If a candidate by Y2038O

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									              The Majority Criterion
If a candidate X has a majority of the first-place
votes in an election, then candidate X should be the
winner of the election.

              The 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 Monotonicity Criterion
If candidate X is a winner of an election and, in a
reelection, the only changes in the ballots are
changes that favor X (and only X), then X should
remain a winner of the election.

  The Independence-of-Irrelevant-Alternatives
                   Criterion (IIA)
If candidate X is a winner of an election and in a
recount one of the non-winning candidates is
removed from the ballots, then X should still be
winner of the election.
                      The Majority Criterion
If a candidate X has a majority of the first-place votes in an
election, then candidate X should be the winner of the election.

If a choice receives a majority of the first-place votes in an election
but does not win the election, we have a violation of the majority
criterion. When there is no majority choice in an election, the
majority criterion does not apply.
     Ex. A candidate that has a majority of the first-place votes is
     automatically the winner under the plurality method so the
     plurality method satisfies the majority criterion.
    Does the Borda count method satisfy the majority criterion?

              Number of 6 3 2
              Voters
              1st choice     C P P
              2nd choice     P S S
               rd
              3 choice       S C C
    C = Coke            P = Pepsi          S = Seven up
   Does the plurality-with-elimination method satisfy the
    majority criterion?
    Yes, if there is a candidate that is the first choice of a majority
    of the voters, then using this method, that candidate will be
    declared the winner of the election in the first round.
   Does the pairwise comparisons method satisfy the majority
    criterion?
    Yes, if candidate X is the first choice of a majority of the
    voters, then every head-to-head comparison between X and
    any other candidate will result in a win for X. X will win
    every pairwise comparison.
                     The 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.

A candidate who wins in every head-to-head comparison against
each of the other candidates is called the Condorcet candidate.
When there is a Condorcet candidate, then that candidate should be
the winner. When there is no Condorcet candidate, the Condorcet
criterion does not apply.
   Which method guarantees that if there is a condorcet
    candidate, then that candidate will win?
   Does the plurality method satisfy the Condorcet criterion?
                     Number of 5         4    3
                     Voters
                     1st choice C        S    P
                     2nd choice S        C    S
                     3rd choice P        P    C
   Does the Borda count method satisfy the Condorcet
    criterion?
         No, in the MAS election, Carmen (C) is a Condorcet
         candidate but Boris (B) is the winner using the Borda
         count method, (Since there is no candidate with a
         majority of first-place votes, the majority criterion is not
         violated.)
   Does the plurality-with-elimination method satisfy the
    Condorcet criterion? Ex #60 a, b
              The Monotonicity Criterion
If candidate X is a winner of an election and, in a
reelection, the only changes in the ballots are changes
that favor X (and only X), then X should remain a
winner of the election.
  Does the plurality method satisfy the monotonicity criterion?
   Yes, if choice X is the winner of an election using the plurality
   method and , in a reelection , the only changes in the ballots are
   changes that only favor X, then no candidate other than X can
   increase his/her first place votes and so X is still the winner of the
   election.
  Does the Borda count method satisfy the monotonicity criterion?
   Yes, if choice X is the winner of an election using this method and ,
   in a reelection, the only changes in the ballots are changes that only
   favor X, then X will get more points while the other candidates’
   points will stay the same or decrease, so X is still the winner of the
   election.
  Does the plurality-with-elimination method satisfy the
   monotonicity criterion?
   Ex # 34
  Does the pairwise comparisons method satisfy the monotonicity
   criterion?
   Yes, if X is the winner of an election using this method and, in a
   reelection, the only changes in the ballots are changes that only favor
   X, then candidate X will still win every pairwise comparison he/she
   won in the original election and possibly even some new ones – while
   no other candidate will win any new pairwise comparisons (since
   there were no changes favorable to any other candidate).
   Consequently, X is also the winner of the reelection.
    The Independence-of-Irrelevant-Alternatives Criterion
If candidate X is a winner of an election and in a recount one
of the non-winning candidates is removed from the ballots,
then X should still be winner of the election.

   Does the plurality method satisfy this criterion?

              Number of 5        4    3
              Voters
              1st choice A       B    C
              2nd choice B       C    B       C drops out
              3rd choice C       A    A
   Does the Borda count method satisfy this criterion?

             Number of 5        3    1
             Voters
             1st choice A       C    B
             2nd choice C       B    C            B drops out
             3rd choice B       A    A

   Does the plurality-with-elimination method satisfy this
    criterion?

    Ex #60 b, c [ B drops out - not D]

   Does the pairwise comparisons method satisfy this criterion?

    Ex #35

								
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