Bayesian Audits in Election Processes
Bayesian audits (by example)
Ronald L. Rivest
MIT
Making Every Vote Count
January 31, 2019
Audits are about:
•
Sampling cast paper ballots at random
•
Figuring out what the sampled ballots tell you
about the reported election results
–
RLAs
–
Bayesian audits (not quite the same, but simpler
to understand)
Bayesian audits are not RLAs
(but are a “close cousin”)
•
RLA Question
:
What is current ``
risk
’’ (probability that if
reported winner is incorrect, audit would
nonetheless accept it if audit stopped now)?
•
Bayesian Question
:
What is (model-based) “
upset probability”
that reported winner would lose if all ballots
were examined?
Bayesian Method (ballot polling)
1.
Start:
draw initial sample of paper ballots
2.
Extend:
simulate
what you might see for
remaining ballots: replace each draw of a
paper ballot with copy of random earlier ballot.
3.
Find winner
for all (drawn and simulated)
ballots.
4.
Repeat
steps 2—3 many times, measuring
fraction of time reported winner loses.
5.
Escalate
to larger sample if fraction > limit.
Example
•
Hershey’s Kisses
(Silver) versus
Reese’s Pieces
(Gold)
•
Reported 9 Kisses (H) versus 3 Reeses (R)
•
Sample 3H / 1R
17.4 % won by Reeses
•
Sample 4H / 1R
7.5 % won by Reeses
•
Sample 5H / 1R
2.3 % won by Reeses
•
Sample 6H / 1R
0.4 % won by Reeses
Remarks
•
Bayesian methods extend to:
–
Ballot-comparison audits
–
Hybrid audits (CVR and no-CVR strata)
–
IRV (RCV) or other complex voting schemes
(since method uses social choice function as a
“black box” at the end of each simulation trial)
•
For more details see
https://arxiv.org/abs/1801.00528
Thanks for your attention!
(and thanks to NSF CSOI and to
Verified Voting!)
The End
Bayesian audits, introduced by Ronald L. Rivest, offer a method to validate election results by sampling and analyzing paper ballots. They address the probability of incorrect winners being accepted and the upset probability of reported winners losing if all ballots were examined. The Bayesian method, like ballot polling, involves drawing samples, simulating remaining ballots, and measuring the fraction of times the reported winner loses. These audits can be applied to various voting systems and offer a nuanced approach to election result verification.
Download Presentation
Please find below an Image/Link to download the presentation.
The content on the website is provided AS IS for your information and personal use only. It may not be sold, licensed, or shared on other websites without obtaining consent from the author. Download presentation by click this link. If you encounter any issues during the download, it is possible that the publisher has removed the file from their server.
E N D
Presentation Transcript
Bayesian audits (by example) Ronald L. Rivest MIT Making Every Vote Count January 31, 2019
Audits are about: Sampling cast paper ballots at random Figuring out what the sampled ballots tell you about the reported election results RLAs Bayesian audits (not quite the same, but simpler to understand)
Bayesian audits are not RLAs (but are a close cousin ) RLA Question: What is current ``risk (probability that if reported winner is incorrect, audit would nonetheless accept it if audit stopped now)? Bayesian Question: What is (model-based) upset probability that reported winner would lose if all ballots were examined?
Bayesian Method (ballot polling) 1. Start: draw initial sample of paper ballots 2. Extend: simulate what you might see for remaining ballots: replace each draw of a paper ballot with copy of random earlier ballot. 3. Find winner for all (drawn and simulated) ballots. 4. Repeat steps 2 3 many times, measuring fraction of time reported winner loses. 5. Escalate to larger sample if fraction > limit.
Example Hershey s Kisses (Silver) versus Reese s Pieces (Gold) Reported 9 Kisses (H) versus 3 Reeses (R) Sample 3H / 1R 17.4 % won by Reeses Sample 4H / 1R 7.5 % won by Reeses Sample 5H / 1R 2.3 % won by Reeses Sample 6H / 1R 0.4 % won by Reeses
Remarks Bayesian methods extend to: Ballot-comparison audits Hybrid audits (CVR and no-CVR strata) IRV (RCV) or other complex voting schemes (since method uses social choice function as a black box at the end of each simulation trial) For more details see https://arxiv.org/abs/1801.00528
The End Thanks for your attention! (and thanks to NSF CSOI and to Verified Voting!)
