The Median Voter Theorem
Using the median voter theorem to approach elections in a more strategic maner
ABSTRACT
The median voter theorem is a tool used in political science to explore strategic decision making. Its application can be used by politicians to pick an optimal platform to campaign on in order to maximize votes and additionally by voters to intentionally skew elections towards their own preferences. In this article I first present the theorem in its plainest form and then further explain it by presenting both of the aforementioned usages: first by running through a hypothetical election from the perspective of a politician in order to win the majority vote, and second from the perspective of an educated voter trying to get a preferential candidate through the primary round of an election.
It’s 2023, and if you live in America you know that this means that the 2024 presidential election cycle is already underway. In reality it started moments after Joe Biden was announced to be the 2020 president elect, but a more meaningful start date could be pinned to January 2022 when President Biden announced his intent to run again as the Democratic nominee. So while many Democratic voters are expecting to be represented by Biden on the ballot, Republicans and third-party voters aren’t sure yet who their candidates may be. With Donald Trump and Ron DeSantis being two current frontrunner candidates and the Republican primary being less than a year away, you may be asking yourself: who should I vote for?
While it’s important to consider the pertinent topics of the day and what matters to you, there is a correct way to approach this topic. The answer to that question, “who should I vote for?”, involves thinking strategically and can be applied far beyond the reaches of United States presidential elections. But it’s important to note that there is a solution if you’re trying to maximize your own preferences. The answer comes in the form of the median voter theorem.
This theorem is relatively simple and intuitive. It states that in an election politicians will tend towards the median position of the voting base. Understanding this is key to understanding so much in the American political system. If you’re looking to get the majority of votes to ensure your victory, you don’t need to appeal and appease everyone. You simply need to be slightly better than the next most viable option. Let’s see how this works.
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On the number line, there are 7 integers arranged from smallest to largest. Imagine these as policy positions across a single axis: this could represent any issue from gun control to tax rates to farm subsidies to public transit to any number of positions. In this scenario, consider Abdul. He’s a politician who personally aligns with position 2, and he’s running against Lena who’s campaigning on position 5. Assume every other number represents one voter at different points on this spectrum.
As previously discussed, everyone has preferences. We can assume that these are rational actors, meaning that they try to maximize their happiness. Given this we know that everyone would prefer to be at exactly their preference, or in other words everyone would choose the policy position that falls exactly on their preferred point of the number line. However, there are only two candidates to choose from, so they must decide which one they’ll vote for. They do this by figuring out which is closer to their most preferred point. In political science, we make the generalization that voters are equally dissatisfied moving away from their ideal point irregardless of direction. Therefore, if I’m voter 4, I’m just as okay voting for 5 as I am voting for 3 - they’re equal distance from my ideal spot. Given all of this, we can accurately describe the election of our number line example.
We’ll start by describing who will vote for Abdul. It goes without saying that since Abdul prefers point 2, he’ll vote for himself. There’s nobody running on point 1, and moving up the number line the first candidate voter 1 would reach is Abdul, so the voter would cast that vote accordingly. Voter 3 has the chance to go either way, being equally satisfied with both 2 or 4. However, given that there is a candidate on 2 and not 4, they’ll end up voting for Abdul. Those are all of the votes Abdul is able to secure in this scenario.
The remainder of the votes would end up going to Lena, winning her the election. The voters on 4 and 6 work exactly the same as voter 3 worked for Abdul: there’s nobody running on their ideal point, so they’ll settle for the nearest candidate who's only one point away. As for 7, they’ll settle for Lena as well. While they’d prefer not moving two full spaces down the number line, that’s far better than moving five spaces all the way down to policy position 2 where Abdul has been campaigning. Finally Lena would vote for herself, as she prefers to see herself elected.
So there you have it. Without knowing anything about either candidate or even what policy position they’re in disagreement over, we can accurately predict how this election would shake out given where the voters fall in relation to the candidates. Abdul would secure three votes including his own, and Lena would take the remaining 4 which gives her a winning majority. But is there a way that Abdul could win? Yes, if he follows the logic of the median voter theorem.
Think back to voter 7, and how they had to pick between moving five spaces or two spaces for their candidate. While neither is great, one is certainly much closer to where they’d like to be, so that’s who will win their vote. If Abdul understands this and understands the preferences of the voter base, the smart move for him would be to change his platform to one that advocates position 4.
While this isn’t personally satisfying to Abdul, who would prefer position 2, policy 4 is still closer to their ideal point than 5 is. So, by changing platforms he’s able to retain voters 1 and 3, the new voter on 2 will prefer position 4 to 5, and Abdul will vote for himself on position 4 which would secure the winning majority. By appealing to the median position, and therefore the median voter, this politician was able to win a majority of the vote and keep things closer to their idealized point.
Now let's try to step back from the theoretical and return to the real world and the real Republican primary. If you recall the leadup to the 2016 presidential election there were a total of 17 major candidates who were vying for the nominee of the Republican party. That was massive assortment that provided a great deal of choice to their voter base. Given that there were so many candidates running at the height of the primary it’s likely there was someone who aligned fairly closely with the views of most Republican voters. So that’s who they should’ve voted for in the primary election, right? Shouldn’t they have voted for the candidate who was most similar to their own preferences. Not necessarily.
Think back to Abdul and the decision he had to make in order to secure a majority of votes and win his election. He had to appeal to the moderate median voter in order to pull a vote away from his opponent. So as a voter if you recognize that politicians will vie for that median voter in order to secure a majority, you want to strategically pull that median position closer to your preferred point.
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Consider once again our number line, but this time imagine that it’s a hypothetical Republican primary. Each of the 7 numbers represents a different candidate. There’s additionally 8 voters heading to the poll to select who their nominee will be - one voter for each of the 7 candidates, and the 8th voter who we’ll study for this example. We’ll call her Agnes.
Agnes personally aligns herself with candidate 3, but as a student of political science she recognizes that in the general election the Republican nominee will adopt a more moderate position in order to try and sway the median voter. So, instead of voting for her actual preferred candidate she acts strategically and votes for candidate 2, ensuring their victory. The hope from here is that the moderate position that candidate 2 then campaigns on in the general election is that of position 3 which is what Agnes preferred from the beginning.
By using the logic of the median voter theorem, one can act much more strategically in all types of situations. There’s the obvious and discussed example of election primaries, where you should vote more radically in order to get a representative that will end up more closely aligned to your own position in subsequent elections, but this can be extrapolated into much lower stakes examples. Consider something as silly as deciding where to go for dinner with a group of friends.
There may be a group of you who all have differing tastes and preferences. You might really be wanting to go try a new pho restaurant that opened up last month, but you know what everyone around you is likely to pick. If you meet somewhere closer to the middle and rally behind a conciliatory option, say the all too common pizza, you might end up at your second or third most preferred choice as opposed to your seventh.
While this is admittedly a fairly frivolous usage of the theorem it helps demonstrate the value in strategic decision making. All of us, even the most neutral and anodyne amongst us, have some things we prefer over others. If we take a moment to step back and consider the likely actions of those around us, we’re better able to strategize our own actions. Through the consideration and usage of the median voter theorem one can make a deliberate effort to steer their life in a preferential direction
Note from the author:
I consider this to be my most technical and abstract piece. I tried to connect it to grounded examples in order to demonstrate the theorem, but understand that I may not have done a sufficient job. I encourage anyone with any lingering confusion to leave a comment, which I would be happy to reply to.
I really appreciate the restaurant metaphor, while it may seem frivolous it added another layer of understanding to a slightly convoluted topic.