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MA 125 - In-Class Assignment 1 - Spring 2008
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- Five hundred students at a university are voting for a new school mascot. After 300 votes have been counted, the tallies are as follows.
Purple People Eaters 106 Flying Squirrels 98 Rambling Platypi 96
(a) What is the minimum number of the remaining votes needed to guarantee that the new mascot will be the Purple People Eaters? Explain.
(b) What is the minimum number of the remaining votes needed to guarantee that the new mascot will be the Flying Squirrels? Explain.
(c) What is the minimum number of the remaining votes needed to guarantee that the new mascot will be the Rambling Platypi? Explain.
- Suppose there were 15,364 votes an election involving six candidates.
(a) If a candidate is required to have majority of the votes cast to be considered the winner, what is the minimum number of votes needed to win? Explain.
(b) If a candidate is needs a plurality of the votes cast to be considered the winner, what is the minimum number of votes a winning candidate can have and still win the election? Explain.
- A university has 75 faculty members, and they need to vote for a faculty representative to the Board of Trustees. There are four candidates running for this position, and the preference rankings are as follows.
Number of Voters 10 8 9 4 14 6 11 13 Adkins 1 1 3 2 2 3 2 2 Blythe 2 4 1 1 3 2 3 4 Cassidy 3 2 4 3 1 1 4 3 Dearborn 4 3 2 4 4 4 1 1
(a) Which candidate wins a plurality election?
(b) Which candidate wins a plurality election with a runo§ between the top two Önishers?
(c) Which candidate wins a plurality election with a runo§ between the top three Önishers, and then a runo§ between the top two Önishers of the Örst runo§?
(d) In a plurality election, could those who ranked Adkins as their top candidate have achieved a preferable outcome by voting strategically if the others voted as shown in the table? Explain.
(e) In a plurality election with a runo§ between the top two Önishers, could those who ranked Blythe Örst and Dearborn second have achieved a preferable outcome by voting strategically if the others voted as shown in the table? Explain.
