sunshinekathy
01-05-2009, 11:57 PM
A new simpler and more accurate estimate for calculating 99% Confidence election audit sample sizes is now available and could help to implement better post-election audits.
FYI, today I derived a new simpler alternative formula for post-election auditing amounts that manually audit sufficiently to ensure accurate election outcomes to at least 99% probability for detecting an outcome-altering level of miscount. (or other desired confidence level)
In the process of trying to derive a more accurate estimate for post-election audit sizes that election officials would find easy-to-use, I developed a simpler, more accurate formulaic estimate (beginning with MIT Professor Ron Rivest's original estimate of the Dopp/Stenger numerical method) that I think election officials could easily use in a spreadsheet, because I both simplified it and made it more accurate by using a more accurate margin error bound.
This new formulaic estimate has potential for being simple enough to replace the inequitable, and most often either insufficient and ineffective, or wasteful and inefficient fixed rate election audits that all states that audit elections employ today.
My new formula is shown in row three of the table on page 6 under "99% confidence audits" in this revised doc:
http://electionmathematics.org//ucvAnalysis/US/paper-audits/legislative/AnalysisHoltElectionAudit2009.pdf
The actual audit sample size would be somewhat larger that the formulaic estimate due to making the random selections district-wide (House contests) or state-wide (Senate contests) first and then randomly selecting an additional audit unit in each election jurisdiction where no audit units had been selected.
In other words, if US Representative Rush Holt's election auditing bill would require using this formulaic estimate nationwide with a requirement for 1 audit unit per election jurisdiction (county or township), then the number of precincts audited overall nationwide could be approximately equal to the 3, 5, 10% plan but be more evenly allocated to House districts and states depending on reported margins, and achieve a higher overall confidence in election results, and provide voters and candidates more equal confidence in diverse states and districts.
The constants in the formula I derived, such as 0.4 (the assumed maximum rate of margin error) and 0.01 (the desired maximum chance of not detecting the minimum level of outcome-changing vote miscount) could be changed. For instance, the 0.4 max margin error rate might be as high as 0.5 and the 0.01 max chance of missing outcome-altering vote miscount might be raised to as high as 0.05. However, if we raised the 0.01 probability to a 0.05 chance (for not detecting the smallest error required to alter an outcome), then it would be better to raise the 0.4 maximum possible margin error to 0.50 to keep the audit sample sizes conservatively large enough.
Please look at the formula and tell me if you think that election officials could understand and employ this formula? Is it simple enough?
This estimate is not as exact as more complex methods because it does not use the detailed precinct-level vote counts and only uses the total overall reported vote counts, the number of ballots cast and the total number of precincts (or other auditable vote counts).
However, the new formula is a lot more accurate and equitable than any fixed rate audit, including U.S. Representative Rush Holt's 3, 5, 10% proposal; and it is a lot simpler than other methods that require taking all the detailed vote counts into account when determining sample sizes, and I've converted the formula into a form that is simpler for election officials to understand than Ron Rivest's initial formula. As well, the new formula I derived is more accurate because I'm using it with an accurate upper margin error bound that all election auditing math experts (Professors Ron Rivest and Philip Stark, and myself) now all seem to agree on.
I've explained the formula in footnote #3 and given one Excel version for it.
I should show the derivation of this formula still (perhaps I'll write some more about it), but experts in election auditing mathematics may understand it immediately without the derivation.
Please read it and let me know if you agree that this new estimate might be a possibility (in place of a the simpler-sounding 3, 5, 10% tiered fixed rate audits) for state or federal legislation?
Actually omitting *any* precise formulas in legislation might be best, (like I've done in our shortened Utah election audit proposal (that we have given up trying to pass in Utah this year due to funding constraints)
http://electionmathematics.org//ucvAnalysis/US/paper-audits/legislative/Vote-Count-Audit-Bill-2009.pdf
but a version of my new formula could be required or recommended for estimating audit amounts because it is not too difficult for election officials to calculate simply in any spreadsheet. Certainly state-level election offices can manage using it even if a few county-level officials in some states might have trouble figuring it out if they don't use spreadsheets. (I could write a paper explaining it more clearly.)
It is true that the more complex, efficient method recommended by Aslam, Rivest, and Popa and myself, if the correct margin error bounds are used, would be more precise, but would require using all the detailed reported vote counts to calculate, and is more difficult to explain to election officials and legislators.
So, how about this compromise formula? What do you think? Is it simple enough to be easily understood and used by election officials?
This new formula is on p. 6, 3rd row, 2nd column in:
http://electionmathematics.org//ucvAnalysis/US/paper-audits/legislative/AnalysisHoltElectionAudit2009.pdf
Well, this new simpler formula is an easier one that election officials could now use to achieve a higher overall confidence in election outcome accuracy than any fixed rate audits, regardless.
