Self Check Answers

1. Obama’s adjusted percentage is 55,848/136,490. The numerator 55,848 is the number of votes Obama received. The denominator 136,490 is the sum of the votes cast for candidates that receive at least 15% of the votes.
2. Stephen Jones’s adjusted quota 3.524 is the adjusted percentage 70.479% times 5 delegates.
3. If Ann announced a policy position of 5 instead of 7, then the midpoint between Bob’s position of 2 and Ann’s position of 5 is . All voters with ideal points less than 3.5 vote for Bob. There are 10 such voters. The 11 other voters with ideal points greater than 3.5 vote for Ann. Ann wins the election.
4. If Ann announces the policy position 4 and Bob announces 3.9, then voters with ideal points greater than or equal to 4 vote for Ann. There are 11 such voters, so Ann wins the election 11 to 10. If Bob changes his policy to 4.1, then the 11 voters with ideal points less than or equal to 4 now vote for Ann. Ann still wins the election 11 to 10.
5. There are 10 numbers in the list 0, 1, 1, 2, 2, 3, 3, 3, 3, 4. The 5th and 6th numbers in the list are 2 and 3. The extended mean is the interval [2, 3].
6. If Carl announces policy position 7, then voters with ideal points 6 or greater vote for Carl. Carl receives 8 of the 13 votes and wins the election because the other 13 voters split between Ann and Bob.
7. If all voters with ideal points between the policy positions of and voted for , then less than 1/3 of all the voters would vote for . Because and are equidistant from the median and the distribution is symmetric, and split the remaining votes. Both and receive more votes than .
8. The median of the 9 voters’ ideal points is 5. The medians of the districts {1, 3, 5}, {2, 6, 8}, and {4, 7, 9} are 3, 6, and 7, respectively. The equilibrium position is 6.
9. The weighted median is the extended median of 1, 2, 2, 3, 3, 3; it is the interval [2, 3].