The election of the chancellor of the University of Iceland took place in two rounds in the spring of 1997. A rule existed providing for a second round between the two candidates who received the largest number of votes, if no candidate received majority support. This was the first time the rule needed to be invoked. All professors at the University are eligible for election, but on this occasion five of them had indicated an interest in standing for the position. In the preliminary heat, the candidates received 25%, 21%, 22%, 15% and 11% of the votes. The one with the smallest following then retired from the contest. In the election that followed a month later, the four remaining contestants received 27.2%, 28.6% 21.3% and 21.2% respectively. A second round of voting took place a week later between the two candidates who emerged with the largest number of votes from the first round; their relative positions remained unchanged.
No investigation was performed as to whether, in the first round, any voters failed to vote for the candidates of their choice out of the conviction that they would have little hope of going forward to the second round. Nor was there an investigation into how voters mentally ranked the candidates they did not vote for. Let us imagine that the two candidates who received the most votes in the first round were those who were considered the worst choices by those voters who did not vote for them. Let us also imagine that the two candidates who received the least support were actually regarded as the second-best choices of those who did not vote for them. There is no evidence to indicate that this was the case, nor any grounds to suspect that it was; nevertheless, if it is the case, this procedure can, in the second round of the election, result in a contest between the two candidates that most of the voters actually wanted least, with the result that one of them would be elected.
Let us consider how the situation would have turned out with sequential choice, based on the premises used in the above hypothesis, i.e. with A and B placed at the bottom of the list by those who did not rank them in first place and C and D ranked as the second choice of all those who did not rank either of them in first place. The votes in the actual election are rounded to the nearest whole numbers: A 27, B 29, C and D tying with 21 each. The outcome with sequential choice would have been as follows:
27 |
29 |
21 |
21 |
A |
B |
C |
D |
C,D |
C,D |
D |
C |
B |
A |
A,B |
A,B |
The scores would have been:
A: 27x3+21x0,5+21x0,5=102 (A and B share points for 3rd place)
B: 29x3+21x0,5+21x0,5=108
C: 27x1,5+29x1,5+21x3+21x2=189 (C and D share points for 2nd and 3rd place)
D: 27x1,5+29x1,5+21x2+21x3=189
The result is that C and D would have received the same number of points, and considerably more than A and B, who went ahead to the second round in the actual election.