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Game Theory in Voting: Duverger’s Law

Despite record high-interest in the campaign, recent results of U.S. elections have popularly been deemed as “disastrous.” According to an article by the Huffington Post, an overwhelming number of Americans were surprised by Donald Trump’s victory in 2016, the majority of them were unhappy with the result of the election, and a similar number of people have low to very low expectations of the new administration. Why is this the case, if Trump won?

Perhaps, the answer can be explained by game-theory. U.S. democracy operates upon a first-past-the-post system: the candidate with the plurality of votes becomes the winner-take-all. While intuitively, this system appears to be democratic and make sense, as explained in the YouTube video by CGP Grey, it often inevitably leave many voters dissatisfied. In an environment that begins with a large number of candidates (which it should, since people tend to have a variety of opinions), even if the difference in support amongst the candidate is near-evenly distributed, minority supporters will eventually be incentivized to giving up support for their first-choice candidate and instead support someone who has a high chance to win.

In game-theory terms, the voter would have two strategies: 1) to vote for a losing candidate, receiving 0 utility should a candidate with opposing views win, or 2) to vote for a winning candidate with slightly similar views and gain some utility. Clearly, the second option presents a dominant strategy. This tactical approach to voting eventually results in a two party-system (a phenomenon known as “Duverger’s Law”) , where minority opinions are eliminated from the table, and voters are left with two choices: someone who is terrible, and someone who is “not too bad.” This was likely what happened in 2016. Neither Clinton or Trump were viewed by the public as good candidates for the position. Yet, they both won their respective party’s candidacy with ease because voters know their next best competitors won’t survive in a general election.

Reflecting further upon what I’ve learned from these findings, I suddenly realized how absurdly strange it is for a nation as diverse as the U.S. to be functioning on a two-party system, where political discussion is separated to just two-sides; where opinions are either red or blue. If you want to vote for a candidate to support climate change and LGBT issues, chances are that person won’t support gun-rights or small government policies. Why does this have to be the case? I personally have found it difficult to associate myself either political parties – and I’m sure I share this struggle with a large number of Americans. If a problem like this exists within presidential elections, one has to wonder what state, county, or local district elections are like. Why do certain states essentially remain “red” or “blue” forever, leaving the opposing candidate without incentive to even spend the money to rally support there? Not only does this problem exists in the U.S., but it is ever-present in other democracies as well. To fix this problem, we must learn from the consequences of game-theory and propose a solution in which game-theory would work in the public’s favor.

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