40% of citizens support Mr.Rabbit for mayor, and 60% of citizens suppot Mrs.Hare?

Question

1/4 of Mr.Rabbit supporters do not bother to vote.
All of Mrs.Hare supporters vote, but the probabilty that those voters will punch the correct chad is only 2/3.

Who will win the election?

Answer 1

Mr. Rabbit should expect to win. Percentages is of the total # of people.

10% of all the voters will sit at home.
30% will vote (correctly) for Mr. Rabbit
40% we expect will vote (correctly) for Mrs. Hare.
20% we expect will vote (incorrectly) for Mr. Rabbit.

Totals:
Sit at home: 10%
Vote for Mr. Rabbit: 50%
Vote for Ms. Hare: 40%.

So Mr. Rabbit will have 5/9 of the votes to Mrs. Hare's 4/9.

Answer 2

Let's say there are 100 people. 40 support R, 60 support H.

Of the 40 that support R, 30 will vote for R, 10 will watch TV.

Of the 60 that support H, 40 will vote correctly for H, 20 will vote for R by mistake.

In all, R expects to get 50 votes, H will get 40.
So R should win with a 5/9 majority of the voters.

NOTE that R wins if at least 11 of H's supporters vote for him by mistake. If they use a ballot system like the 2000 US presidential elections, then it is possible for R to still lose. This will happen if at least 11 of H's supporters miss the correct box but do not hit the wrong one ie their votes get rejected because of uncertainty.