Update: I have added a tool to do the math illustrated below!

Those are the words of Washington State Democratic Party Chair Paul Berendt, who wrote them in a note to supporters following the results of the manual recount in the Washington State Governor's race, attempting to justify Christine Gregoire's path to the state governor's mansion over Republican candidate Dino Rossi, who had previously won the original count as well as the mandatory machine recount.

It would seem to me that Paul Berendt has never had the responsibility of producing a product that demands high quality, where accuracy in how all the product's components fit and function together is paramount in ensuring that the product itself will not be defective. Apparently, neither has Democratic Party spokeswoman Lisa Cohen, who said of the election in King County:

"It's been the most closely observed election in our lifetimes, I think. What's very important to realize and keep in context is that King County and the other counties say that their accuracy rate is more than 99.9 percent."

So that got me thinking about how overall product quality may be determined. Here, the product is election results, which are made of the components of the votes totaled in each of Washington's thirty-nine counties. The 99.9% accuracy figure Lisa Cohen cites for each county can only be obtained by taking the total number of votes in each county, subtracting out the "errors," and then dividing the answer by the original number of votes counted. This math produces the accuracy rate for the election in each county, which also represents the probability that each component is accurate. The is the accuracy rate that Lisa Cohen has latched onto to represent the probability that the election results from the state's manual recount is both accurate and decisive.

One may calculate the overall probability that the certified results of the election represents the actual outcome by multiplying the accuracy rate of each component (or county) together. If we take each of the thirty-nine counties election accuracy rate to be 99.9%, the math for finding the overall election accuracy rate would be as follows:

It would seem definitive from this result that Christine Gregoire is the winner.

Unfortunately for Christine Gregoire, Lisa Cohen and Paul Berendt, this result is completely wrong.

The reason the result is wrong is because errors at individual precincts within each county can become "washed out" at the county level. An example of this error "washout," may be found in the case of matching the number of voters to the number of ballots cast. Here, a precinct that has more voters than ballots cast can be offset by a precinct that has more ballots cast than voters. The accuracy of the election results produced at the county level will then appear to be better than it really is.

In reality, the individual components that are added together to produce election results are the vote totals from each precinct within the state, and this is the proper basis for determining the accuracy of the overall election results. King County alone has 2,600 precincts, so just applying the same 99.9% accuracy rate to each precinct within King County would produce the following result:

In other words, the overall probability that the election results produced in King County are accurate is 7.4%, even though each precinct has an assumed vote counting accuracy rate of 99.9%. Considering the individual errors that are being found at each precinct/polling place in King County, it is highly unlikely that the county's accuracy rate is even that high. (Please don't get me started on the effect the shenanigans in Wisconsin are having on election accuracy there....)

The remaining calculation of the actual overall election accuracy rate in King County, and the rest of the state of Washington, is left as an exercise for Sound Politics' Stefan Sharkansky, who has just the database to do it.

Improving the accuracy and validity of election results is another matter. For those following events in Washington, Josef A.K. at Josef's Public Journal and Stefan Sharkansky continue to perform yeoman's work in shining the light on the efforts of public officials who are trying to provide cover and rally around embattled King County Elections Director Dean Logan, who has apparently begun outsourcing key components of his legally mandated duties to the public. Special kudos go to Stefan, who is going the extra mile by also taking on some of Logan's troublesome responsibilities in ensuring the integrity of elections in Logan's portion of Washington State.

It's good to know somebody is willing to work at it.

Update: At a February 9, 2005 press conference (reported here by Sound Politics' Stefan Sharkansky, King County Executive Ron Sims and Dean Logan claimed that King County had just 1,800 errors in 900,000 votes, representing an overall accuracy rate of 99.98%. Applying this accuracy rate across King County's 2,600 precincts in the math above would indicate that King County had a 59.4% chance of being truly accurate.

But, STOP THE PRESSES! Stefan did the math on the spot and found that King County's actual accuracy rate is just 99.8% (or 900,000 minus 1,800, then divided by 900,000.) This would mean that the probability that King County's election results for the 2004 Washington State governor's race are accurate is just 0.5%!

You would think that after being pounded by blogs on a regular basis that they might start reading them....

- posted by Ironman at 6:51 AM | Permalink | |