Simple Nonmonotonic Example

Blake Cretney bcretney at
Sun Oct 25 13:22:43 PST 1998

On Sat, 24 Oct 1998 19:04:47   DEMOREP1 wrote:
>The problem with ALL examples with changed votes is that there is only ONE
>election at a time-- NOT continuous replays of the election with some voters
>knowing how other voters have voted so that they can change their votes and
>produce strange new results.
>Thus, most, if not all, of the various criteria involving changed votes are
>totally irrelevant for election reform purposes.
>I mention again that any election reform method operates on the votes that are
>counted on election day- NOT on election day plus one, plus two, etc.
Generally, people don't present the two election examples because
they actually think there will be two elections.  They are
trying to show how the election can be affected by various changes.

So, for example, if a method violates rich-party, this will usually
be shown as a two-election example.  The example shows that running
more candidates can be advantageous under the method.  Not just in
the second of two elections, but in any election.

Likewise, people complain about monotonicity violations, not because
they think that multiple elections will actually be held, but
because they think that a decrease of support should not cause a
victory, and the two election example proves a violation.

So, the two election examples are a way of proving that a problem
exists.  That something affects the election in a different way
than we would want.  They are not founded on the belief that there
would actually be two elections.  The two elections are just a 
convenient way of thinking about the problem.


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