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    Math and Politics HW #1

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    julia.mole
    The US federal system satisfies some criteria for an ideal voting system but not others. It satisfies the monotonicity and decisiveness criteria as adding support keeps a bill passing and there is always a winner. However, it does not satisfy the anonymity criterion due to the presidential veto power, nor the neutrality criterion as it is easier to defeat than pass bills. The weighted simple majority method described is effectively the same as an unweighted simple majority method as no combination of weighted votes exceeds 50% of the total. In the examples given, different voting methods like plurality, Borda count and anti-plurality can produce different winners from the same ballots. Some positional voting methods like P(4,3,2,

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    Math and Politics HW #1

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    julia.mole
    31 views4 pages
    The US federal system satisfies some criteria for an ideal voting system but not others. It satisfies the monotonicity and decisiveness criteria as adding support keeps a bill passing and there is always a winner. However, it does not satisfy the anonymity criterion due to the presidential veto power, nor the neutrality criterion as it is easier to defeat than pass bills. The weighted simple majority method described is effectively the same as an unweighted simple majority method as no combination of weighted votes exceeds 50% of the total. In the examples given, different voting methods like plurality, Borda count and anti-plurality can produce different winners from the same ballots. Some positional voting methods like P(4,3,2,

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    Math 1007 hw #1 100% grade recived

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    The US federal system satisfies some criteria for an ideal voting system but not others. It satisfies the monotonicity and decisiveness criteria as adding support keeps a bill passing and there is always a winner. However, it does not satisfy the anonymity criterion due to the presidential veto power, nor the neutrality criterion as it is easier to defeat than pass bills. The weighted simple majority method described is effectively the same as an unweighted simple majority method as no combination of weighted votes exceeds 50% of the total. In the examples given, different voting methods like plurality, Borda count and anti-plurality can produce different winners from the same ballots. Some positional voting methods like P(4,3,2,

    Copyright:

    © All Rights Reserved
    Download as DOCX, PDF, TXT or read online from Scribd
    Download as docx, pdf, or txt
    31 views4 pages

    Math and Politics HW #1

    Uploaded by

    julia.mole
    The US federal system satisfies some criteria for an ideal voting system but not others. It satisfies the monotonicity and decisiveness criteria as adding support keeps a bill passing and there is always a winner. However, it does not satisfy the anonymity criterion due to the presidential veto power, nor the neutrality criterion as it is easier to defeat than pass bills. The weighted simple majority method described is effectively the same as an unweighted simple majority method as no combination of weighted votes exceeds 50% of the total. In the examples given, different voting methods like plurality, Borda count and anti-plurality can produce different winners from the same ballots. Some positional voting methods like P(4,3,2,

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    © All Rights Reserved
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    Download as docx, pdf, or txt
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    Math and Politics HW #1

    1.10
    a. The US federal system satisfies the anonymity criterion because of the presidential veto,
    making the president's vote more powerful than any other vote in congress, thus defeating
    the anonymity criterion.
    b. The US federal system does not satisfy the neutrality criterion because it is easier to
    defeat a bill than pass it. This is because if the president has the ability to veto any bill, in
    order to be passed it would then need to have a ⅔ supermajority in both the House and
    the Senate. This means that it is easier for a bill to fail than be passed, defeating the
    neutrality criterion.
    c. The US federal system satisfies the monotonicity criterion because, if the bill were to
    pass, and were then to receive more support from other members of congress the bill
    would continue to pass.
    d. The US federal system satisfies the decisiveness criterion, because there will always be a
    winner, and a vote can never end in a tie.

    1.12
    This method is in effect the (unweighted) simple majority method, because even with the
    assigned weights, there is no combination in which two voters weighted votes will hold the
    simple majority (over 50%) of the votes. This means that 3 of five of the voters will need to vote
    the same way to hold the simple majority, which is what produces a simple majority in an
    unweighted simple majority method as well as in this weighted simple majority method.

    2.2

    4 3 3 2 1 2 1 2

    A B C D D E E F

    B E F F F D D C

    D C D B E B F B

    E D B E C C B A

    F F E A A A C E

    C A A C B F A D

    a. Candidate A wins with plurality, with 4/18 first place votes.


    b. Candidate B wins with the Borda count method, having 57 points, in comparison to
    candidate A with 29 points, candidate C with 39 points, candidate D with 54 points, and
    candidate E with 47 points.
    c. Candidate C wins with the Hare method. Candidate F would be eliminated first, than
    candidates B,D, and E would all be eliminated because they were tied for the same
    amount of least first place votes. This leaves candidates A and C. Candidate A had 6 first
    place votes and candidate C had 12, making candidate C the winner.
    d. Candidate D wins with the Copeland method, with 4.5 points.

    e. Candidate E wins with the anti-plurality method, with 18 points. They are the only
    candidate that had no last place votes making them the winner.
    f. Candidate F wins with the vote-for-two method, with 8 points.
    2.6

    2 3 2 4 3

    A A D B C

    C B C C B

    D D B D D

    B C A A A

    Where A wins for plurality, B wins for Bonda Count, C wins for vote-for-two, and D wins for
    Anti-plurality.

    2.10
    a.
    B C A

    D D D

    A A C

    C B B
    As seen in this profile, with the Borda count method there would be one winner (Candidate D),
    whereas with the P(4,2,1,0) method there would be a tie between Candidate A and Candidate D.
    b. The P(4,3,2,1) method will always give the same result as the Borda Count Method
    because it still considers being ranked first as the most valuable, and each following
    position being less valuable with being ranked last as the least valuable. This means that
    even though no candidate is receiving zero points, they are still receiving the least
    amount of points for being ranked last, and the most amount of points for being ranked
    first. Meaning, that this method will always result in the same winner as the Borda Count
    Method.
    c. The P(8,6,4,2) method will always give the same result as the Borda Count Method
    because it still considers being ranked first as the most valuable, and each following
    position being less valuable with being ranked last as the least valuable. This means that
    even though no candidate is receiving zero points, or points are continually decreasing by
    1, they are still receiving the least amount of points for being ranked last, and being
    continually given less points for their rank, and the most amount of points for being
    ranked first. Meaning, that this method will always result in the same winner as the Borda
    Count Method.
    d. The positional voting method P(12,9,3,0) always selects the same winner as the Borda
    Count method.

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