out their ballot? Comment on any ways you think this problem could be solved by telling each member of the group to do the same thing. 

While it might seem bizarre, the best way to accomplish this problem is by using probability. If every member of this group of republicans left their vote up to probability, we could rely on statistics to get us our best outcome. If we knew that we need 50% of the group to vote third party for the best possible outcome, we would tell the group of voters to leave it up to chance and flip a coin to decide whether to vote third party or not. Margin of error based on the number of people in the group would also have to be considered to make sure they don’t face the worst possible outcome of losing the election for their party.

It seems strange to encourage your voters to leave their vote up to chance, but under these circumstances it might just be the best way to get what you want. 

Also this is Sonny Jim. He smiles a lot.  

Bibliography

Neumann, Jon Von. "Game Theory & The US Presidential Election." Linkedin.com. N.p., n.d. Web.

"Networks." Game Theory of Voting for a Third Party Candidate : Networks Course Blog for INFO 2040/CS 2850/Econ 2040/SOC 2090. N.p., n.d. Web. 16 Apr. 2017.