Now in February, 2016, four months before the presidential election in Iceland, held every four year, there is uncertainty concerning candidates. Some are worried, if the number of candidates will be as much as 10, as some seem to expect, that the president can be elected with only 11% of the votes. In that case maybe 89% of the voters is directly against him, but the ballots will not show it. Although the case does not become so extreme one should be aware of the fact that only one Icelandic president has been elected with the majority of the votes, namely Kristjan Eldjarn in 1968. Vigdis Finnbogadottir was elected president with a third of the votes in 1980. When Olafur Ragnar Grimsson was elected president for first time (in 1996) he received just a little more than 40% of the votes. This didn´t mean that those who then voted for him backed him up from then. The rule for presidential election in Iceland does therefore, as a matter of fact, not guarantee that the president is really backed up neither in his first period nor later.
In the discussion it is now proposed in order to secure that the elected president will be backed up by the people to apply the rule to elect in two rounds, the second round being between the two that got most votes in the first round. This has been the rule for the election of the vice-chancellor in the University of Iceland. Figures from that election in 1997 show that the second round can be between the two which the most like least (cf. my book Democracy with sequential choice and fund voting, Chapter II.A.3). This rule is applied in the election of the French president. That election in 2002 was in the second round between Jacques Chirac which received 80% of the votes, while he got 20% in the first round. Jean-Marie Le Pen entered the second round with barely 17% of the votes; it was right before the third. In the second round, Le Pen got barely 18%. It showed that among those who elected others than the two in the first round—they were 13, nearly everyman elected Chirac. They did therefore in fact not back him, but they elected him to avoid whom they found was worse. Election in two rounds need therefore not tell that who is elected is backed by the people.
Presidential election by the rule sequential choice
Let us study if sequential choice leaves people in the impasse described above. To simplify the study let the number of voters be 100. We assume that in the election 11 voters rank one of 10 candidates number one, but the others are not ranked there as often. In sequential choice it is not only possible for the voter to show whom he likes most, but also whom he likes least and all there between. We assume that 89 like the above mentioned candidate least. The voter shows it by ranking him on the bottom. A candidate which is ranked number one by 10, gets 9 points; he gets one point for every time he his above an other in the ranking. A candidate which is below all the others in a sequence gets therefore no points. The candidate A which 11 rank first gets then 9x11=99 points. Every ballot gives 9+8+7+6+5+4+3+2+1=45 points. 100 ballots give altogether 4500 points. Of these A has, as said, 99 points. The remaining 9 then receive altogether 4401 points. It makes in the average 489 points, nearly five times the number of points he who the most ranked number one gets. Sequential choice, therefore, will give the winner in the conventional election a disgraceful result.
The settlement of every sequence is in the same manner as the settlement in a chess tournament where everybody plays against everybody. In a chess tournament it is the clear how superior the winner is the more participate. How strong the voters back up the winner (the elected) in sequential choice becomes by same reasons the more clear the more candidates there are.
Færðu menn snimma niður korn sín. Honorary writing for Jonatan Hermannsson seventy years, 107-108.
Korpuforlagid, Reykjavik 2016 [translated from the Icelandic]