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 gonna pick as close as we can get right. We're gonna pick the option that's closest to our preference when 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 gonna start here by defining the median. Okay, So the median, remember when we studied algebra others, the mean, the median, the mode. These were all different ways to discuss the middle. So, we're gonna 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 gonna be the number, the specific number, right? In the middle. All right. So, if you guys don't remember, let's do a really quick easy way to do medians. Um Let's just pick a five number dataset. We've got, let's say 25 14, 38 and 12. Right? We've got these five numbers, you can see them up there, yep. And uh we want to find the median here. Well, if we want the median, the easiest way to do it is we're just gonna take off the top number and the bottom number, and we're gonna keep doing that until we're left with just one number. Okay, So let's see here, the highest number was 25 the lowest number was three. So, we're gonna cut those out. And now let's do the same thing, highest and lowest. Well, that's 14 and eight. And we're left with 12. 12 would be our median in that data set right there. Okay, So let's go on to our example and see how this median and the median voter theorem, uh work out. So, we're gonna have in this example, we have different preferences for military spending. We're gonna say there's only five people in this community and they all have a different preference for their military spending and is a pacifist and wants zero spending on the military. Benito 20 Kathy 50 dug 80 and Edward 1 40. All right. So, before we think about this, let's go ahead and find the median in the in this data set. So, we've got five 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 gonna see that that is going to be what gets voted on, median is gonna 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 gonna have a vote between a budget of $20 and a vote between a budget of $20 and a budget of $50. Okay, so all the voters are gonna get to choose between 20 and 50. And remember they're gonna vote as close to their preference as they can write if they can't get exactly what they want. They're gonna vote as close as they can to what they want. So, let's start here with an if Anne had to pick between a $20 budget and a $50 budget. Well, she wants a budget of zero, right? So, she's gonna pick the lower number. She's gonna pick 20 because it's closer to her preference of zero. What about Benito? Well, he wants 20 and 20 is an option. So, he's gonna get exactly what he wants in the vote and he's gonna vote for 20. Right? Same thing with Kathie. She wants 50 and she's gonna 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 gonna vote for 50, he'd rather have 50 than 20 because he wants a high budget. And Edward the same thing. Edward wants 140. So, he's gonna pick 50 because it's closer to his his preference than the $20 budget. He wants a bigger budget. He's gonna vote for 50. All right. So, what happens in this case we've got to voters for 23 voters for 50. 50 wins in this vote, right? 50 is the winner between 20 and 50. Now, let's assume the different something different where we've got a higher budget versus the $50 budget. Right now, we've got $100 verse 50. How is the how is the vote gonna go now? So an has to pick between 50 and 100 right? She's gonna pick something closer to her preference of zero, and she's gonna vote for the 50 right? Because that's to her that's a better option than 100. She doesn't want any spending. Benito the same thing, he only wants 20. So he's gonna vote for 50 as well, because it's closer to his preference than 100 kathie, again, being our median voter, she's gonna get what she wants and she's gonna vote for 50 Right? That is her preference. How about Doug Doug wants $80 right? He he wanted an $80 military budget and he has to choose between 50 and 100. Well, he's gonna pick 100 right? That's closer to his to his wants there. So he's gonna 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's still three votes for 50 and two votes for 100. So, again, 50 wins the vote. Alright, 51 in both cases. And what we're gonna see this median voter theorem is that that median voter determines the outcome of elections, they're gonna determine the outcome because everyone below it is gonna want to get closer to that median, right? It's gonna be their preference. Just like we saw when there's a high high versus the median and when there's a low versus the median, everyone above the median is gonna want to side with the median, So the median ends up winning every time. Alright, but what are the implications here? It means that many people are gonna be dissatisfied with the results, right? Think about an an is gonna be dissatisfied. She wanted a zero budget and she had to choose between 2050, 100 and she ends up with 50, right? She's not gonna be satisfied. A lot of people aren't gonna be satisfied with the results of the vote. So, what can people do? 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 gonna 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. All right, So, the median voter theorem, the median voter wins. Alright, let's go ahead and move on to the next video

Median Voter Theorem

Median Voter Theorem

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?