[EM] Introducing Pivot

Kristofer Munsterhjelm km_elmet at t-online.de
Wed Dec 19 14:07:36 PST 2018

On 12/12/2018 21.20, Kristofer Munsterhjelm wrote:

> I'd like to make a test set, but I've recently found myself rather short
> on spare time, so I don't think I could contribute much, at least not at
> the moment.

Here's a test entry that I made while constructing a Smith,Minmax
mono-add-top failure example with as few voters as possible:

Election 1:

8: B>D>A>C
9: C>A>B>D
3: C>D>A>B
5: D>A>B>C

The Smith set is {A, B, D}. C is the Plurality winner and also the
Minmax winner. Schulze elects A.

Election 2:

8: B>D>A>C
9: C>A>B>D
3: C>D>A>B
5: D>A>B>C
1: A>B>C>D
1: A>C>D>B

The Smith set consists of all four candidates, and the outcomes should
be the same.

This is a Smith,Minmax failure example because C is automatically
disqualified in the first election since C is not in the Smith set; but
adding some A-first ballots gets C into the Smith set, after which it wins.

Incidentally, I haven't been able to find a four-candidate Smith,Minmax
failure example that also fails MAM. That might be a good challenge to
either show impossible or to devise.

Finally, there are example elections where every positional system
except Plurality fails Majority. Could those be good test cases?

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