[EM] Ranked Pairs Feint to Max Gradient Chain Building ... Update

Forest Simmons forest.simmons21 at gmail.com
Mon Feb 6 23:09:47 PST 2023


To prioritize simplicity here's my current thinking:

Gauge pairwise defeat strength with pairwise margins: winning votes minus
losing votes.

To summarize:

Initialize a pairwise defeat chain with the defeat having the greatest
defeat margin.

Until the head of the chain is uncovered,  replace it with the candidate
that covers it with the greatest margin of defeat.

Then elect the final head of the chain.

A candidate X is uncovered if it can defeat every challenger Z in two or
fewer steps ... i.e. if an uncovered X is defeated by some challenger Z,
then there is some intermediate candidate Y that is defeated by X but not
defeated by Z.

[or defeats Z but not X]

I doubt that there is any other monotone, clone-independent, Landau
efficient method that is easier to understand or tally.

Landau efficient means that it always elects an uncovered candidate.
In general, every Smith candidate has a beatpath to every other candidate.
Every Landau candidate has a short beatpath to every other candidate. How
short? At most two steps.

So every uncovered candidate is a member of the Smith set ... therefore
when the Smith set has only one member it is the one and only uncovered
candidate.

Any RCV method that elects a covered candidate X should be sued in court by
the supporters of the candidate(s) that cover X.

Part of the court's remedy, besides punitive damages, would have to be a
mandate to adopt a Landau efficient method ... which might be the easiest
route to getting this method adopted.

Once somebody is familiar with this method, why would they propose some
other voting method?

Well, suppose the method turned out to be easy to manipulate ... and that
problem could not be fixed by changing the defeat strength gauge ... then
we would cheerfully tacharlo.

So now, the more people that can test it on their favorite ballot profiles,
the better.

In particular, somebody with a computer should try it on all seven of
Kevin's standard 3-candidate test cases.

Thanks!

-Forest

On Tue, Jan 31, 2023, 6:32 PM Forest Simmons <forest.simmons21 at gmail.com>
wrote:

> I seem to have lost a draft of a reply ... I won't try to repeat the whole
> thing ... just that many numerical experiments are in deed needed ...
> specifically to find the best performing defeat strength measures.
>
> Here's one worth exploring ...
> max(winning Top, losing Bottom)
>
> Here's an example ...
>
> 8 A>B (Sincere is A>C)
> 6 B>C
> 4 C (Sincere is C>A)
>
> A>B winning top 8, losing bottom 4
> B>C winning top 6, losing bottom 8
> C>A winning top 4, losing bottom 10
>
> The max strength is 10 for C>A
>
> This restores the win to the sincere CW.
>
> I like it!
>
> This rule seems to be the best expedient against  Dark Horse winners that
> some methods elect when the middle range category is the vague,
> other/default category ... in this case the outer categories of definite
> approval (equal Top) and definite disapproval (equal Bottom) leave the
> middle category as the vague "other" default ... a dark horse red flag for
> the method inventor.
>
> Our remedy is the defeat strength's prominent usage of the max value of
> the two definite categories as a guard against an unknown nobody winning by
> default.
>
> -Forest
>
> On Tue, Jan 31, 2023, 4:16 AM Kristofer Munsterhjelm <km_elmet at t-online.de>
> wrote:
>
>> On 1/26/23 21:53, Forest Simmons wrote:
>>
>> > [Again, we used the fact that all candidates are uncovered ... which
>> > makes the initial chain head the winner. This helps explain Krisyofer's
>> > original observation that got this whole thing started. So you can see
>> > why I'm tempted to call this the KKF method!]
>> >
>> > What do you think?
>>
>> Sounds good! But I'm increasingly feeling that it's hard to understand
>> the tradeoffs of a method without having a view to their behavior, like
>> simulations. So if it turns out to be awful in practice, then perhaps
>> I'll have to retract my statement :-)
>>
>> On a broader level, I'm wondering if we should pool our simulators
>> somehow to not duplciate the effort it takes to implement methods. But
>> my own main simulator is not the prettiest of code, so I would have to
>> clean that up first. And then I don't get much further than that!
>>
>> -km
>>
>
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