 In our previous video, we introduced an example of a math club election that was kind of weird in that anyone could win the election depending upon the voting method that we introduced. So in any election, we have candidates, we have voters who vote for the candidates, but the election method itself has a huge impact on the outcome of the election. And so because of this, we have to study what are possible voting methods that we can use. As we're very early on in this unit, it makes sense to begin with the most common voting method, at least historically, that's used. We will refer to this as the plurality method. There's lots of different names for this method. We'll just call it the plurality method. The idea is this is the method where you vote for your favorite. We saw this with our SU Math Club example as well. You vote for your favorite and whoever your favorite is, that you cast their name on the ballot and nothing else. And whoever has the most votes, the most number of first place votes would be the election. Plurality is a very simple voting method. And so let's do some examples of this. Imagine we have an election with four candidates and we will call them candidates A, B, C, and D, in which case voters will, you will actually look at their complete preference schedule so that as we see all of the voters' preferences, that helps us analyze things in this election here. And so we get the following, 14 people voted for candidate A as their top choice, then B, then C, then D. So the 14 people preferred alphabetical order. Then 10 people voted candidate C as the top choice there, then B, then D, then A. Eight people voted for D, then C, then B, then A. Four people voted for Bravo, then Delta, then Charlie, then Alpha. And then one person voted Charlie, Delta, Bravo, Alpha. So Charlie was their first choice, Alpha was their last choice. That's how you wanna interpret this thing here. So who is the winner of this election? So all we have to do is we just have to count how many first place votes that everyone get. So we only have to look at the first line of this voting, of this preference schedule here. So let's look at the candidates we'll go in alphabetical order here. So candidate A received 14 first place votes, only people in the first column put A as their first choice. There'll be at 14 there. If we look at candidate B, looking only at the first one, we have candidate B right here was voted first place four times. Then candidate C, there was two different types of voting profiles that place candidate C at the top. 10 for the first one, one for the next one. So candidate C is gonna end up with 10 plus one, which ends up being 11. People voted for candidate C as their first choice. And then for candidate D, there was only eight people that put D as their first option. So that's how we have it there. And so then the winner of the election would then be candidate A who received the first, the most number of first place votes. But in fact, we can do the following here. We can do a complete ranking of this thing. So the first place votes go to candidate A who got 14, second place would then go to candidate C who got 11, third place would go to candidate D who got eight points. And then lastly, we have fourth place goes to candidate B who ended up with four first place votes there. So that would be the outcome of this election. And again, like I said, candidate A would be the first one to win there. But there's sort of a weird thing going on in this election here, things I wanna note. If you were to take the total number of votes here, all right, 14 plus 10 plus eight plus four plus one, that adds up to be 37. There were 37 people who participated in this election, okay? For which case, if you then look at the margin here, 14 divided by 37, you end up with 38%. So candidate A wins this plurality vote here, but they only had 38% of the voter support. Now, conversely, if 14 people put A as their first place vote, that means 23 people put A as not their first place vote and that gives you 62%. So the thing is, we have that a majority of the people did not place A as their first place vote, but yet A is the winner of this election. And in fact, I wanna illustrate this even more. Look at this right here. In this election, everyone who didn't vote for A as their first choice put A as their last choice. So 62% of the voters here put A as their last choice. A majority of the voters think of A as the worst of the four candidates. But by plurality, A would win because A has the most first place votes, right? That's a curious thing happening here. With plurality, it's possible that a candidate who has a majority of last place votes can still win the election because they happen to have the most first place votes Is that really a fair thing? We'll talk about that another time. Let's look at another example of an election. This time we're gonna have five candidates, ABCDE. And we have three, there's only three voting profiles that manifest themselves. 49 people voted alphabetically ABCDE. 