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

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@york.cuny.edu

web page:

http://york.cuny.edu/~malk/

From: Election-Methods [election-methods-bounces@lists.electorama.com] on behalf of Forest Simmons [forest.simmons21@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

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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