Here is another example
of an election with three
candidates (call them A, M, and Z).
Suppose the preferences of the voters
are as follows:
| Candidate | First choice percent | Second choice percent |
| A | 40 | 9 |
| M | 24 | 76 |
| Z | 36 | 15 |
A top-two system would result in A and Z
being the finalists, with Z winning
51-49. This is different from
the example in the previous post
because most of the voters who prefer
M have Z as their second choice.
Now consider a system where
dropping out is optional if a candidate
reaches a certain threshold in
the first round (suppose the
threshold is 20 percent). In this
system the second round is decided
by plurality.
In this case Z would not
drop out (unlike in the previous
post). If M drops out, then Z wins.
The A voters would prefer
it if A dropped out and M stayed in,
so that M would win (since M is the
second choice of both A and Z voters).
However, A is unlikely to drop out after
receiving the most votes in the
first round. If nobody drops
out, and the second round is
decided by plurality, then A
would win.
There is the question:
would M drop out? Maybe A and Z
totally detest each other, but maybe
M only somewhat dislikes both A and Z.
In this case M might not want to drop
out because M voters don’t really care
a lot whether A or Z wins, although
they have a bit of preference for Z
over A. However, in that case Z
voters would have an incentive
to misrepresent their preference
and vote for M, becuase they would
rather have M win instead of letting
A win with a plurality of 40 percent.
As the Arrow theorem predicts, a
three-way race is complicated, and
it is hard to predict who will win
and it is hard to decide who should win.
……………..
–Douglas Downing
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