 In this video, we provide the solution to question number 11 for practice exam number 3 for math 1030 In which case we need to find an example of a time where the plurality method might violate the Condorcet criteria. So we need a Condorcet winner who's not the plurality winner And so how do you do that? There's all I should mention that answers may vary on this one So I'm going to give you an example But this example is not the only one that you potentially could do So I'm going to come up with a preference schedule in the following way. So we're going to have five candidates first second third fourth and fifth For which we're going to have three profiles one with 49 votes one with 48 votes and One with three votes like so for which we're going to vote for a B and C and then BEB For second place third place is CDE fourth place is going to be DCD and Then finally we're going to get E a A like so so some things to note about this where I came up with it the plurality winner is going to definitely be player a right here, so the winner of the method is Player A Player candidate a had 49 votes the closest comparison would be B with 48 C got 3 and D and E got no first place votes So that's the winner of that election But some other things to note here is that player a is in dead last with regard to the others like so Notice that the majority of the votes actually put a in last place Which is kind of a curious thing and so that's how I'm kind of making this thing work A is definitely not going to be the Congress say winner here Who is then who is going to be the Congress say winner? It kind of seems like B seems very likely So if we look at B for example here if we look at pairwise comparisons first notice that a versus B With regard to a versus B Sure a has 49 first place votes is more preferred to be here But on the other hand with this one B is preferred with 48 and then since a is in dead last B is preferred here as well. And so that actually gives us 51 votes compared to 49 So B is the winner in that comparison there If you do I just want to show that B is a Congress say winner So I'm just going to do B versus C next So again in this one B wins with 48 votes And this one C would be more preferable with three votes, but then this one over here B is more preferable So actually it's 97 to 3 so B is the winner in that situation as well And again if you want to write out the numbers 49 to 51 This one was 97 to 3 if you do B versus D in that situation B is actually always preferred to D So in that situation B is the winner It would be a hundred to zero and the same thing happens with E E is always below B and all of these rankings here So a hundred to nothing again. So sure enough B B is the Condorcet winner which doesn't have to be one But in this example, I did come up with one so this was an example that I came up with to demonstrate that Plurality can violate the condorcet criterion that is the condorcet winner might not be the winner of the election But there could be many many other examples you could come up with to solve this problem