[EM] Introducing Pivot

[Kristofer Munsterhjelm]

On 01/03/2019 01.10, Carl Schroedl wrote:
> Thanks Kristofer! I hadn't considered developing distinct structures for
> relative and absolute scenarios. I have updated the GitHub repo to
> attempt to match your proposed structure. How does it look to you?

In
https://github.com/pivot-libre/ranked-ballot-scenarios/tree/master/scenarios/relative
you have the directories

https://github.com/pivot-libre/ranked-ballot-scenarios/tree/master/scenarios/relative/smith-minmax-failure

and

https://github.com/pivot-libre/ranked-ballot-scenarios/tree/master/scenarios/relative/smith-minmax-mono-add-top-failure

The former has before/ and after/ but doesn't say what the criterion
being failed *is*. (I assume it's mono-add-top.) The latter says what
criterion it is, but has only one set of ballots. So something is wrong
with the ballots.

I unfortunately haven't had the time to look at it more closely to find
out what; you might have copied my examples incorrecly, I'm guessing.

I've been more occupied with bugfixing my own program. As part of doing
so, I created the following ballot sets:

1:A>B>C>D
1:B>A>C>D
1:B>C>A>D
2:C>B>D>A
1:C>D>B>A
1:D>B>C>A

with Condorcet matrix

- 1 2 3
6 - 4 5
5 3 - 6
4 2 1 -

i.e. the upper right half of the matrix is "1 2 3 4 5 6" from left to
right, and the lower right half, reading from top to bottom and left to
right, is "6 5 4 3 2 1".

This is in row beats column form, i.e. one voter ranks A over B, two
rank A over C and so on.

A related example:

2:B>A>C>D
2:B>C>D>A
1:C>B>A>D
1:C>D>A>B

has Condorcet matrix

- 1 2 3
5 - 4 5
4 2 - 6
3 1 0 -

Pretty much every method elects B in both of these cases. They can be
used to test ballot-parsing and pairwise matrix functions.

In case I mistyped, you can verify these examples with LeGrand's rbvote:
https://www.cse.wustl.edu/~legrand/rbvote/calc.html. Select "calculate
all winners" to get the Condorcet matrix.