Math 110 Prep questions and answers 2025
Plurality Method
a voting method that ranks candidates based on the number of first-place votes they receive.
the candidate with the most first place votes wins
Condorcet Criterion
If candidate X is preferred by the voters over each of the other candidates in a head-to-head
comparison, then candidate X should be the winner of the election.
The plurality method violates the condforcet method
monotinicity criterion
If voter change their votes to increase their preference for a choice, then it should not harm
that choices chances of winning.
Majority Criterion
If a choice has a majority of first-place votes, that choice should be the winner.
Independence of Irrelevant Alternatives (IIA)
If choice A is preferred over choice B, then removing or introducing a choice should not cause B
to lose. IT IS IMPOSSIBLE TO FIND A VOTING METHOD THAT SATISFIES ALL 4 CRITERIA.
pros of plurality method
simple
fast to process
cons of plurality method
vote splitting
doesn't fully consider voter opinion
encourages insincere voting (voting for a less desired choice for strategic reasons)
Instant Runoff Voting
, voters rank candidates by order of preference. If no candidate wins a majority, the candidates
with the fewest votes is eliminated and those votes are assigned to the voters' second choice
until one candidate attains a majority
pros of Instant Runoff Voting
reduces vote splitting
reduces insincere voting
empowers voters/increases voter turnout
reduces negative campaigning and prevents Lakehead situation
cons of Instant Runoff Voting
more complicated than plurality
harder to understand
start up costs and non-standard equipment required because of ranking
INSTANT RUNOFF VOTING VIOLATES THE CONDORCET CRITERION
Borda Count Method
Each place on ballot is assigned points depending on the number of candidates and the
candidate with the highest point total wins. Number starting at 1 from the bottom then
multiply the point by the number of votes
Borda Count pros
good for compromising
empowers voters
reduces vote splitting
encourages informed voters
reduces insincere voting
reduces negative campaigning
Borda Count cons
Plurality Method
a voting method that ranks candidates based on the number of first-place votes they receive.
the candidate with the most first place votes wins
Condorcet Criterion
If candidate X is preferred by the voters over each of the other candidates in a head-to-head
comparison, then candidate X should be the winner of the election.
The plurality method violates the condforcet method
monotinicity criterion
If voter change their votes to increase their preference for a choice, then it should not harm
that choices chances of winning.
Majority Criterion
If a choice has a majority of first-place votes, that choice should be the winner.
Independence of Irrelevant Alternatives (IIA)
If choice A is preferred over choice B, then removing or introducing a choice should not cause B
to lose. IT IS IMPOSSIBLE TO FIND A VOTING METHOD THAT SATISFIES ALL 4 CRITERIA.
pros of plurality method
simple
fast to process
cons of plurality method
vote splitting
doesn't fully consider voter opinion
encourages insincere voting (voting for a less desired choice for strategic reasons)
Instant Runoff Voting
, voters rank candidates by order of preference. If no candidate wins a majority, the candidates
with the fewest votes is eliminated and those votes are assigned to the voters' second choice
until one candidate attains a majority
pros of Instant Runoff Voting
reduces vote splitting
reduces insincere voting
empowers voters/increases voter turnout
reduces negative campaigning and prevents Lakehead situation
cons of Instant Runoff Voting
more complicated than plurality
harder to understand
start up costs and non-standard equipment required because of ranking
INSTANT RUNOFF VOTING VIOLATES THE CONDORCET CRITERION
Borda Count Method
Each place on ballot is assigned points depending on the number of candidates and the
candidate with the highest point total wins. Number starting at 1 from the bottom then
multiply the point by the number of votes
Borda Count pros
good for compromising
empowers voters
reduces vote splitting
encourages informed voters
reduces insincere voting
reduces negative campaigning
Borda Count cons
