 In this video, we're going to look at various election criteria. We'll look at 1. Vote splitting. Vote splitting occurs when voters can only vote for one candidate. Because a voter can't support the two or more candidates she wishes, the vote splits between those candidates. This also occurs from only being able to rank one candidate as first. 2. Independence of irrelevant alternatives. When a system violates this criterion, it's allowing a candidate that loses to change the outcome of the election. We typically think of irrelevant alternatives as fringe spoilers, but competitive candidates can also be irrelevant alternatives. 3. Non-monotonicity. Non-monotonicity is when supporting candidates can hurt them and voting against candidates can help them. This is the Alice in Wonderland election world where up is down and down is up. 4. Condorcet Criterion. A condorcet candidate is a candidate that can beat every other candidate in the head-to-head matchup. You can think of this candidate as an undefeated round robin winner. When this candidate is selected by the election method, the condorcet criterion is met. We're also going to apply these election criteria to different voting systems. We'll look at plurality. This is the classic loop for one. Most votes wins. Approval Voting. Here you vote for as many as you want. Again, most votes wins. Instant runoff voting, also known as IRV or Ranked Choice Voting. Here you rank your choices. See if anyone has more than 50% of the first-choice votes. If not, look to the candidate with the least first-choice votes. Then, look at the voter's next preference and transfer the votes to that candidate. Repeat until a candidate has greater than 50% of the remaining balance. We're also highlighting condorcet. When another system lines up with a condorcet selection, the nut system is picking the condorcet winner, the beat all winner. Let's go ahead and take a look at what we have in front of us. Up top, we have a normal distribution. We'll keep a normal distribution for our voters. The election system hardly matters at all when we only have two candidates. But the system really matters when we have more than two. So let's add a third candidate. Adding a third candidate, we can already see red and yellow are splitting the vote against green under plurality. Now, let's make sure we understand the interface before moving on. The colored area along the width is a range where a particular candidate wins when voters center on that point. The small circle indicates which system is being used and where the distribution of voters is focused. The color of the circle spilling indicates the winning candidate. The shade in the distribution itself indicates which candidate's voters are voting for. Up top, we can see the balance and exact results. Also, our voters in these simulations are voting honestly. Let's take a look at a familiar fringe spoiler scenario of the sort that we saw when Nader ran in 2000. We see here that plurality is extremely vulnerable to vote splitting, even with fringe candidates that get very low support. These fringe candidates can also be called irrelevant alternatives. Here, red is that irrelevant alternative. That's because red doesn't win. Yet, red's presence changes the winner. We see here that without red, then green wins. Red's presence causes the vote to split between red and green, resulting in yellow winning. Insert runoff voting, on the other hand, is resistant to these fringe spoilers. When red is present, he gets eliminated with instant runoff voting. Red's votes get transferred to green as those voters' next preference. But as we'll see soon, instant runoff voting can't muscle up resistance against more competitive, irrelevant alternatives. If we were to think in terms of a perfect candidate, where would we place her? What kind of candidate would she be? A perfect candidate would appeal to the most voters. She would be a centrist candidate. So, we place the perfect candidate in the center, and bulk of where voters prefer. Let's place green in the center as our perfect candidate. Now, let's make the selection more competitive, to see how these systems perform under a little pressure. We're going to have red and yellow encroach on green's territory. And now we see green's opportunity of winning under priority, vanishing away, until they're completely eviscerated. Even with the bulk of voters, focusing on the perfect green candidate, priority refuses to elect green, who is again, our perfect centrist candidate. Let's turn our attention to instant runoff voting. Red and yellow are going to invade more green space. Now we're seeing these slivers of color begin to appear. What does that mean? It means our IRV election has gone non-monotonic. We've now walked through the looking glass, where we can hurt our candidates by voting for them, and help them by voting against them. We also see that aligning voters directly over the perfect green candidate will no longer elect green. So right now, IRV is electing yellow. Let's say we want yellow to win by even more. What would we do? Pushing more votes towards yellow makes sense to give him the landslide victory. So let's do that. Did that cause yellow to win by more? No, it didn't. Instead, giving more votes to yellow caused green to win. So why would green win by more people voting for yellow? That's because IRV eliminated red for having the least first-choice votes, and red's votes transferred to green. So let's try to do a favor for green now, and give green more votes. So what happens? Yellow wins. Why is yellow winning? Yellow wins because green got eliminated, and the bulk of green's next-choice votes went to yellow. But why would IRV eliminate green in the first place? Our perfect centrist candidate. Just like priority splits votes, so does IRV split first-choice preferences. Red and yellow moving in on green chipped away at green's first-choice votes. And that's why IRV eliminated the near-perfect green here. Because IRV splits first-choice votes, it can cause perfect candidates to get eliminated first, and thus have no opportunity to win. And that's exactly what happens when red and yellow split green's votes even further. Now, just like priority did earlier, IRV has completely barred the perfect green candidate from winning. Like priority, IRV is also not kind to centrist candidates. Now let's turn our attention to approval voting. Here we've got red and yellow. They're still about a standard deviation away from green. And at this point, both priority and and surround-off voting have denied the perfect candidate, green, the opportunity to win. But approval voting has consistently elected green when green is the perfect candidate. So why do voters elect green under approval voting? That's because approval voting lets voters vote for more than one candidate, which prevents vote splitting. Some voters like green and yellow is candidates. And approval voting lets them support both. Even more, why is it best for the voters that like yellow more than green to vote for both of them? That's because these voters really don't like red. If they bullet-voted for just yellow, they'd risk the disaster of red triumphing, and they don't want that. It's not until we get to the voters that really don't like both red and green before they start to bullet-vote for yellow. And approval voting doesn't select yellow until we move over the entire distribution. And at that point, when the distribution is completely over yellow, it makes sense for yellow to win. Also, we've seen that during this whole video, approval voting is lined up with the Condorcet method. As we recall, that means approval voting has been selecting the Condorcet winner, the Beat All winner. So has a loser red kept green from winning under approval voting? No. And that's because approval voting is immune to vote splitting. And even tactical voters can give their support to red if they honestly prefer red as their favorite candidate. They can always throw in another vote for their more competitive preference of green. And finally, regardless of where red sits, approval voting refuses to let red split green's vote to allow yellow to win.