 Welcome to our advanced course on game theory. This course covers the topics of social choice, mechanism design and auctions. And essentially it asks the question, if I know that agents are going to behave game theoretically, how can I design interactions for them that lead to good social outcomes? The first topic we're going to think about is called social choice. And here, leaving aside the question of strategic behavior, we ask about how to aggregate different people's preferences together in a sensible way. I'm Kevin Layton Brown. I'm from the University of British Columbia. My co-instructors who you'll meet in subsequent videos are Matt Jackson and Yoav Shoham from Stanford University. Let's get started. So social choice is essentially the problem of voting. And the first thing that you might think is that voting seems like an incredibly simple thing to study. How hard can it be to study something that after all involves just filling in one of the boxes out of some small set of different candidates? Well, I want to argue that voting actually is tricky enough that we want to have a mathematical theory of it. Here's an example. In the year 2000, the US presidential election came down to who won Florida? And it was incredibly close. After complicated recounts and an appeal to the Supreme Court, George Bush turned out to be the winner by 537 votes. However, Ralph Nader, a third party candidate with a pretty limited amount of support, got 97,000 votes. In surveys that were taken after the election, it turned out that about twice as many Nader voters would have chosen Al Gore instead of George Bush if Nader hadn't been a candidate in the election. Now, leaving aside whatever preferences we might have about who should be president of the United States, this seems like a bad outcome because it seems like more people overall preferred Gore to Bush in Florida, and nevertheless, Bush was the winner. So it seems like we didn't do a very good job in this election about taking everybody's preferences into account and selecting the right winner. Indeed, recently there have been popular movements around the world demanding new voting systems. Here, I'm showing protests in London and in Ottawa by British and Canadian citizens who think that they should have new voting systems that do a better job of taking their whole preferences into account. In this week of the course, we're gonna ask whether it's really true that there are other voting systems that are better and what better actually means. So we're gonna start by looking at different voting schemes, seeing how they work. We're gonna see that each of these voting schemes is sometimes able to give rise to kind of paradoxical outcomes where it seems like something wrong can sometimes happen. And we're gonna culminate in a famous proof that shows that in a really formal mathematical sense, it just isn't possible to avoid these kinds of failures. So thanks for joining our course and look forward to having you for the videos to come.