do we have more info on this topic?

• Zero-Knowledge Proof (ZKP)
• using ZKP in voting systems

Here is an example:
https://github.com/microsoft/electionguard

==
https://medium.com/edge-elections/what-is-a-zero-knowledge-proof-aebe33cb47af
Verifying a secret’s truthfulness without revealing the secret itself
Have you ever tried to demonstrate to another person that you know a secret without revealing the secret itself? It might seem difficult to convince them that you have specific knowledge without telling them what that knowledge is. However, this is the exact scenario for many digital and online processes in which the system must verify that certain information is correct or true without disclosing the potentially sensitive content (such as personal data). This is precisely where zero-knowledge proofs (ZKPs) come in.

A ZKP is a cryptographic protocol between a prover, who we can call Peggy, and a verifier, Victor, in which the former tries to convince the latter that some statement is true without revealing any information other than the truthfulness of the statement. The theory behind ZKPs is explained rather well in the article How to explain zero-knowledge protocols to your children.

The story tells of a magic cave whose entryway forks into two dark winding passages: one to the left and the other to the right. Apparently, deeper into the cave, the two paths migrate back toward one another and almost connect to form a continuous, circuitous path, but remain separated by a wall. Therefore, if you decide to run into one passage, you must get out of the cave by turning around and taking the same passage back.

Nevertheless, the cave holds a secret: whispering the magic words “open sesame,” the wall between the passages opens and they become connected. Peggy tells Victor that she knows the magic words that open the wall, but he wants her to demonstrate that this is indeed true. In order to do so, Victor proposes a challenge: he will wait at the entry of the cave and will ask Peggy to go into the cave using the left-hand passage and to come out using the right-hand passage. This is only possible if Peggy knows the magic words, so if she successfully completes the challenge, Victor can be convinced that Peggy knows the magic words despite neither of them telling the other what the magic words are.

In this way, a zero-knowledge proof should satisfy the following properties:

Completeness: If the statement is true, the prover can succeed in convincing the verifier that it is true.
Soundness: If the statement is false, a prover cannot succeed in convincing the verifier that it is true.
Zero-knowledge: If the statement is true, a verify does not learn anything more about the statement other than that it is true.

How are zero-knowledge proofs used in online voting systems?
Zero-knowledge proofs are a key element when talking about verifiability or vote correctness in online voting systems (to learn more about security requirements for online voting, check out this article).

Vote correctness
Let’s think of a referendum in which the voter is presented with a list of questions, and they have to answer either yes or no to each one of them. In order to encrypt these answers, the voting device (a mobile phone, a laptop, etc.) understands the answer yes as a 1 and the answer no as a 0. In this kind of system, it is important to demonstrate that the value encrypted is indeed a 1 or a 0, in order to prevent a malicious voting device from voting more than once for a question, e.g.: encrypting a choice with the number 3, giving 3 yes votes to a single question. In order to do that, the system generates a zero-knowledge proof to prove that the value encrypted is either a 1 or a 0 without giving any clue about the exact choice that was encrypted.

Universal verifiability
In order to provide universal verifiability, an online voting system should generate evidence which enables anybody to check that the election results have been calculated from votes cast by eligible voters, and that these votes have not been manipulated during the counting process. This evidence is usually provided in zero-knowledge proofs.

Independently of the anonymization mechanism used during the counting process (such as mixing or homomorphic tallying), votes must be decrypted. Decryption is a sensitive operation that needs a private key to be executed. This key must be protected in order to preserve each voter’s privacy. If we want to verify that the decryption process has been done correctly and that no votes have been modified, added, or deleted during the process, zero-knowledge proofs are generated in order to demonstrate that the decrypted votes are those that were encrypted, without leaking any information about the election private key and the contents of each vote.

Zero-knowledge proofs are just one of the many security protocols that can be implemented in an election with online voting, and they specifically help to offer verifiability and a certain level of transparency while still protecting voter privacy and overall election integrity. If you’re interested in taking a deep dive into ZKPs and other security mechanisms and processes used for online voting, take a look at our resource center.

Assuming that these best practices are followed:
https://www.fairvote.org/best_practices_for_releasing_rcv_election_results

• Release a preliminary round-by-round tally on Election Night
• Continue to release preliminary tallies as more votes are counted
• Conduct vote total checks with each release of preliminary results
• Publish the full ballot record so that anyone can verify the result
• Make use of existing tools for visualizing RCV results
• Clearly communicate expectations, timelines, and results

To what extend are these points still valid / invalid:
● Less accountability due to required centralized tabulation. RCV presents serious barriers to local oversight of elections, compromising checks and balances. Local elections officials are unable to generate the ballot sub-totals required for local audits. In contrast, all other voting methods considered here allow local tabulation (e.g, precinct-level tallies), which ensures that there can be checks and balances with a multitude of witnesses at each local tally and ease of audits at the local level.
● Lack of precinct summability results in compromised election security. Ballot centralization presents serious issues for election security.
Complexity in the many round tabulation process means that any errors or tampering which may occur are much harder to detect, and that less people overseeing the election would be able to identify an issue even if they were looking in the right place.

