Chapter 1, Problem 40E

Top-Two Instant-Runoff Voting. Exercises 39 and 40 refer to a simple variation of the plurality-with-elimination method called top-two IRV. This method works for winner-only elections. In top-two IRV, instead of eliminating candidates one at a time, we eliminate all the candidates except the top two in the first round and transfer their votes to the two remaining candidates.

Find the winner of the election given in Table 1-40 using the top-two IRV method.

Table 1-40

Number of Voters	7	6	5	5	5	5	4	2	1
$1st$	$D$	$C$	$A$	$C$	$D$	$E$	$B$	$A$	$A$
$2nd$	$B$	$A$	$B$	$A$	$C$	$A$	$E$	$B$	$C$
$3rd$	$A$	$E$	$E$	$B$	$A$	$D$	$C$	$D$	$E$
$4th$	$C$	$B$	$C$	$D$	$E$	$B$	$D$	$E$	$B$
$5th$	$E$	$D$	$D$	$E$	$B$	$C$	$A$	$C$	$D$