Homework exercises.

1.  Construct an example in which plurality and plurality with runoff methods give the same results but the Borda count gives a different result.

2.  Construct an example in which Plurality and Hare methods give the same result, but plurality with runoff gives a different result.  What are the results in your example if the Borda count is used?  
What are the results in your example if the Coombs method is used?
If these results are the same, can you modify your example so as to make the results according to Borda and according to Coombs different from each other?

3.  For any of the examples you have created for problems 1 and 2, determine which method is most susceptible to manipulation by insincere voting.