math
Is the set of positive integers a group under the operation of addition?
-No, it is not a group. There is no identity element in the set of positive integers under the operation of addition. -No, it is not a group. There is at least one positive integer that does not have an inverse in the set of positive integers under the operation of addition.
The apportionment method that uses a modified quota that is always rounded down to the nearest integer is
Jefferson method
a standard quota rounded down to the nearest whole number is called an _______quota
lower
the apportionment method that uses a modified quota that is always rounded to the nearest integer is _____ method
webster
the apportionment method that uses a modified quota that is always rounded to the nearest integer is __________ method
webster
Is the set of rational numbers a group under the operation of addition?
Yes, it is a group.
Is the set of rational numbers a commutative group under the operation of division?
-No, it is not a commutative group. The set of rational numbers is not closed under the operation of division. -No, it is not a commutative group. There is at least one rational number that does not have an inverse in the set of rational number under the operation of division -No, it is not a commutative group. There exist rational numbers a, b, and c such that (a/b) / c= a / (b/c) -No, it is not a commutative group. There exist rational numbers a and b such that a/b=b/a
When an increase in the total number of items to be apportioned results in a loss of an item for a group, the _____ paradox occurs
Alabama
A voting method that may not satisfy any of the fairness criteria is the _________ method
Borda Count
The voting method in which voters rank candidates from most favorable to least favorable is called the __________ method.
Borda Count
A voting method that always satisfies the majority criterion and head-to-head criterion, but may not satisfy any other criterion, is the ___________________ method.
Pairwise Comparison
Which of the following is not a flaw in the Hamilton method of apportionment?
The quota paradox
Explain why the plurality method satisfies the monotonicity criterion.
When a voter moves a candidate to first place in his or her ballot, that candidate's first-place votes increase.
Is the set of integers a commutative group under the operation of addition?
YES, The set of integers is a group under the operation of addition, because (1) the system is closed under addition, (2) there is an identity element in the set of integers for addition, (3) every element in the set of integers has an inverse underaddition, and (4) the associative property holds under addition. The set of integers is a commutative group under addition because the commutative property holds as well.
The apportionment method that uses a modified quota that is always rounded up to the nearest integer
adams method
Which of the following election methods may violate the majority criterion
borda count method
When using the pairwise comparison method, the number of comparison, c, needed when there are n candidates is determined by the formula c
c=n(n-1)/2
The total population under consideration divided by the number of items to be allocated is called the standard
divisor
If a candidate is favored when compared separately with every other candidate in an election, then that candidate should be declared the winner. This criterion is called the __________criterion
head-to-head
If a candidate wins an election and, in a recount, the only changes are that one or more of the other candidates are removed from the ballot, then that candidate should still win the election. This criterion is called the _________ criterion
irrelevant alternatives
A candidate who receives more than 50% of the votes in an election is said to have a ______ of votes
majority
If a candidate receives a majority of first-place votes in an election, that candidate should be declared the winner. This criterion is called the ______________ criterion.
majority
Jefferson's method, Webster's method, and Adams's method require using a _____ quota
modified
If a candidate wins a first election then gains additional support without losing any of the original support, then that candidate should also win a second election. This criterion is called the ________criterion
monotonicity
If the addition of a new group changes the apportionment of other groups, the _________ paradox occurs
new states
The voting method in which each candidate is compared with each of the other candidates is called the ________ method.
pairwise comparison
The voting method in which each voter votes for one candidate and the candidate receiving the most votes is declared the winner is called the _____ method.
plurality
The voting method that may involve a series of elections or eliminations using a preference table until a candidate receives a majority of the votes is called the __________ with elimination method
plurality
When group A loses an item or items to group B even though group A's population grew at a faster rate than group B's, the ______ paradox occurs
population
A table that shows how often each particular outcome occurred and that summarizes an election's results is called a ________ table
preference
Adam's method and Webster's method favor ______ states
small
The rule stating that an apportionment should always be either the upper quota or the lower quota is called ____ rule
the quota
