[EM] The heuristics for gauging defeat strength by winner security plus loser insecurity

[Forest Simmons]

Thanks, Joe.  I'm aware of this, but haven't yet given it the attention it
deserves.

-Forest

On Fri, Oct 28, 2022, 6:30 PM Joe Malkevitch <jmalkevitch at york.cuny.edu>
wrote:

> Dear Forest,
>
> I assume you have seen
>
> https://arxiv.org/pdf/2210.12503.pdf
>
> Best wishes,
>
> Joe
>
> ------------------------------------------------
> Joseph Malkevitch
> Department of Mathematics
> York College (CUNY)
> Jamaica, New York 11451
>
> My email is:
>
> jmalkevitch at york.cuny.edu
>
> web page:
>
> http://york.cuny.edu/~malk/
> ________________________________________
> From: Election-Methods [election-methods-bounces at lists.electorama.com] on
> behalf of Forest Simmons [forest.simmons21 at gmail.com]
> Sent: Friday, October 28, 2022 7:22 PM
> To: EM
> Subject: [EM] The heuristics for gauging defeat strength by winner
> security plus loser insecurity
>
> CAUTION: This email originated outside of CUNY.edu. Do not click on links
> or open attachments unless you recognize the sender and know that the
> content is safe. Never send login credentials, financial information, or
> sensitive information by email. Report suspicious email to
> reportspam at york.cuny.edu
> Let's say that an alternative X is inimical  or friendly to alternative Y
> depending on whether or not it defeats Y pairwise.
>
> And by extension a ballot B is inimcal or friendly to Y according to the
> hostility or friendliness of it's too ranked alternative.
>
> The more you are surrounded by friends, generally speaking, the more
> secure we feel. Conversely, the more we are beset by enemies, the more
> insecure we feel.
>
> These considerations motivate the following definitions: the insecurity of
> an alternative is the percentage of the ballots that are unfriendly to it.
> The security of an alternative is the percentage of the ballots that are
> friendly to it.
>
> Now consider the defeat X>Y in terms of the security of X and Y. The more
> secure X, the greater percentage of ballots friendly to X, which tends to
> corroborate the X>Y "proposition", in the language of Condorcet.
>
> Also the greater the insecurity of Y, the greater percentage of the
> ballots that are hostile to Y, which also tends to corroborate the
> hypothesis X>Y.
>
> This suggests that the sum
>
> security(X)+insecurity(Y)
>
> makes sense as a measure of defeat strength.
>
> I believe that this is the best known defeat strength gauge that we have
> found so far for the classical Universal Domain Condorcet methods (Ranked
> Pairs, Schulze, and River).
>
> It seems to me to be the most natural extension of the fpA-fpC solution to
> the basic Condorcet cycle problem.
>
> -Forest
>
>
>
>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.electorama.com/pipermail/election-methods-electorama.com/attachments/20221028/029b3faf/attachment.htm>