[EM] Most important/used election methods?

Richard, the VoteFair guy electionmethods at votefair.org
Sat Oct 16 16:39:23 PDT 2021

```Kristofer, thank you for this insight! I passed it along to a local
advocates as a result of this insight. And I too am adjusting my
understanding of the Minimax variations, which previously I hadn't paid
much attention to (because of course I prefer the Condorcet-Kemeny method).

Once again, thank you for another great contribution to this forum!

Richard Fobes

On 10/15/2021 9:26 AM, Kristofer Munsterhjelm wrote:
> 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
>
```