ACCURACY OF THE COUNTING MACHINES

If a machine is designed and constructed for counting, then it is important to measure its counting accuracy. If  we do not allow a machine that is built for counting money to commit an error, then it is equally that we do not allow a machine that counts our votes to miscount these votes.

A vote counting machine may commit a false positive error when it decides that a ballot has one vote for a candidate even if the ballot does not have a valid mark (or a valid vote) for the candidate. Thus, the vote counting machine erred when one vote is added to this candidate when the candidate should not have.

A vote counting machine may commit a false negative error when it decides that a ballot has no vote for a candidate even if the ballot has a valid mark (or a valid vote) for the candidate. Thus, no vote is added to this candidate. Thus, the vote counting machine erred when no vote is added to this candidate when the candidate should have a vote.

A technique by comparing the total votes of a candidate using the MANUAL COUNT (which is the TRUE COUNT) and the total votes of a candidate using the MACHINE COUNT can not detect the MISCOUNTED VOTES or errors of the MACHINE COUNT if the counting machine committed both the false positive errors and the false negative errors on the votes of this candidate.

Suppose that a ballot box contains 18 ballots and one COUNTING MACHINE is use to read the votes of these 20 ballots. Further suppose that the COUNTING MACHINE reads ten ballots and assigns 10 votes to candidate Y and the COUNTING MACHINE correctly counted these votes for candidate Y. 

Then the COUNTING MACHINE reads 5 additional ballots and it added five votes to candidate Y. Now, the MACHINE COUNT has 15 votes for candidate Y. However, each of the five ballots has no valid vote for candidate Y. The MACHINE COUNT has miscounted five votes for candidate Y. 

Hence, The are 5 FALSE POSITIVE ERRORS of the MACHINE COUNT on the votes of candidate Y. 

Then the COUNTING MACHINE reads 5 more ballots and each of these 5 ballots has a valid vote for candidate Y. But, the machine did not add 5 more votes to candidate Y. Thus, MACHINE COUNT has still 15 votes for candidate Y.  The MACHINE COUNT has committed 5 FALSE NEGATIVE ERRORS.

After reading all the 20 ballots, the MACHINE COUNT has 15 votes for candidate Y. The TRUE COUNT for candidate Y is also 15 votes. 

The absolute difference between the MACHINE COUNT and the TRUE COUNT for candidate Y is | 15 -15 | = 0. Thus by the COMPARISON TECHNIQUE, the MACHINE COUNT has no error and the ACCURACY RATING of the MACHINE COUNT on the votes of candidate Y is therefore 100%.

But, the MACHINE COUNT committed 5 FALSE POSITIVE ERRORS and 5 FALSE NEGATIVE ERRORS on the votes of candidate Y or a total of 10 COUNTING ERRORS.

The COUNTING MACHINE appreciated 20 ballots for candidate Y and it committed a total of 10 COUNTING ERRORS.

Therefore, the Error Rating of the MACHINE COUNT on the VOTES of candidate Y must be 10/20 or 50% and not 0%. 

the COMPARISON TECHNIQUE on the MACHINE COUNT and the TRUE COUNT on the votes is useless since it could not determine accurately the ACCURACY RATING and the ERROR RATING of the MACHINE COUNT.

Therefore, the COMELEC must STOP using the COMPARISON TECHNIQUE in determining the ACCURACY RATING OF the PCOS MACHINES.

Any procedure that determines the accuracy rating of the PCOS MACHINES must take into account the FALSE POSITIVE ERRORS and the FALSE NEGATIVE ERRORS of the MACHINE COUNT. It can be determined using the AUDIT LOG of the PCOS MACHINE, the BALLOT IMAGES and the  REAL BALLOTS.

Felix P. Muga II
Associate Professor, Mathematics Department, Ateneo de Manila University
Senior Fellow, Center for People Empowerment in Governance

The Mathematics of Politics