MA-351 Homework 5
Due Tuesday, Dec 5, 2023, 23:59pm
All solutions must be submitted on the Moodle web site
for the class at wolfware.ncsu.edu.
You may upload a photo of your handwritten solution or
a file of your typed solution.
Note my office hours on my
schedule.
Please give an example of a group profile such that
Jean-Charles de Borda's count group
consensus function violates Kenneth Arrow's Property 2
(Axiom 2) [Irrelevant Alternative].
As weights, please use
$\frac{1}{N}$
for first place,
$\frac{1}{N\u20131}$
for second place,
$\frac{1}{N\u20132}$
for the third place,
...,
$\frac{1}{1}=1$
for the last place, in the presence of
$N$
candidates,
where the smaller weighted Borda number ranks higher.
Note that after eliminating the irrelevant alternative, the first place
has weight
$\frac{1}{N\u20131}$,
the second place
$\frac{1}{N\u20132}$
...,
the last place 1.