48 people, their profile was 48 had B, E, D, C, then A and then three people put C, then B, then E, then D, then A. So again, as we work through these things, candidate A had 49 first place votes. candidate B had 48 first place votes. candidate C had three. And then candidate D and E, they never got any first place votes whatsoever, all right? It's kind of a curious thing there. So with regard to plurality, we would get again that A is the winner there. So with a complete ranking, we get first place is A with 49 votes, second place would then go to B with 48 votes. With C, you only have that's third place with three votes. Then when it comes to fourth place, it turns out that we actually get a tie, a tie there. As in two people got the same score, not like a tie fighter from Star Wars or anything like that. It turns out B and E got a tie with zero there. So this is a common thing that sometimes has to happen in an election, that if you have a tie, you need some method of breaking the tie in order to get a ranking. Now, if you only care about the first place vote, that's not as much of a problem, but of course it's possible that people can have a tie with regard to first place as well. So tie breakers are things you do have to incorporate in elections. We're not gonna worry about ties so much right now. Maybe we'll talk about this a little bit later. But we saw the same problem that we saw before, right? Less than a majority of people supported the first place candidate. And in fact, there's 100 voters total here, 49 plus 48 plus three is 100 here. If 49 people did vote it for A, that means 49% of the electorate voted for A as their top choice, but look at it again. Everyone who didn't vote for A in the first place voted for A in the last place. And so in this situation, you're gonna end up with 51% of the population that voted against A. So 49 liked them, 51 didn't. So in majority of the people didn't like A again, all right? And so let me also point out one thing that happened here. When you look at these people, these candidates here, we see that a lot of people supported A. So I mean, unlike the previous one, there is a lot of support for A. I mean, it wasn't a majority, it's really close. Yet 48 people that voted for B. So A and B are like neck and neck in this situation. But then you have C right here. C got three votes, which compared to the other two is completely insignificant. But the margin of votes that C got, if it were given to a different candidate, would have tipped them into the majority situation. Let's say that C didn't run in the election for whatever reason, C dropped out before election day. Then if C didn't perform in the election, these people who would voted for C, their second choice would have been B. So if C had dropped out of the election, these people would have voted for B instead. In which case then B would have not gotten 48 votes. B would have gotten 51 votes for which that would have been the majority and more points than A. And so in some respect, the only reason that A won was because C ran in the election. This is an example of what we call the spoiler effect. The spoiler effect is that the outcome of the election would have been different if a candidate, known as a spoiler in the situation, had not run. If C hadn't had run, then B would have probably won the election and not A. So it's perhaps a possibility that C spoiled the election for B there. That's sort of a curious thing. It reeks of sort of unfairness, but again, these are topics we're going to talk about in the future. I want you to understand how the plurality method works, but it's also a good opportunity to talk about why the plurality method might not be the most fair method. Don't get me wrong, it's not completely garbage, but it does have some issues. All right, so as we end lesson 17, I do want to end us with a real life example. So all the previous ones have been fictitious so far, but I want to give you an example for real life. Let's look at the 2010 governor's race in the state of Maine. Why? Why would we look at that one? It turns out there's some curious things going on here. So in that race, we have five candidates that you can see right here. The two that I want you to pay attention to are going to be right here, Elliot Cutler and Paul LePage. Okay, what's so significant about these two candidates? Well, one, look at what percentage of the votes they got here. So these are the total number of votes they got. And then it was 38.2% went to LePage, 36.5% went to Cutler. And then the next one, the Democratic candidate, Libby Mitchell, she received 19.3% of the vote. And then we had two other independents who received less than 5%, less 5% each, right? So these are the top three candidates. Cutler and LePage were neck and neck in this election. It turns out we actually go back to the voting data. The early voting, it was winning for Cutler, but then, because cities often get votes in faster than rural areas, oftentimes, not always the case, but that was the case in this situation. As as more of the rural vote came in, LePage then passed Cutler and won the election. So LePage was the elected governor from the 2010 election right there. It was really, really close. You'll notice that in this situation, none of the candidates received a majority of the votes and Cutler and LePage were really, really close together. Now, some things that happened here. Cutler