[EM] Most important/used election methods?

Kristofer Munsterhjelm km_elmet at t-online.de
Fri Oct 15 09:26:20 PDT 2021

```On 15.10.2021 06:42, Richard, the VoteFair guy wrote:
> In the Wikipedia article about the Minimax method, the section titled
> "Satisfied and failed criteria" indicates that the "winning votes" and
> "margins" versions are Condorcet compliant, but the "pairwise
> opposition" version is not.
>
> https://en.wikipedia.org/wiki/Minimax_Condorcet_method#Satisfied_and_failed_criteria
>
>
> Specifically it says:
> "When the pairwise opposition variant is used, minimax also does not
> satisfy the Condorcet criterion."
>
> That seems to conflict with what Kristofer is saying here:
>
>> El jue., 14 de oct. de 2021 1:45 p. m., Kristofer Munsterhjelm
>>     Minmax(wv) passes the Condorcet criterion:
>>
> https://en.wikipedia.org/wiki/Minimax_Condorcet_method#Satisfied_and_failed_criteria
>
>>     Are you referring to another method here?
The confusion, I think, is that you originally said:

> And I believe it would include the version of Minimax that uses
> winning votes -- even though this variation does not always elect the
> Condorcet winner.

Since you said "winning votes", I took that to mean Mimax(wv), which
Wikipedia calls the winning votes version. This is distinct from the
pairwise opposition version, which doesn't use winning votes; it uses
the raw Condorcet matrix instead without any transformation.

> My point was that although it does not fit the official category of
> "most of the Condorcet methods" (according to Wikipedia), I would expect
> that most of the people who signed the "Declaration of Election-Method
> Reform Advocates" would regard that method as also worth considering for
>
> I mentioned the method because the first steps toward adopting better
> methods in governmental elections require simplicity, and the pairwise
> opposition version is easier to explain (and easier to calculate) for
> non-math-savvy folks.

I would say the "bad-example" would, if not make people drop MMPO
outright, at least be considered *very* unintuitive. It is this:

3950000000: A
1: A=C
1: B=C
3950000000: B

and C wins. (Feel free to substitute a larger number if you desire!) In
the words of Chris Benham:

> The result is completely outrageous and absurd.
>
> The correct result is an A=B tie.  All but 2 of the voters were
> wronged, because their favourites should have a 50%  probability of winning.

Faced with something like that, I'd rather take the phrasing that "A's
score in the A vs B matchup is his margin of victory in the simulated
runoff".

Minmax(wv) would be better still, but it's harder to describe since it
involves a threshold.

-km
```