**Review Final Examination (Spring 2007)**

Honors Seminar (Humanities 320)

prepared by:

Joseph Malkevitch

Department of Mathematics and Computing

York College (CUNY)

Jamaica, New York 11451

Email: malkevitch@york.cuny.edu (for additions, suggestions, and corrections)

1. Decide the winner (if there is one) of the following elections using:

a. Plurality

b. Run-off

c. Sequential Run-off

d. Borda Count

e. Condorcet

f. Nanson

g. Coombs

(Note: Also, construct the vote matrix in each case)

I.

II

III

2. Determine the minimum winning coalitions and the Banzhaf power for the players in the following weighted voting games:

a. [11; 8, 4, 3]

b. [13; 8, 6, 5, 3]

c. [14; 8, 6, 5, 3]

d. [15; 8, 6, 5, 3]

3. For house sizes of:

a. h = 10

b. h = 11

c. h = 12

d. h = 100

use the methods:

i. Hamilton

ii. Webster

iii. Adams

iv. Jefferson

(Would it make any difference whether each state (party) is required to get at least 1 seat?)

to find the number of seats each state (party) would get if the populations (votes) involved are:

A = 10000

B = 8000

C = 6000

D = 1000

4. For the "estates" and claims below determine the amount that would be given to each claimant using:

a. Total equality of gain

b. Total equality of loss

c. Maimonides gain

d. Maimonides loss

e. Shapley

f. Proportionality

g. Contested garment rule

h. Aumann/Maschler

i. E = 210; A = 180, B = 120

ii. E = 240; A = 180, B = 120

iii. E = 270; A = 180, B = 120

iv. E = 100; A = 180, B = 120

v. E = 240; A = 180, B = 120, C = 100