Number of Voters 14 10 8 4 1
1st Choice A C D B C
2nd Choice B B C D D
3rd Choice C D B C B
4th Choice D A A A A

___________________________________________________________

Voting Methods

  • Plurality Method
  • Borda Count Method
  • Method of Pairwise Comparisons
  • Plurality with Elimination

Fairness Criteria

  • Condorcet Criterion
  • Majority Criterion
  • Monotonicity Criterion
  • Independence of Irrelevant Alternatives Criterion

For each election method, describe:

  1. How are votes tabulated?
  2. How do we decide which candidate wins?
  3. Which candidate wins in the election above if we use this method?
  4. Rank the candidates in the election above, using the appropriate ranking extension for this method.
  5. Name at least one fairness criterion that this method violates.

Describe each fairness criterion, and name at least one voting method that violates this criterion, and one voting method that satisfies this criterion.

To the best of your ability, describe the Electoral College system.  Include all details you remember, but make sure to include:

  1. The roll of Electors in the E.C. system.
  2. The roll of Electoral Votes in the E.C. system.
  3. How many Electoral Votes does a candidate need to win an election?
  4. If no one gets the number of votes from question (3), who decides the president, and how?
  5. Name at least one fairness criteria that the Electoral College system violates and at least one that it satisfies.  Explain how it violates/satisfies the ones you chose.

List any other questions you have about voting theory, the Electoral College system, or Life, the Universe and Everything.

Voting Methods

Plurality Method:

  1. 1. How are votes tabulated?

The plurality method counts the total number of first place votes received by each candidate.

  1. 2. How do we decide which candidate wins?

The candidate with the most first place votes wins.

  1. 3. Which candidate wins in the election above if we use this method? Candidate A wins.
  2. 4. Rank the candidates in the election above, using the appropriate ranking extension for this method. A, C, D, B
  3. 5. Name at least one fairness criterion that this method violates.

The plurality method violates the Condorcet criterion, since it is possible for a candidate to win in a head to head competition with every other candidate and still not have a plurality of the first place votes.

Borda Count Method:

  1. 1. How are votes tabulated?

Points are given for each vote received by a candidate, with 1 point for each last place vote, 2 points for each second-to-last place vote, etc.

  1. 2. How do we decide which candidate wins?

When using the Borda Count Method, count the total number of points each candidate receives, and the candidate with the most points wins.

  1. 3. Which candidate wins in the election above if we use this method? Candidate B wins.
  2. 4. Rank the candidates in the election above, using the appropriate ranking extension for this method. B, C, D, A
  3. 5. Name at least one fairness criterion that this method violates.

The Borda Count Method violates the Majority Criterion, since a candidate could get a majority of the first place votes, but be placed last on all of the rest of the ballots, and then not receive the most points.

Method of Pairwise Comparisons:

  1. 1. How are votes tabulated?

Each candidate goes head to head with every other candidate, and receives 1 point for winning a one-on-one competition over another candidate, ½ point for a tie, and 0 points for a loss.

  1. 2. How do we decide which candidate wins?

Count all points received during the head to head competitions, and the candidate with the most points wins.

  1. 3. Which candidate wins in the election above if we use this method? Candidate C wins.
  2. 4. Rank the candidates in the election above, using the appropriate ranking extension for this method. C, B, D, A
  3. 5. Name at least one fairness criterion that this method violates.

The method of pairwise comparisons violates the Independence of Irrelevant Alternatives criterion, since adding or subtracting an extra candidate, even one without a chance to win overall will affect create extra head to head competitions and result in more points given out – which could change the winner.

Plurality with Elimination:

  1. 1. How are votes tabulated?

Look for a candidate receiving a majority (more than half) of the first place votes.  If no such candidate exists, then eliminate the candidate(s) with the fewest first place votes and do a recount.  Repeat until a majority candidate is found.

  1. 2. How do we decide which candidate wins?

The candidate receiving a majority of the first place votes (after any necessary eliminations) wins.

  1. 3. Which candidate wins in the election above if we use this method? Candidate D wins.
  2. 4. Rank the candidates in the election above, using the appropriate ranking extension for this method. D, A, C, B
  3. 5. Name at least one fairness criterion that this method violates.

The Plurality with Elimination method violates the Monotonicity Criterion.  This means we could have a candidate win an election, but if votes are shifted that only benefit this candidate, it could cause him to lose overall.

Fairness Criteria

Condorcet Criterion: The Condorcet Criterion says that if Bob beats every other candidate in a head to head competition, that Bob (the Condorcet Candidate) should be the winner.  This criterion is satisfied by the Method of Pairwise Comparisons, and violated by the other three methods we studied.

Majority Criterion: The Majority Criterion says that if Jane receives a majority (more than half) of the first place votes in an election, Jane should be the winner.  This criterion is violated by the Borda Count Method and the Method of Pairwise Comparisons, and satisfied by the Plurality Method and Plurality with Elimination.

Monotonicity Criterion: The Monotonicity Criterion says that if Fred wins an election, and then votes are changed in such a way that the changes only benefit Fred, then Fred should still be the winner.  This criterion is violated by the Plurality with Elimination method, and satisfied by the Plurality Method.

Independence of Irrelevant Alternatives Criterion: The IIA Criterion says that if Rita wins an election and then a non-winning candidate is eliminated (or added) to the election, then Rita should still win.  This criterion is violated by the Method of Pairwise Comparisons and satisfied by the Plurality Method.

Electoral College System

Electors: When I cast a vote for president, I am truly casting my vote for a party (i.e. Republican, Democrat, Green Party, etc.), and that party’s electors.  These electors are generally high ranking members of a party, and each party will have a number of electors from each state equal to the number of Electoral College votes a state has.  If a party wins the popular vote in a state, then that party’s electors will go to the state capitol and each cast one vote for president.  In general, an elector will vote for his own party’s candidate.  If not, he is called a faithless elector.  There is no federal law that prevents faithless electors.

Electoral Votes: Each state has a number of Electoral Votes equal to the number of senators and representatives they have in Congress (in addition, Washington, D.C. gets 3 Electoral College votes).  When a party wins the popular vote in a state, that party’s electors each cast one Electoral Vote for president.  Since there are 538 total Electoral Votes, and a majority is necessary to win, a candidate needs 270 Electoral Votes to win a presidential election.

How many Electoral Votes does a candidate need to win? Since there are 538 total Electoral Votes, and a majority is necessary to win, a candidate needs 270 Electoral Votes to win a presidential election.

If no one receives the number of Electoral Votes from (3), who decides the president, and how? If no candidate receives a majority of Electoral Votes, then the House of Representatives votes, choosing among the top three candidates.  When doing this, each state delegation receives one vote and a candidate must receive a majority of the votes to win.  If the House of Representatives cannot decide before a president is to take office, then the sitting vice president becomes the president.

Name at least one fairness criteria that the Electoral College System violates and at least one that it satisfies.  Explain: Answers will vary.

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