MA-351, 2024, Homework 5
Due Tuesday, Dec 3, 2024, 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.

1. 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 $2^{N–1}$ for first place, $2^{N–2}$ for second place, $2^{N–3}$ for the third place, ..., $2^0=1$ for the last place, in the presence of $N$ candidates, where the larger weighted arithmetic Borda average ranks higher. Note that after eliminating the irrelevant alternative, the first place has weight $2^{N–2}$, the second place $2^{N–3}$ ..., the last place 1.