Unexpectedly Intriguing!
March 17, 2005

Update: Welcome fans of Will Franklin's Willisms!

I have previously looked at the issue of accuracy in elections, but until now, I haven't provided a tool to do the math. Speaking of which, here is how accuracy in an election within a given voting precinct should be determined (the method is similar to that used to predict the likelihood that a complex manufactured assembly is free of defects):

Precinct Election Accuracy (%) = Number of Ballots Counted - Number of Discrepancies * 100

Number of Ballots Counted

Once this calculation is performed for each voting precinct in an election, the next step is to multiply the results together to arrive at the odds the overall election results are accurate:

Overall Election Accuracy = Accuracy for Precinct 1 * Accuracy for Precinct 2 * et cetera

The calculator below will perform this math by assuming that the number of reported discrepancies is distributed among the indicated number of precincts. As such, the results calculated will represent the best case outcome in determining election accuracy, since a higher concentration of discrepancies in a given precinct will reduce the actual election accuracy below the level calculated.

Warning: The calculator will not work for especially large numbers of precincts. This condition is a constraint of the JavaScript programming language. If you are looking to calculate the accuracy for a major election, you may need to break it down into smaller pieces, and then multiply the percentage odds for each piece together to arrive at your desired solution.


Election Data
Input Data Values
Number of Ballots Counted
Total Number of Precincts with Ballots Counted
Total Number of Reported Ballot Discrepancies
Number of Precincts with Reported Discrepancies
Number of Ballots Counted in Discrepant Precincts




Chance That Election Results Are Accurate
Calculated Results Percentages (%)
Errors Distributed Equally Among All Precincts
Errors Distributed Equally Among Discrepant Precincts

So now, having done the math, what does it take to determine if an election is accurate enough to declare a winner? To my way of thinking, I believe that the following two conditions must be met for an election to be certified as being representative of the actual ballots cast in the election:

  1. The margin of victory must be greater than the number of reported discrepancies.
  2. If the first condition is not met, the percentage odds of the election being accurate determined for the case where the number of reported errors are equally distributed among the number of precincts reporting discrepancies must be greater than 50%.

I believe the conditions listed above are the minimum necessary to be able to accept the outcome of an election as being generally accurate. Every voter in the democratic process is entitled to have confidence in the outcome of an election, and it is up to each public election official within a democracy to ensure that these minimal levels of accuracy are maintained. If they are not, then these same public officials should be held strictly accountable for failing to ensure the integrity of the voting process. Otherwise, how else are we supposed to be able to judge how well democracy actually works?

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