Here are some guidelines on what to study for the second exam. Rather than
distributing review worksheets with extra problems, I'll point out that
your homework assignment this week is exactly that: a bunch of review
problems. I'll also mention a few other problems you could/should try.
In general, this test covers chapters 1, 2, and 3. I won't give you any
formulas, because there aren't any formulas to give!
*** FINAL VERSION -- I fixed a typo, and added one more SSPI hint ***
NOT ON THE TEST
* Recursive Ranking Methods (pp21-24.)
Note that the _Extended_ Ranking methods (pp19-21) _are_ on the test.
ADDED TO THE TEST
* Approval Voting Method.
This is not in your textbook, but it's been covered in class twice, and
there's a description on the webpage.
CHAPTER 1 - VOTING SYSTEMS
* You should know what the following terms mean:
Preference ballot, preference schedule, insincere voting,
Concorcet Candidate, Arrow's Impossibility Theorem
* Given a preference schedule, you should be able to determine winners
using the following methods:
Plurality, Borda Count, Plurality with Elimination,
Method of Pairwise Comparisons
You should also be able to rank the candidates using the extended
version of these voting methods.
* Know the four fairness criteria, and be able to recognize situations
where they are not satisfied:
Majority, Condorcet, Monotonicity, Independence of Irrelevant
Alternatives
* Given the number of candidates, be able to calculate the total number of
pairwise comparisons. (If I ask you this, I'll give you the formula
for combinations.)
* You should be able to construct a preference schedule which shows how the
Borda Count method violates the Majority Criterion. (Hint: try using
four candidates and just two columns in your preference schedule, with
a small number of votes.)
* You should be able to construct a preference schedule which shows how the
Plurality method violates the Independence of Irrelevant Alternatives
Criterion. (Hint: try using three candidates and three columns in your
preference schedule, and use a small number of votes.
WEIGHTED VOTING
* You should know what the following terms mean:
dummy, dictator, veto power, king/queen-maker [defined in class]
weight, quota, motion, coalition, critical player, sequential
coalition, pivotal player
* You should recognize when a given weighted voting system is valid.
(Mostly this means: is the quote valid? or too high? too low?)
* Given a weighted voting system, calculated the Banzhaf Power Index (BPI)
or Shapley Shubik Power Index (SSPI) of each player.
Involved in this means you could write down the winning coalitions, find
critial players, write down sequential coalitions, find pivotal players,
etc. You should be able to calculate the total number of sequential
coalitions for N players.
Some of the questions involve Power Indices will be easier if you know
what's going on: for example, if a unanimous vote is required to pass a
motion, then each player has equal power, regardless of how many votes
each one has.
It could also help to recognize when a player is a dummy. For example,
In the weighted voting system [30:10,10,8,8,1], Player 5 (with one vote)
is a dummy. You can tell this without any calculation: Player 5 can
never turn a losing coalition into a winning one, so Player 5 can never
be critical (or pivotal), so always has a BPI or SSPI of 0%.
* You should be able to do the city council / mayor example in the
Shapley-Shubik Power Index section, or any similar problems. (For example, I
might give you a problem which is almost the same, except the number of
council members is different.)
* Suppose a committee has 20 members. 10 of them have veto power, and you need
15 members to pass a motion. Write down a description of this system in the
form [q: w_1, w_2, w_3, ..., w_20]
FAIR DIVISION
* You should know what the following forms mean:
fair share, fair division, continuous and discrete fair division
schemes
* Given enough information about players' preferences, you should be able
to carry out the following fair division schemes (or answer questions to
show that you know how):
Divider/Chooser, Lone Divider, Lone Chooser, Last Diminisher,
Sealed Bids, Markers.
It's possible that I might ask you to do the lone divider or lone chooser
methods with more than three people; if so, it will be very similar to
the odd-numbered questions in your book (so you can check your answers).
Good luck and happy studying!