Consider the following society:

Share of voters 32% 33% 34%

First choice a b c

Second choice b c a

Third choice c a b

These are the voters' true preferences.

(i) What is the outcome under plurality voting if everyone votes sincerely?

(ii) Assuming voters in groups 2 and 3 vote sincerely, could voters in group 1 misreport to get a better outcome? How many in group 1 need to vote this way for it to work?

(iii) Assuming voters in groups 1 and 3 vote sincerely, could voters in group 2 misreport to get a better outcome?

(iv) Assuming voters in groups 1 and 2 vote sincerely, could voters in group 3 misreport to get a better outcome?