Assuming that each precinct publishes periodically preliminary RCV totals (publishing 'raw data' maybe a challenge) - questions:

• Q1: Theoretically we should be able to relatively easilly audit the election - right?
• Q2: Are the 'RCV best practices published by FairVote (releasing RCV election results 'good enough'?
• Q3: What else is missing in the 'RCV audit best practices'
• Q4: To what extend the challenges related to 'RCV transparency / security challenge / overseeing the election' remain in place even after publishing the best practices?
• Q5: I do not understand this objection "Local elections officials are unable to generate the ballot sub-totals required for local audits".

As a devils advocate - security challenges are present with every voting method (including STAR Voting)
finding errors, potential tampering, etc.

I agree that a central tabulation requirement for RCV is a huge bummer - but security issue / auditing / checking totals - is not that different than any other voting method - right?

Maybe I do not understand the challenge though:
RCV example - precinct 1
3: B>A
1: A>B
RCV example - precinct 2
2: B>A
8: A>B

RCV example - totals from all precincts:
5: B>A
9: A>B

How is it different (from Audit perspective / checking totals) from STAR Voting:
STAR Voting example Precinct 1
3: B=5, A=4
1: A=5, B=4

STAR Voting example Precinct 2
2: B=5, A=4
8: A=4, B=4

STAR Voting example - totals from all Precincts:
5: B=5, A=4
9: A=5, B=4

I am member of member of STAR Voting Local Chapter - https://www.facebook.com/groups/209427010120253

I am interested in:

• Voting software simulation, voting file formats
• How to make small, single winner elections simple and fun - web voting and voting simulations
• Voting apps on iPhone / Android

I like Approval Voting for its simplicity and STAR Voting for its Expressiveness and Accuracy.

Phone +1-919-602-5424
email: masiarek@gmail.com

What to do with floats in STAR Voting?

Single winner
See example 'test_original_example' at https://github.com/Equal-Vote/starpy/blob/main/STAR_Test.py

Example:

• A[1.0] B[3] C[4.9]

Option 1 - Use 'as-is' - assume more accurate data is a good thing?

• if allow - how many digits?

Option 2 - round it to nearest integer?

I assume that a warning message should be issued "Scores provided as 'floats' - expected scores as whole numbers {0, 1, 2, 3, 4, 5}.

• no warning in this case - correct?
  A[1.0] B[3.00] C[4.0000]

How about STAR Multi-winner?
Any special considerations related to Multi-winner?

My brain melts when reading this article: Are Condorcet and Minimax Voting Systems the Best? by Richard B. Darlington:
https://arxiv.org/pdf/1807.01366.pdf

What is 'minmax-TD' and how does it compare to STAR Voting?
Are the conclusions correct in this article?

thank you
adam
https://arxiv.org/pdf/1807.01366 - current version: [v10] Mon, 9 May 2022 13:44:20 UTC (506 KB)

@keith-edmonds https://www.votingtheory.org/forum/topic/241/zero-knowledge-encryption-using-in-voting-methods?_=1664064515062

Do we have a list of GitHub links with Voting methods, test cases and expected results?

This is what I found so far:

• https://github.com/endolith/elsim/tree/master/elsim/methods

Dear team,
I would like to sincerely apologize for my mistake regarding the graphics shared in the public forum.

I acknowledge that I did not follow the proper protocol for graphics in draft status and in private channels,
and
I also understand the importance of maintaining the context and consent when sharing someone else's work.

My main objection - loss of expressive ballot.

Plurality voting is among the least expressive voting methods there is available.

2CV method seems to force voter to express opinion on two candidates only (lost expressiveness of the voting ballot).

You may very well have opinions about some or all of the candidates on a ballot, and yet you only get a say about two candidates only.

Other voting methods allow you to express yourself in different kinds of ways — for example:

• approval voting allows voters to choose any number of candidates;
• RCV lets you rank candidates by preference;
• score or range voting asks voters to give each candidate a score, with the winner being determined by the candidate with the highest total or average score.
• STAR Voting - multiple candidates - both score and preference !

Please add your comments, thoughts, suggestions directly to the file:
STAR Voting - testing file format (upload files used for testing)

• format specification, ballot data and expected results
  https://docs.google.com/document/d/1lEed7HsjJ92KuxwYzScjfAb47ztskbrflGB58oV5FxA/edit#

We need three small, illustrative elections to demonstrate each ‘problematic’ box separately (avoid ‘Less Problematic’ Exhausted Ballots).

Assumptions:

• ranking limit 3 (or 5 if easier to re-create)
• number of candidates 5 (or less if easier)
• all voters correctly rank all the ballots (no spoilers, no bullet voting)
• all voters rank all ranks within Ranking Limit (3 or 5)

Context:

• article https://docs.google.com/document/d/1ASC5BS10rCfAYZWGeCyS7dKdKc4p5wwI6DHs4F7ScGc/edit

• presentation https://docs.google.com/presentation/d/1ipof9WSSy0GenVKWfKLu_jlYwUIT0TU0WVSAap0VZ5Q/edit#slide=id.g27f6bb33467_0_1

Comments, feedback - very much appreciated!

