Penguins of Antarctica Hold Elections - Political Science Assignment Help

Assignment Task :

Project Overview
The penguins of Antarctica hold elections every twenty years. They use an unusual voting process where if there are n candidates in an electorate, each voter has n votes to distribute amongst them in any pattern they want. A voting paper is formal iff it contains exactly n marks (corresponding to the n candidates) each in the range 0..n inclusive and adding up to no more than n. So for an election with four candidates, all of the following would be formal papers:
4,0,0,0
2,0,0,2
0,0,3,0
0,2,1,0
1,1,1,1
Obviously many other formal votes are possible. All of the following would be informal papers: 
3,0,2,0   - total too high
3,0,2,-1  - negative votes not permitted
3,0,0     - too few marks
3,0,0,0,0 - too many marks

To determine the winner of the election, first of all the informal papers are discarded, then two separate totals are calculated for each candidate.
• The number of votes for a candidate is the sum of the votes given to that candidate on each formal paper. So given the nine papers above, the total vote for the first candidate would be 4+2+0+0+1 = 7. The total votes for the other candidates would be 0+0+0+2+1=3, 0+0+3+1+1=5, 0+2+0+0+1=3 respectively. 
• The number of wins for a candidate is the number of formal papers on which they receive the highest number of votes, each one divided by the number of candidates who receive that highest number. So given the nine papers above, the total wins for the first candidate would be 1.0+0.5+0.0+0.0+0.25 = 1.75. The total wins for the other candidates would be 0.0+0.0+0.0+1.0+0.25=1.25, 0.0+0.0+1.0+0.0+0.25=1.25, 0.0+0.5+0.0+0.0+0.25=0.75 respectively. 
 

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