Navigate to http://www.math.union.edu/locate/MFA-09-2008/voting-rules.html
to complete this assignment.

In this demonstration, you can not add new fixed points, but you can add
voters to each ranking by repeatedly clicking on the corresponding hex
vertex, or remove voters from a vertex by ALT-clicking on it. As the red
point moves around, __the green point shows which hex vertex is closes to
the movable point__.

- When the
**mean**button is pushed, the label on this closest vertex gives the winner for the standard Borda count election. - When the
**mediancentre**button is pushed, the green line similarly indicates the "M^{c}Borda" election winner. "M^{C}Borda" is a new voting rule — we have only just begun to explore its properties.

- Show that Borda and M
^{C}Borda are different as voting rules by coming up with a profile^{*}for which the Borda winner and M^{C}Borda winners are different. Describe your setup.

^{*}Recall that adescribes how many ballots were case for each of the size rankings. You will generate a profile by clicking a certain number of times for each vertex (and zero times is certainly allowed). The total number of times that you clicked corresponds to the total number of voters in your profile.profile

- Try to find an example of a profile in which there is a tie in the Borda election (you will see more than one green line) but no tie in the M
^{C}Borda election.

- Is the opposite situation also possible (a profile that yields a tie in the M
^{C}Borda election but no tie in the Borda election?

- One attractive property of the M
^{C}Borda rule is that it is very decisive — there are ties, but very few of them. Can you come up with a general rule that states exactly which profiles yield a M^{C}Borda tie?