Graph and Game Theory Concepts Applied to the 2016 Presidential Election
So, I read an article recently and the article claimed that Biden running would hurt Hilary a lot more than it would hurt Sanders. Now this really surprised me. A lot of Sanders support is coming from the anyone-but-Hilary demographic. And surely Biden would be an acceptable choice; in fact, since Biden is closer to Hilary in policies, I wouldn’t just consider him acceptable but actually more likely to get this demographic. But then I thought about it more and I came to agree with the article.
The anyone-but-Hilary demographic has largely already picked sides. Biden and Sanders are both pretty close in polls despite the fact that Biden isn’t even running (had Biden been running when the demographic picked sides, things would likely be a lot more skewed away from Sanders). So let’s assume the anyone-but demographic has been researching which side to switch to and only a marginal amount will switch sides after Biden announcing because they’re probably already invested in their candidate.
But now let’s also consider that Sanders is kind of an odd duck out in the Democratic Party: he affiliates as an independent and uses the “s” word that has been so tainted in America. Why does Biden running help this? Well, as mentioned, Biden is a lot more like Hilary than Sanders is. That means that Biden and Hilary both draw from the same support base.
Now let’s talk about some game theory. What does drawing from the same support base mean? Well let’s assume Biden and Hilary are equally liked by a support base of 100 people. If neither run, neither gets any votes. If Biden and Hilary both run, both get 50 votes. If only one runs, that one gets all 100 votes. We can assume that Sanders is drawing from a separate support base for this game and that Sanders receives a constant amount of votes. Well, this amount matters. If Sanders gets 75 votes, then Sanders wins the primary if both run (and gets to claim the larger pie). If Sanders base is less than 50 votes, than Sanders loses the primary.
Of course this model is very simple. For instance, there is instability of support base, especially when the debates hit. But the point is that Hilary is currently on a downward trend, Sanders is on an upward trend, and Biden running will further fragment votes between Hilary and Biden. When two candidates with similar ideals run, neither wins.
Think back to your elementary school. Remember those student council elections? At my school at least, I found that whenever 2 members of gender Y went against 1 member of gender X, gender X won. This is because the gender line in a given grade roughly 50/50, the votes in elementary school really aren’t based on much more than gender, and 2 members from the same gender causes a split in that gender (so whereas both members of gender Y would get 50% of their gender, gender X would get the whole pie).
The above train of thought is also why primaries are so important: a party doesn’t want two candidates in the final vote. The party will end up split and lose if more than 2 candidates enter the presidential voting round (look at the Presidential Election of 1860). This is why Trump announcing he would run with or without the Republican Party nomination was very bad for the Republican Party as a whole (Trump has since taken that statement back).
With that said, I think I should also note a bit about game theory on the Republican side. There were seventeen candidates at the Fox News Debate. Trump went it with the lead: 23.4%. That means Trump did not have 76.6% of the vote. Of the 76.6%, about 70% of it was split amongst what one might consider traditional candidates (the term traditional being defined as having major previous political experience). From that, I am going to guess that if a single traditional candidate went against Trump before this election (rather than around fourteen), then that candidate would’ve had the vast majority of support. But so many members of the same party are fighting for the same large pie (traditional conservatives) that Trump, who has the entirety of a much smaller pie (those who want the Republican Party to be shaken up a bit), ends up with more support.
And the fact that Trump has the largest slice (even though it is from a small pie) means that his slice is likely to grow faster than anyone else’s. As other candidates have mass exoduses (as Bush and Walker already have had) – well supporters of these candidates are going to speak with colleagues about who to switch to and since Trump has the most support the colleague being spoken to has the highest chance of being a Trump supporter. The rich get richer.
Now, before I conclude this post, I want to give a shout out to Carson too. Carson is in second now and is also going for that non-traditional candidate pie. And the Trump plus Carson pie has now grown to over fifty percent of Republican voters. Unless the traditional pie stops being so splintered, the non-traditional pie is likely to grow due to the rich get richer concept. And once primaries hit, one candidate is going to get it all.
What this means is that we have a very interesting election ahead of us. Both the Republican and Democratic Party have a non-traditional candidate with a very good chance of winning in the respective primary, and therefore the election too. And the reason for the rise of the non-traditional candidate can actually be explained with very simple game theory and graph theory concepts that we have already learned in class.
http://elections.huffingtonpost.com/pollster/2016-national-gop-primary
http://elections.huffingtonpost.com/pollster/2016-national-democratic-primary