Cheers,
Kathy Dopp
http://utahcountvotes.org
http://electionmathematics.org
http://kathydopp.com/serendipity/
Post-Election Vote Count Audit
A Short Legislative & Administrative Proposal
http://electionmathematics.org//ucvAnalysis/US/paper-audits/Vote-Count-Audit-Bill-2009.pdf
History of Confidence Election Auditing Development & Overview of Election Auditing Fundamentals
http://electionarchive.org/ucvAnalysis/US/paper-audits/History-of-Election-Auditing-Development.pdf
FYI, today I derived a new simpler alternative formula for post-election auditing amounts that manually audit sufficiently to ensure accurate election outcomes to at least 99% probability for detecting an outcome-altering level of miscount. (or other desired confidence level)
In the process of trying to derive a more accurate estimate for post-election audit sizes that election officials would find easy-to-use, I developed a simpler, more accurate formulaic estimate (beginning with MIT Professor Ron Rivest's original estimate of the Dopp/Stenger numerical method) that I think election officials could easily use in a spreadsheet, because I both simplified it and made it more accurate by using a more accurate margin error bound.
This new formulaic estimate has potential for being simple enough to replace the inequitable, and most often either insufficient and ineffective, or wasteful and inefficient fixed rate election audits that all states that audit elections employ today.
My new formula is shown in row three of the table on page 6 under "99% confidence audits" in this revised doc:
http://electionmathematics.org//ucvAnalysis/US/paper-audits/legislative/AnalysisHoltElectionAudit2009.pdf
The actual audit sample size would be somewhat larger that the formulaic estimate due to making the random selections district-wide (House contests) or state-wide (Senate contests) first and then randomly selecting an additional audit unit in each election jurisdiction where no audit units had been selected.
In other words, if US Representative Rush Holt's election auditing bill would require using this formulaic estimate nationwide with a requirement for 1 audit unit per election jurisdiction (county or township), then the number of precincts audited overall nationwide could be approximately equal to the 3, 5, 10% plan but be more evenly allocated to House districts and states depending on reported margins, and achieve a higher overall confidence in election results, and provide voters and candidates more equal confidence in diverse states and districts.
The constants in the formula I derived, such as 0.4 (the assumed maximum rate of margin error) and 0.01 (the desired maximum chance of not detecting the minimum level of outcome-changing vote miscount) could be changed. For instance, the 0.4 max margin error rate might be as high as 0.5 and the 0.01 max chance of missing outcome-altering vote miscount might be raised to as high as 0.05. However, if we raised the 0.01 probability to a 0.05 chance (for not detecting the smallest error required to alter an outcome), then it would be better to raise the 0.4 maximum possible margin error to 0.50 to keep the audit sample sizes conservatively large enough.
Please look at the formula and tell me if you think that election officials could understand and employ this formula? Is it simple enough?
This estimate is not as exact as more complex methods because it does not use the detailed precinct-level vote counts and only uses the total overall reported vote counts, the number of ballots cast and the total number of precincts (or other auditable vote counts).
However, the new formula is a lot more accurate and equitable than any fixed rate audit, including U.S. Representative Rush Holt's 3, 5, 10% proposal; and it is a lot simpler than other methods that require taking all the detailed vote counts into account when determining sample sizes, and I've converted the formula into a form that is simpler for election officials to understand than Ron Rivest's initial formula. As well, the new formula I derived is more accurate because I'm using it with an accurate upper margin error bound that all election auditing math experts (Professors Ron Rivest and Philip Stark, and myself) now all seem to agree on.
I've explained the formula in footnote #3 and given one Excel version for it.
I should show the derivation of this formula still (perhaps I'll write some more about it), but experts in election auditing mathematics may understand it immediately without the derivation.
Please read it and let me know if you agree that this new estimate might be a possibility (in place of a the simpler-sounding 3, 5, 10% tiered fixed rate audits) for state or federal legislation?
Actually omitting *any* precise formulas in legislation might be best, (like I've done in our shortened Utah election audit proposal (that we have given up trying to pass in Utah this year due to funding constraints)
http://electionmathematics.org//ucvAnalysis/US/paper-audits/legislative/Vote-Count-Audit-Bill-2009.pdf
but a version of my new formula could be required or recommended for estimating audit amounts because it is not too difficult for election officials to calculate simply in any spreadsheet. Certainly state-level election offices can manage using it even if a few county-level officials in some states might have trouble figuring it out if they don't use spreadsheets. (I could write a paper explaining it more clearly.)
It is true that the more complex, efficient method recommended by Aslam, Rivest, and Popa and myself, if the correct margin error bounds are used, would be more precise, but would require using all the detailed reported vote counts to calculate, and is more difficult to explain to election officials and legislators.
So, how about this compromise formula? What do you think? Is it simple enough to be easily understood and used by election officials?
This new formula is on p. 6, 3rd row, 2nd column in:
http://electionmathematics.org//ucvAnalysis/US/paper-audits/legislative/AnalysisHoltElectionAudit2009.pdf
Well, this new simpler formula is an easier one that election officials could now use to achieve a higher overall confidence in election outcome accuracy than any fixed rate audits, regardless.
Cheers,
Kathy Dopp
http://utahcountvotes.org
http://electionmathematics.org
http://kathydopp.com/serendipity/
Post-Election Vote Count Audit
A Short Legislative & Administrative Proposal
http://electionmathematics.org//ucvAnalysis/US/paper-audits/Vote-Count-Audit-Bill-2009.pdf
History of Confidence Election Auditing Development & Overview of Election Auditing Fundamentals
http://electionarchive.org/ucvAnalysis/US/paper-audits/History-of-Election-Auditing-Development.pdf