[EM] The critical importance of Precinct Summability.

[Kristofer Munsterhjelm]

On 2024-08-27 05:14, robert bristow-johnson wrote:
> 
> 
> I was away from home in my previous reply and using my phone.  About the other part ...
> 
>> On 08/26/2024 11:44 AM EDT Closed Limelike Curves <closed.limelike.curves at gmail.com> wrote:
>>
>   ...
>> I think we really need to be much more careful about
>> precinct-summability. If we're not careful, we're going to hit a
>> massive wall as soon as we talk about multi-winner systems, which
>> usually aren't precinct-summable.
> 
> If you're doing PR (which I think is the purpose of RCV in
> multi-winner election), then it's gonna be something like the Gregory
> method with Droop quota and surplus votes transferred and runoffs
> eliminating the weakest candidates.  And it's not precinct summable.

I think that's his argument.

If Droop-proportional PR methods are desirable,
and (strong) summability is desirable,
and Droop proportionality is incompatible with strong summability,
then we have to give something up.

Which is it going to be?

There may be ways to solve or circumvent the dilemma. I can think of these:

- If it turns out that DPC is not actually incompatible with strong 
summability, and we can invent a strongly summable method of a 
reasonable order, then no problem.

- We could use party list instead of candidate-centered PR, or relax the 
type of proportionality required and fill the gap with DMP or party 
list-based top-up seats. For instance, Forest's method described in 
https://rangevoting.org/PuzzQWEAns15.html uses a weaker sense of 
proportionality ("color proportionality") and is summable.

- We could use small district sizes and hope that/determine if weak 
summability is good enough. Weak summability says that if we hold the 
number of seats constant, then the method is summable, though it may be 
non-summable if we're allowed to vary the number of seats.

- It's possible that PR isn't actually needed if the single-winner 
method is good enough; or that 2- or 3-seat districts suffice for the 
same reason. Robbie Robinette argues for Condorcet this way. 
https://medium.com/@robbierobinette/american-politicians-are-divided-but-the-people-are-not-9e944b90fc0a 
and https://betterchoices.vote/head-to-head-in-congress. This is related 
to the idea that proportionality of representatives isn't needed if 
their *decisions* are representative. I still would think that PR is 
good in a non-polarized system so reps with different points of view 
could discuss where they're coming from, but it's possible that the loss 
isn't as great as we think. (More on polarization here: 
https://link.springer.com/article/10.1007/s10602-022-09378-6 and 
https://arxiv.org/pdf/2306.07147)


>> Precinct verifiability is enough. In theory, it might be possible
>> to  drop the need for precinct verifiability, if you have some kind
>> of end-to-end auditable procedure?
> 
> In the U.S. serialized ballots ain't gonna cut it.  Then we lose our vote by secret ballot.

It might be possible. For instance, Warren Smith and Ron Rivest 
mentioned a method where voters cast three ballots, two of which cancel 
each other out, and then take the identifiers of some (but not all) of 
them to use to verify the results later. The idea is that you can then 
verify that the ballots you chose were counted, but people who are 
coercing your vote can't know if you gave them the ID to your real 
ballot or to one that cancels another out.

Apparently, it's been found to be flawed if the ballot asks for results 
for multiple races. 
https://en.wikipedia.org/wiki/ThreeBallot#Broken_encryption But perhaps 
something similar can be devised.

The main problem with cryptographic schemes, I think, is that they make 
the election process more opaque. The ThreeBallot scheme can at least be 
understood by ordinary voters; even so, it's harder to deal with than no 
encryption at all. But computer cryptography would be completely opaque. 
The people would have to trust the voting machines.

Another human-legible method has apparently been tried in practice: 
https://en.wikipedia.org/wiki/Scantegrity#Use_in_public_elections

-km