was declared as an independent, but independents still have to have some type of policy platform. And if you were to analyze Cutler's platform, it sounded very liberal and thus was very similar, not the same, but similar to the democratic platform that Mitchell had ran under. LePage here as a Republican, of course, supported conservative platform and policies. And therefore, people who might have voted for Cutler might have also voted for Mitchell. And therefore, this 19% who voted for Mitchell, if Mitchell hadn't run, might have voted for Cutler. But also goes the other way around. Had Cutler not ran in the election, these 36% of people would very likely have voted for Mitchell instead. We don't exactly know, because the data doesn't have a complete preference schedule like we did with our fictitious elections here. But the thing is, when you add 36.5% with 19.3%, that gives you a total that's bigger than 38.2. So if one of those two people hadn't run, Cutler or Mitchell, then it might have been the case that the other one, the other liberal candidate would have won and had beaten the conservative candidates. Maybe, again, these are all hypotheticals. It can't be certain, but there was a lot of finger pointing here. Mitchell was saying that Cutler was a spoiler, but Cutler's like, uh-uh, you're the spoiler. And so the outcome of the election might have been different if one of these candidates not had run. But the reason, the main reason I'm including this, has to do with some things that Cutler had done. And I don't mean about the arrest of Cutler in 2022, that I'm not gonna talk about that. I mean that in the 2010 election, Cutler ran, among other things, with the platform that maybe the election, the electoral system in Maine should change. That is, instead, they should use something called rank choice voting. Rank choice voting. This is a topic we will talk about much more detail in future lessons here. Rank choice voting, without going into all the details of things, it doesn't just look at your first place vote, it actually uses all of your preferences to help determine the outcome of the election. And one thing that rank choice voting does well is it avoids the spoiler effect that the plurality method we've been talking about is a victim to. Because people who think Cutler was the best choice can still give some, they can still influence the outcome of the election for Mitchell. But likewise, people who had Mitchell as their first choice could still put support behind Cutler. They could actually support both of their candidates they like that are similar simultaneously. It doesn't have to be like a death match between two similar candidates here, all right? And so it turns, this election actually sort of was the start of the conversation behind rank choice voting in the state of Maine. In 2014, there was another election between Cutler and LePage. I mean, there was other people running as well. LePage had won, he was the governor in 2010. He won reelection in 2014. Cutler got nowhere near as much support in 2014 as he did in 2010. But nonetheless, the conversation of rank choice was still in conversation. And so it actually turns out in the year 2016, the state of Maine actually did pass a law that then allows for rank choice voting in elections. I don't think they're allowed by their constitution to use rank choice voting for governor races. So it still wouldn't have helped Cutler in that situation. And then also Cutler's never running for office again. But like I said, we're not talking about the 2022 arrest or anything like that. So Maine was the first state in the United States to pass rank choice voting. And this election obviously had a huge impact on voters voting for this new electoral system. So why did they do it? Well, a lot of people felt like they're wasting their vote if they didn't vote for one of the top two. But that might not be that your sincere vote in a democratic republic, it's important that voters express their sincere preference, not some strategic vote like, oh, Libby doesn't stand a chance, I'm gonna vote for Elliott. That's not how people should vote. We should vote by our hearts, by our desires, by our platforms, by our policies, or I should say candidates who support those things. And it could be the case that the plurality method is obstructing people's desire to vote sincerely. And alternatives like rank choice might actually be better in that. Now, I'm not gonna advocate that rank choice voting is the best voting method in the world. But as we explore this over the next couple of lessons, we might start to see why rank choice voting is superior to this plurality method. Even if itself is not perfect, it could be a step towards a more perfect union. And so with that, we're gonna end lesson 17. We'll talk about some more voting next time. If you did learn a lot about voting in these videos and the mathematics related to it, please like these videos, share them with friends or colleagues. You might benefit from them as well. Subscribe to the channel to see more videos like this in the future. And of course, if you have any questions whatsoever, please post them in the comments below and I'll be glad to answer them as soon as I can.