Number of Votes First Place Second Place Third Place Fourth Place
5 D C B A
2 C B D A
4 A B C DIn this case, no candidate has a majority, and it now goes to a runoff
between A and D as before, which D wins. However, if your faction
switches the votes for A and B, the tabulation changes.Number of Votes First Place Second Place Third Place Fourth Place
5 D C B A
2 C B D A
4 B A C DThis forces a runoff between B and D, which (mercifully), B wins 6
to 5.
That’s sausage making for you. This tactic, which has occurred count-
less times in the history of elections, is known as insincere voting. Al-
though your faction prefers A, it will settle for B, and the possibility of D
winning is sufficiently terrifying that your faction will not vote for its
true preferences in order to avoid that outcome.
This example also illustrates two conditions that are necessary in order
for insincere voting to be effective: the decision method must be known
in advance (in this case, top-two runoff), and the votes of the others must
be known in order that a strategy can be accurately plotted. In the exam-
ple we have been studying, if the votes of the other factions are not
known, you could inadvertently undermine your own desires by switch-
ing your first-place vote from A to B. The only reason to vote against your
preferences is if you know that you can gain by doing so.
Recall that when Kenneth Arrow first began his investigations, he was
looking for a system of transferring the preferences of individuals into
the preferences of the society, and he attempted to find one that would
simultaneously satisfy several apparently desirable attributes. Although
Bismarck might have nodded approvingly about how the possible was
brought about in the previous example, it is clear that the outcome that
was achieved resulted from knowledge of the votes already cast. Intui-
tively, it seems clear that the knowledge of the votes that have already
been cast put those voting last in a more favorable position than those vot-
ing first. This certainly seems to add an element of jockeying for position
to an election, as well as violating the “one man, one vote” idea that is
The Smoke- Filled Rooms 225