Median Voter Theorem - Online Tutor, Practice Problems & Exam Prep

The median voter theorem illustrates how voting outcomes often reflect the preferences of the median voter, who is positioned at the center of a distribution of preferences. In a voting scenario, individuals select options closest to their preferences, leading to the median choice prevailing. For example, with military spending preferences ranging from 0 to 140, the median of 50 consistently wins votes, demonstrating that many voters may feel dissatisfied. This concept highlights the significance of the median in determining policy outcomes and the potential for individuals to relocate to align with their preferences.

Median Voter Theorem

So now let's consider the topic of voting and discuss the median voter theorem. So when we think about voting, we don't always get exactly what we want, right? We don't always get our preferred choice. When we don't get our preferred choice, well, we're going to pick as close as we can get, right? We're going to pick the option that's closest to our preference when we vote if we can't get exactly what we want, okay? So that leads us to the idea of the median voter theorem, and we're going to start here by defining the median. So the median, remember when we studied Algebra, the mean, the median, the mode, these were all different ways to discuss the middle. So we're going to focus here on the median. The median being the value that separates the higher half of a data set from the lower half, alright? So it's going to be the number, the specific number right in the middle, alright? So if you guys don't remember, let's do a really quick, easy way to do medians. Let's just pick a 5-number data set. We've got, let's say, 25, 14, 3, 8, and 12. Right? We've got these five numbers. You can see them up there. Yep. And, we want to find the median here. Well, if we want the median, the easiest way to do it is we're just going to take off the top number and the bottom number and we're going to keep doing that until we're left with just one number. So let's see here, the highest number was 25, the lowest number was 3, so we're going to cut those out and now let's do the same thing, highest and lowest. Well, that's 14, and we're left with 12. 12 would be our median in that data set right there. So let's go on to our example and see how this median and the median voter theorem work out.

So we're going to have in this example, we have different preferences for military spending. We're going to say there's only 5 people in this community and they all have a different preference for their military spending. Anne is a pacifist and wants 0 spending in the military. Benito, 20. Kathy, 50. Doug, 80. And Edward, 140. So before we think about this, let's go ahead and find the median in this data set. So we've got 5 different preferences, what is the median? So let's take off the highest and the lowest, highest and the lowest, again highest and the lowest and we're left here with a median of 50, right? 50 is our median and we're going to see that that is going to be what gets voted on. The median is going to win this vote no matter what, alright? So let's see how that comes to play.

So our first example here, let's say we're going to have a vote between a budget of $20 and a budget of $50. Well, all the voters are going to get to choose between 20 and 50 and remember they're going to vote as close to their preference as they can, right? If they can't get exactly what they want, they're going to vote as close as they can to what they want. So let's start here with Anne. If Anne had to pick between a $20 budget and a $50 budget, well, she wants a budget of 0, right? So she's going to pick the lower number, she's going to pick 20 because it's closer to her preference of 0. What about Benito? Well, he wants 20 and 20 is an option. So he's going to get exactly what he wants in the vote and he's going to vote for 20, right? Same thing with Kathy. She wants 50 and she's going to vote for 50, right? Doug, well, Doug if he had to pick between 20 and 50, he's getting he wants 80, right? He wants the budget to be 80, so he's going to vote for 50. He'd rather have 50 than 20 because he wants a high budget. And Edward, the same thing. Edward wants a 140, so he's going to pick 50 because it's closer to his preference than the $20 budget. He wants a bigger budget, he's going to vote for $50. So what happens in this case? We've got 2 voters for 20, 3 voters for 50, 50 wins in this vote, right? 50 is the winner between 20 and 50. Now let's assume something different where we've got a higher budget versus the $50 budget. Now we've got a $100 versus 50. How is the vote going to go now?

