 In this video we provide the solution to question number three for practice exam number three for math 10 30 In which case we're given a voting preference schedule like so And we're asked to determine who is the winner of this election using the board account So the board account gives players points. I should say candidates points based upon their ranking Now since we only have to determine the winner We can either use the traditional board account Which I give four points for first place three points for second place, etc. Or I can use the the reduced board account But I'm only gonna give three points for first player Two points for the second one point for the third and then zero for the fourth I like that one because we have a zero then I don't have to worry about The last place votes there and so let's try to do some calculations here. Let's first think about a for a moment Okay, so a has 25 first place votes so three times 25 is 75 Like so then player. Let's see. Can it to excuse candidate a is gonna have 40 second place votes So you're gonna get a 40 times in this case to so that gives you 80 points and then player candidate a has 20 For third place votes that's worth 20 points right there. So this gives Candidate one hundred and seventy five points. All right. I can it be similar type of thing B is in first place 20 times three times that by three and we're gonna end up with 60 and then how about second place? Oh, can it be is never in second place. How about third place? Can it be shows up there 40 times? So it gives a hundred points. We only have to find the winner So it's not be you know that how about C here so to do CC is in first place 10 times So that's gonna be worth 30 points Candidate C is in second place. We get here in here. So that happens 30 times two times that by two You're gonna get 60 and then how about in third place that happens 25 times Like so 30 plus 60 is 90 plus 25 gives 115 and so that is much less than a So C is not the winner. So let's last now do D here So D is in first place 40 times times that by Three is gonna give you 120 points. I notice that's more than C has and B has total, right? How about second place D is in second place? 25 times that gives another 50 points and then D is in notice right now 120 plus 50 is 170 it's really close to a but this will determine it if you look at then the third option Third place D was in there ten times. So that gives us a hundred and eighty when we're done So only barely did player to candidate to I should say beat a but sure enough They have the highest score even if it's only by five points, you know A W is a W and so we see that candidate D is the winner using the board account