Re: [EM] Election-Methods Digest, Vol 231, Issue 12
Summability also carries with it the implication that the amount of
information a given precinct would need to report is small enough that all
of them can reasonably be expected to report the needed data directly to
the media and public (without relying on an internet connection) so that
anyone anywhere can take that data and come up with the same result as
anyone else (which also implies determinism). For example, I like the idea
of (Optimal) Proportional Approval Voting with 3 winners and a limit of 10
candidates (being the 10 who gather the most signatures to get on the
ballot). This requires at most 120 points of data to be reported from each
precinct or county, which is just barely within the realm of what can be
reasonably expected without centralization. The goal of this is to maintain
the robustness that comes with decentralized systems; it prevents mistakes
and attacks from scaling.
Warren Smith came up with a more precise term for this concept: efficient
parallelizability.
https://www.rangevoting.org/cgi-bin/DoPassword.cgi
On Fri, Oct 6, 2023 at 1:17 PM <
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Today's Topics:
1. Summability criterion: do I have this right? (Rob Lanphier)
2. Re: Summability criterion: do I have this right?
(Michael Ossipoff)
3. Re: Summability criterion: do I have this right?
(Kristofer Munsterhjelm)
Message: 1
Date: Thu, 5 Oct 2023 21:45:15 -0700
From: Rob Lanphier roblan@gmail.com
To: election-methods@lists.electorama.com
Subject: [EM] Summability criterion: do I have this right?
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Hi folks,
I've made a change to electowiki's "Summability criterion" article:
https://electowiki.org/wiki/Summability_criterion
Here's the chunk that I added:
For batch summability to be true, the following must be true:
- Say that candidates "A", "B", and "C" run against each other in an
arbitrary election using single-winner electoral system "S"
- Say that candidate "A" wins in batch "X" (or precinct "X") when
ballots are tabulated using single-winner electoral system "S"
- Say that candidate "A" wins in batch "Y" (or precinct "Y") when
ballots are tabulated using single-winner electoral system "S"
- Therefore, candidate "A" must win when batches "X" and "Y" of
ballots are tabulated using single-winner electoral system "S" for
"S" to
be "batch summable" (and thus, pass the "summability criterion")
(end of definition)
Am I correct? I'm trying to come up with a definition that is easy enough
for a layperson to understand, but is also accurate. I realize that this
definition only captures a subset of elections that demonstrate summability
problems, but this seems (to me) like the core of the problem with
summability.
Rob