Game theory median voter

Not entitled to vote in parliamentary elections. Electoral College votes are cast by individual states by a group of electors; each elector casts one electoral college vote. At- large is a designation for members of a governing body who are elected or appointed to represent the whole membership of the body notably, a city, county, state or province, nation, club or association , rather than a subset of that membership.

At- large voting is in contrast to voting by electoral districts. What is the median voter model? Category: news and politics elections. The median voter theorem implies that voters have an incentive to vote for their true preferences. Finally, the median voter theorem applies best to a majoritarian election system.

What does Duverger's law state? What is public choice analysis? What does political party mean? What is meant by the term rational ignorance? Definition of Rational Ignorance.

What does single peaked mean in math? What is public choice theory quizlet? What are the different types of voting? What do you call someone who doesn't vote? What is the difference between a referendum and a vote? One tip about this, try to identify all the dominated strategies of all players before you delete, then delete. Then look again. Try to identify all the dominated strategies of all players again, and then delete.

That process will prevent you from getting into trouble. So today, I want to be a little bit less abstract, if you like, and I want to look at an application. I want to look at a famous application from politics. The idea is going to be this. So here are the positions.

Very difficult. The idea is that these positions are left wing positions and these positions are right wing positions. Can people not see past the podium? So you could think of these extreme left wing positions. These guys out here, these are the extreme right wing positions. The candidates here are going to try and choose positions.

So they are uniformly distributed. So voters vote for the closest candidate: the candidate whose position is closest to their own. The voters of that position split evenly. What am I missing? We could have assumed that all they really care about is winning and that winning gave them a high payoff and that losing gave them nothing. Or, if this is a primary election, a larger share of the vote gives you a bigger push for the next primary or whatever.

It seems like a pretty natural, pretty important game. There are ten strategies 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, are any of the strategies dominated? Are any strategies dominated? So any strategies dominated? How about this gentleman in blue? So stand up and shout, yeah. Professor Ben Polak: Steven says 1 and So he says that position 1, strategy 1, choosing the most extreme left wing position is a dominated strategy.

What dominates it by the way? Steven, you want to shout it out? Professor Ben Polak: 2. So for example—So our conjecture here is that 2 dominates 1. It means that choosing position 2 always gives me a higher share of the vote than choosing position 1, no matter where the other candidate positions herself. It does not mean 2 beats 1. Well, how about versus 1. So suppose the other candidate has chosen position 1. So the other candidate has chosen position 1. That was pretty easy, right?

He will get or she will get all the voters at 1. So in this case choosing 2 is better than choosing 1. We have to consider other possible positions of my opponent. So suppose my opponent chooses 2. I get all the voters right on top of me at position 1 and she gets everyone else, is that right? And what about if we both choose 2? Everyone happy with that? If I choose 1 against 3, what share of the vote do I get? And if I chose 2 against 3, what do I get? So if I choose 1 against 4, and comparing my choosing 2 against 4.

In the former case if I choose 1 against 4, how many votes do I get? And here if I choose 2 against 4, I get all the people at 1, all the people at 2, and what?

Somebody raise their hand so we can get a micke out there. Can we get a mike on this guy in white? Stand up, stand up, yep, stand up and shout. Professor Ben Polak: 2 is always better than 1, but we can see more than that in the pattern. Mike back here. We had 15, 20, then this one, up to 20, 25 and so on.

Yes, Steven again. So I mean if you want, you can fill in the next—whatever it is—the next 6 positions and see. So, in fact, it is true, it is in fact true, so we can conclude that 2 dominates—in fact, we can do a bit better than that—we can say strictly dominates 1. Is anything else dominated here, Steven already told us that 10 is dominated.

Can everyone see that is symmetric? Hang on a second, everyone see that 10 is going to be dominated by 9 in exactly the same way? Is that obvious? So similarly, 9 strictly dominates Choosing 9 always is better than choosing 10 regardless of what the other person chooses.

There was a question, are we okay? You want to get the mike in for the question? Stand and shout out to everyone. Professor Ben Polak: Okay, well you have one on the handout. Is anything else dominated here? Professor Ben Polak: Sudiptha had suggested earlier on, you want to be close to 5.

So 3 is closer to 5 than 2. Is 2 dominated by 3? Anyone else? Any other hands? Can you get this lady here? Student: Once you delete the dominated strategies, then you kind of go through it again and then 2 is dominated by 3. But what about right now before we delete anything? So how about my payoff versus 1, for example. In particular, if the other candidate were to choose position 1, I would get a higher share of the vote choosing 2 than I would have done if I had chosen 3.

Professor Ben Polak: So Christine has pointed something out. Student: When you delete the dominated strategy of 2 dominating 1, or 1 being dominated, when you delete that and 10, then it is. The voters are still there. Once again, we can try it out. The payoff from choosing 3 against 2 is what? Someone can shout out. So far choosing 3 is better.

Against 4, the payoff from choosing 2 against 4 is what? And again, you can see exactly the same pattern is going to emerge here. The same pattern Steven pointed out before. Okay, so where are we going here? Where are we going? Where is this discussion going to end up? Then we ruled out 3 and 8, and then we ruled out, we would have done 4 and 7 and that leaves just 5 and 6.

So this procedure leads us to conclude that the candidates will choose positions 5 and 6. Does 5 dominate 6, or 6 dominate 5, or anything like that? So this was just a simple exercise, I think. Let me just look out there, is everyone following that okay? In particular, this is a famous model in political science. Consequently as Dr.

Benjamin Polak from Yale University explains in his lecture on the median voter theorem, over the past few decades we can find multiple examples where presidential candidates have taken a rather centrist position. For example, Kennedy in , Nixon in , or Clinton in Another interesting feature of US presidential elections is that candidates for each party are chosen in primary elections. As a result, the median voter theorem predicts that it is optimal for candidates in the Republican and Democratic primaries to choose a stance that appeals to the median Republican and median Democratic primary voter.

For example, positions 3 and 7 in our illustration above. After Joe Biden became the nominee of the Democratic party, he pivoted to the left. One possible explanation for this move is that unlike in our simple model, voters may choose not to vote if both candidates are far from their own preferred position.

For example, a voter located to the far left at position 1 or the far right at position 9 may decide not to vote at all. Thus, Biden may have chosen to move to the left to encourage higher voter turnout among progressive Democrats. While game theory can provide us some insights into campaign strategy, the winning strategy for the election will remain the subject of much debate and speculation until the morning of November 4.

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