Book Chaotic Elections - Saari, page 34:

Strange Plurality voting notation:
A > C > B supported by a 5 : 4 : 2 tally.

Have you seen it somewhere?

Additionally, it is strange to see 'ranks' for plurality voting results/winners (instead of 'chose-one').

8:Ava>Cedric>Deegan>Bianca>Eli
6:Ava=Bianca=Cedric>Eli>Deegan
6:Eli>Ava>Bianca=Cedric=Deegan
6:Deegan>Bianca=Cedric>Eli>Ava
4:Bianca>Ava>Eli>Deegan>Cedric
3:Eli>Deegan>Bianca=Cedric>Ava
2:Deegan=Eli>Bianca=Cedric>Ava

1. preference matrix at https://electowiki.org/wiki/Ranked_Robin:
   

2. preference matrix at - https://www.cs.angelo.edu/~rlegrand/rbvote/calc.html
   

Youtube Video – [02:50..]

Ranks
G,B,P,R,O
18:1,5,4,2,3
12:5,1,4,3,2
10:5,2,1,4,3
9: 5,4,2,1,3
4: 5,2,4,3,1
2: 5,4,2,3,1

Ranks converted into Scores
G,B,P,R,O
18:5,1,2,4,3
12:1,5,2,3,4
10:1,4,5,2,3
9: 1,2,4,5,3
4: 1,4,2,3,5
2: 1,2,4,3,5

Voting Method and Winner
Plurality - Green
Two-Round Runoff- Blue
RCV IRV - Purple
Borda - Red
Range - Red
Approval - Red
Condorcet - Orange
STAR Voting - Orange

Here are my calculations: https://docs.google.com/document/d/1icQZ1efJV4XX7fD0_OTjNnW7uhfFV4lxbz5afTmqcyg/edit

ordered majority rule - Condorcet, IIA, monotonicity-not desirable properties ?!

A Majority Rule Philosophy for Instant Runoff Voting
https://arxiv.org/abs/2308.08430

Conclusions
IRV is the only voting method to satisfy ordered majority rule, which ensures the election of a candidate from the majority coalition while preventing opposition voters from influencing the choice of candidate from the faction they oppose. Ordered majority rule determines the relative social order between any two candidates by counting only ballots from those voters who do not prefer another major candidate, while ignoring all minor candidates.
Ordered majority rule is incompatible with the Condorcet criterion and independence of irrelevant alternatives because Condorcet and IIA demand that the relative social ranking between two candidates should depend on the relative social ranking of these candidates on all ballots. In addition, it is incompatible with monotonicity because monotonicity demands that if supporters of minor candidates have influence over lower ranked candidates, then supporters of major candidates should have equal or greater influence, while IRV does not grant influence over the social ranking of two candidates by voters who prefer a different major candidate. For situations where allowing supporters of a major candidate to have influence over the relative social ranking between other major candidates is deemed inappropriate, compliance with Condorcet, independence of irrelevant alternatives, and monotonicity are not desirable properties of a voting system.

My main objection - loss of expressive ballot.

Plurality voting is among the least expressive voting methods there is available.

2CV method seems to force voter to express opinion on two candidates only (lost expressiveness of the voting ballot).

You may very well have opinions about some or all of the candidates on a ballot, and yet you only get a say about two candidates only.

Other voting methods allow you to express yourself in different kinds of ways — for example:

• approval voting allows voters to choose any number of candidates;
• RCV lets you rank candidates by preference;
• score or range voting asks voters to give each candidate a score, with the winner being determined by the candidate with the highest total or average score.
• STAR Voting - multiple candidates - both score and preference !

Both STAR and RCV can fail to chose CW (Condorcet Winner).

How often does this happen?
Do we have any GitHub simulation software to flash it out (ideally with few example ballots).

Not sure what it is - but I never heard this term before - hence posting it here:

https://stablevoting.org

https://github.com/voting-tools/stablevoting-backend

Is this factually correct - any comments, ideas?https://www.rankthevoteohio.org/rcv_is_not_a_condorcet_system

Are these the best explanations? Anything else worth reading?
https://www.starvoting.org/pass_fail
https://electionscience.org/library/later-no-harm-criterion/
https://en.wikipedia.org/wiki/Later-no-harm_criterion
https://www.rangevoting.org/LNH.html

   A,B,C,D,E
8: 3,0,1,1,1
5: 0,4,0,0,0
2: 0,1,3,2,1
1: 0,2,5,4,3

Who is the Condorcet Looser (CL) and Condorect Winner (CW)?
How to build the Preference Matrix (find CW and CL) - Pairwise comparison.

Assume that election officials tossed a coin ahead of time - and the following Candidates were selected as tie breakers:

1. A
2. B
3. C
4. D
5. E

Tiebreaker candidates are selected from the above list, preferring candidates with lower numbers.

We have 4 seats to win (with 5 candidates) - who should win this election?