So Anne has to pick between 50 and 100, right? She's going to pick something closer to her preference of 0 and she's going to vote for the 50, right? Because that's to her, that's a better option than a 100. She doesn't want any spending. Benito, the same thing. He only wants 20, so he's going to vote for 50 as well because it's closer to his preference than 100. Kathy, again being our median voter, she's going to get exactly what she wants and she's going to vote for 50, right? That is her preference. How about Doug? Doug wants $80, right? He wanted an $80 military budget and he has to choose between 50 and 100. Well, he's going to pick 100, right? That's closer to his wants there, so he's going to vote for 100 as well as Edward, right? That's closer to his preferences there as well. So what happens again here? Notice who voted for what has changed, but the winner has not. There are still 3 votes for 50 and 2 votes for 100, so again 50 wins the vote. Alright, 50 wins in both cases. And what we're going to see with this Median Voter Theorem is that the median voter determines the outcome of elections. They're going to determine the outcome because everyone below it is going to want to get closer to that median, right? It's going to be their preference just like we saw when there's a high, a high versus the median and when there's a low versus the median, everyone above the median is going to want to side with the median. So the median ends up winning every time, right? But what are the implications here? It means that many people are going to be dissatisfied with the results, right? Think about Anne. Anne's going to be dissatisfied. She wanted a zero budget and she had to choose between 20, 50, and 100, and she ends up with 50, right? She's not going to be well. People will relocate to a jurisdiction where the median vote is closer to their preferences, right? They want to be the median voter. If you're the median voter, you're going to get everything you want. So if you're in a district where it seems like the policies are going your way, that means you're pretty much closer to the median voter in that district. Alright, so the median voter theorem, the median voter wins. Alright? Let's go ahead and move on to the next video.

During a political race for mayor, the key issue is spending on a new water park. The town's 500 voters spending preferences are shown in the table. What amount of spending will win the vote?

• A. $0
• B. $20,000
• C. $40,000
• D. $60,000

Here’s what students ask on this topic:

What is the median voter theorem?

The median voter theorem posits that in a majority-rule voting system, the preferences of the median voter will likely determine the outcome of the election. This is because voters will choose the option closest to their preferences, and the median preference will be the most central, thus garnering the most support. For example, if voters have different preferences for military spending, the median preference will win the vote, as it is the most balanced choice among all voters.

How does the median voter theorem apply to policy decisions?

The median voter theorem applies to policy decisions by suggesting that policies will reflect the preferences of the median voter. In a democratic setting, politicians aim to win elections by appealing to the median voter, whose preference is central in the distribution of all voters' preferences. This means that policy outcomes are often moderate, balancing between extreme preferences. For instance, if voters have varying preferences for public spending, the policy adopted will likely be the one that aligns with the median voter's preference.

What are the limitations of the median voter theorem?

While the median voter theorem provides valuable insights, it has limitations. It assumes voters' preferences are single-peaked and that they vote sincerely. In reality, preferences may be multi-dimensional, and strategic voting can occur. Additionally, the theorem does not account for the influence of interest groups, campaign financing, or voter turnout disparities. These factors can skew policy outcomes away from the median voter's preference, leading to less representative decisions.

Can the median voter theorem explain why some voters are dissatisfied with election outcomes?

Yes, the median voter theorem can explain voter dissatisfaction. Since the theorem predicts that the median preference will prevail, voters with preferences far from the median are likely to be unhappy with the outcome. For example, in a vote on military spending, those who prefer very low or very high budgets will be dissatisfied if the median preference is moderate. This dissatisfaction can lead to feelings of underrepresentation and may prompt individuals to relocate to areas where their preferences align more closely with the median voter.

How does the median voter theorem influence political strategies?

The median voter theorem significantly influences political strategies. Politicians and parties often tailor their platforms to appeal to the median voter, as winning their support is crucial for electoral success. This leads to moderate policy proposals and centrist positions, as extreme stances may alienate the median voter. Campaigns focus on swing voters and key issues that resonate with the median preference, aiming to secure the majority needed to win elections.