 In this video we provide the solution to question number 10 for practice exam 3 for math 1030. We're given the following weighted voting system. We have some unknown quota, but we have four players with votes of 11, 33, or 3, 3 and 2. And we're asked which quota, Q, because we don't know what it is yet, will make player 1 into a dictator. As in player 1 is the only player with any power whatsoever that every winning coalition has player 1 on it, okay, and no one else. So let's look at the different quotas. Now let's look at the first one. If the quota was 10, notice that with 10, player 1 has more votes than 10 right there. So and then also the other thing to note here is you need to add up together the other ones, 3 plus 3 plus 2, that's only 8, right? So if there's a quota of 8, those three players by themselves could never give you enough to make a winning coalition, but player 1 by itself has enough votes. So the thing is, if you take a quota of 10, then the coalition of just player 1 has enough votes, so that makes it a dictator, right? If a single element coalition is a winning coalition, that makes that person a dictator. So the correct answer is of course going to be A, which is 10. Now if you look to the other ones, I do want to show you why they don't work. If you tried 18 here, if you did 18, 11 is not enough by itself. So the thing is player 1 by itself is not a winning coalition, which is an equivalent condition to being a dictator. And that's the truth for all the other ones. To be a dictator, the quota needs to be less than or equal to the number of votes that player has. And so 10 is the only one that does that. So that's why the other ones can get ruled out from consideration if you're looking for a dictator.