**Mathematical Modeling: Practice 2: Mathematics of Fairness and Equity**

Prepared by:

Joseph Malkevitch

Department of Mathematics and Computer Studies

York College (CUNY)

Jamaica, New York 11451

email:

__malkevitch@york.cuny.edu__

web page:

__http://york.cuny.edu/~malk/__

1. Consider the election diagram below:

a. How many voters preferred C to B? How many voters preferred B to C?

b. How many voters preferred B to A?

c. How many voters ranked B lowest?

d. How many voters ranked A lowest?

e. How many voters rank C first?

f. How many voters ranked D is second place? How many voters ranked B in third position?

g. Who would win if each of the following methods was carried out?

i. Plurality

ii. Run-off

iii. Sequential run-off

iv. Borda Count

v. Condorcet

vi. Nanson

vii. Coombs

h. What is the ranking that is produced by the Borda count?

i. Construct a matrix whose rows and columns are labeled by the alternatives (candidates) and where the (i, j) entry is the number of voters who preferred candidate i to candidate j.