CEDARVILLE UNIVERSITY INTRO TO MATHEMATICS
QUESTIONS AND CORRECT DETAILED ANSWERS
(VERIFIED ANSWERS) ALREADY GRADED A+
Arrow's impossibility Theorem Ans✓✓✓A method for determining
election results that is democratic and always fair is a mathematical
impossibility
Fairness criteria Ans✓✓✓tests of fairness
preference ballot Ans✓✓✓A ballot in which the voters are asked to rank
the candidates in order of preference
Linear ballot Ans✓✓✓A ballot in which ties are not allowed
preference Schedule Ans✓✓✓grouping together of identical ballots into
a chart
transitive Ans✓✓✓a person who prefers candidate a over candidate b
and prefers candidate b over candidate c automatically prefers candidate
a over candidate c.
what are the two important facts to keep in mind when working with
preference ballots Ans✓✓✓Voter's preferences are transitive
the relative preferences of a voter are not affected by the elimination of
one or more of the candidates.
,plurality method Ans✓✓✓the candidate with the most first place votes
wins
plurality candidate Ans✓✓✓the candidate with the most first place votes
principle of majority rule Ans✓✓✓In a democratic election between two
candidates, the candidate with a majority of the votes should be the
winner.
majority candidate Ans✓✓✓the candidate with a majority of first-place
votes is called the majority candidate.
majority criterion Ans✓✓✓If candidate x has a majority of the first-
place votes, then candidate X should be the winner of the election.
with only two candidate a plurality candidate is also a Ans✓✓✓majority
candidate
The problem with majority rule is that Ans✓✓✓When there are three or
more candidates there is no guarantee that there is gong to be a majority
candidate.
, Condorcet candidate Ans✓✓✓A candidate preferred by a majority of
the voters over every other candidate when the candidates are compared
in head-to-head comparisons
Condorcet criterion Ans✓✓✓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.
what criterion of fairness does the plurality method violate
Ans✓✓✓Condorcet criterion
Voting theory Ans✓✓✓When there are three or more candidates,
determining a winner is much more complicated
Elimination Ans✓✓✓Relative preference are not affected by the
elimination of one or more candidates
What are the strengths of the plurality method Ans✓✓✓-Quick and Easy
to implement
-Satisfies the majority criterion
Weaknesses of the plurality method Ans✓✓✓-Ignores all preferences
other than the first choice
-fails the condercet criterion
-promotes dishonest voting
QUESTIONS AND CORRECT DETAILED ANSWERS
(VERIFIED ANSWERS) ALREADY GRADED A+
Arrow's impossibility Theorem Ans✓✓✓A method for determining
election results that is democratic and always fair is a mathematical
impossibility
Fairness criteria Ans✓✓✓tests of fairness
preference ballot Ans✓✓✓A ballot in which the voters are asked to rank
the candidates in order of preference
Linear ballot Ans✓✓✓A ballot in which ties are not allowed
preference Schedule Ans✓✓✓grouping together of identical ballots into
a chart
transitive Ans✓✓✓a person who prefers candidate a over candidate b
and prefers candidate b over candidate c automatically prefers candidate
a over candidate c.
what are the two important facts to keep in mind when working with
preference ballots Ans✓✓✓Voter's preferences are transitive
the relative preferences of a voter are not affected by the elimination of
one or more of the candidates.
,plurality method Ans✓✓✓the candidate with the most first place votes
wins
plurality candidate Ans✓✓✓the candidate with the most first place votes
principle of majority rule Ans✓✓✓In a democratic election between two
candidates, the candidate with a majority of the votes should be the
winner.
majority candidate Ans✓✓✓the candidate with a majority of first-place
votes is called the majority candidate.
majority criterion Ans✓✓✓If candidate x has a majority of the first-
place votes, then candidate X should be the winner of the election.
with only two candidate a plurality candidate is also a Ans✓✓✓majority
candidate
The problem with majority rule is that Ans✓✓✓When there are three or
more candidates there is no guarantee that there is gong to be a majority
candidate.
, Condorcet candidate Ans✓✓✓A candidate preferred by a majority of
the voters over every other candidate when the candidates are compared
in head-to-head comparisons
Condorcet criterion Ans✓✓✓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.
what criterion of fairness does the plurality method violate
Ans✓✓✓Condorcet criterion
Voting theory Ans✓✓✓When there are three or more candidates,
determining a winner is much more complicated
Elimination Ans✓✓✓Relative preference are not affected by the
elimination of one or more candidates
What are the strengths of the plurality method Ans✓✓✓-Quick and Easy
to implement
-Satisfies the majority criterion
Weaknesses of the plurality method Ans✓✓✓-Ignores all preferences
other than the first choice
-fails the condercet criterion
-promotes dishonest voting
