THREE METRICS FOR THE PCOS MACHINES

A PCOS MACHINE BY SMARTMATIC

In measuring the accuracy of the PCOS COUNT we propose that the COMELEC shall establish a metric for three areas where the PCOS is making a decision when it scanned a ballot. These are: 

1.  Decision on whether a ballot is valid or not,
2. Decision on whether an over-voting occurs in a certain position, and
3. Decision on whether an oval has a valid mark or not.

A Metric for the PCOS Decision on the Validity of a Ballot

A ballot contains around 20 to 25 votes, about 10 different elective positions, and around 400 to 500 ovals.

 If a PCOS machine decides that a ballot is invalid when it is not, then about 20 to 25 votes are lost and the PCOS COUNT will be incorrect. A PCOS machine may decide that a ballot is valid even if it is not and proceed to count the votes in the ballot. Thus, a metric shall be established to measure the accuracy of the PCOS Machines in determining whether a ballot is valid or not.

In finding the accuracy of the PCOS machines on the validity of a ballot we have to determine the maximum number of ballots that a PCOS machine will scan since any accuracy rating that can be established in this number of ballots, then it will be true for a smaller number of ballots.

I think it is safe to say that a PCOS machine will scan less than 1,000 ballots in the coming elections. Hence, COMELEC shall require that the error rating of the PCOS MACHINES in determining whether a ballot is valid or not shall be at most 1 error out 1,000 ballots.

Therefore, the COMELEC shall require that the accuracy rating of the PCOS MACHINES in determining whether a ballot is valid or not is 99.9%.

A Metric for the PCOS Decision on Over-Voting

A ballot may contain about 10 elective positions. An elective position may have one vote as in the case of the Party List Position or of the Member of the House of Representative in a Legislative District. It may contain an elective position that allows at most 12 votes as in the case of the Senatorial Position.

If a voter voted for more than the required number of votes in an elective position, then an over-voting occurs. If it happens then the vote or votes in that elective position will not be counted. However, a PCOS MACHINE may decide that no over-voting occurs even if there is one, and may proceed to count the vote or votes in that position. The PCOS MACHINE may also decide that there is an over-voting in an elective position even if the voter voted for less than the allowed number of votes.

Thus, we have to devise a metric to measure the accuracy of the PCOS MACHINE in determining whether there is an over-voting or not in an elective position.

A PCOS MACHINE may scan on the maximum about 1,000 ballots. Since a ballot may contain at most 10 elective positions, a PCOS MACHINE is giving a decision whether an over-voting occurs to about 10,000 elective positions. Thus, the COMELEC shall require an error rating of at most 1 error out of 10,000.

Therefore, the COMELEC shall require an accuracy rating of 99.99% for deciding over-voting in an elective position.

A Metric for the PCOS Decision on the Validity of a Mark

If a ballot is valid and no over-voting occurs, then we shall proceed to determine the accuracy of the PCOS COUNT on the votes of all the candidates appearing in the ballot.

A PCOS MACHINE is designed to scan a ballot and determine whether an oval has a valid mark or not. An oval has no valid mark if it is empty or if the amount of shading does not pass a required threshold which can be calibrated in the PCOS MACHINE.

If a PCOS MACHINE detects a valid mark on an oval, it will add one vote to the candidate that corresponds to the validly marked oval. If the PCOS MACHINE decides that the oval has no valid mark, then no vote will be added to the candidate that corresponds to the oval.

An error occurs when a PCOS MACHINE add one vote to a candidate, when the oval corresponding to the candidate is not validly marked. This PCOS COUNT error is called a FALSE POSITIVE ERROR.

Another error occurs when a PCOS MACHINE does not add a vote to candidate, if the oval corresponding to the candidate is validly marked. This PCOS COUNT error is called a FALSE NEGATIVE ERROR.

The RMA commissioned by the COMELEC in 2010 and the mock election supervised by CSER last month compared the PCOS COUNT and the MANUAL COUNT on the votes of each candidate. This COMPARISON TECHNIQUE cannot detect really detect the difference of the PCOS COUNT from the MANUAL COUNT.  If we assume that the MANUAL COUNT is the TRUE COUNT then the COMPARISON TECHNIQUE cannot detect the errors of the PCOS COUNT.

For example, in a precinct with 100 ballots, the PCOS COUNT counted 90 votes for candidate Y and the MANUAL COUNT for candidate Y showed 90 votes also, then the COMPARISON TECHNIQUE will conclude that the PCOS COUNT and the MANUAL COUNT are the same and the PCOS COUNT is a 100% match to the MANUAL COUNT on the votes of candidate Y.

If the MANUAL COUNT is the TRUE COUNT, then the COMPARISON TECHNIQUE will conclude that the PCOS COUNT is 100% accurate on the votes of candidate Y.

However, it is possible that the PCOS COUNT counted correctly the first 90 ballots and computed 85 votes for candidate Y. It is also possible that in the next five ballots, the PCOS COUNT committed 5 FALSE POSITIVE ERRORS and added 5 votes to candidate Y even if the ovals corresponding to candidate Y were not validly marked. Thus, candidate Y has 90 votes after counting the 95 ballots. It is also possible that in the last five ballots, the PCOS COUNT committed 5 FALSE NEGATIVE ERRORS and did not add 5 more votes to candidate Y even if the ovals were validly marked. Therefore, it is possible that PCOS COUNT and MANUAL COUNT matched even if the PCOS COUNT committed 10 ERRORS. This is possible, if the number of FALSE NEGATIVE ERRORS and the number of FALSE POSITIVE ERRORS are equal.

Since the PCOS MACHINES scanned 100 ballots, it made decision on whether 100 ovals corresponding to candidate Y were validly marked or not. Since the PCOS COUNT committed 10 errors, it follows that the ERROR RATING OF THE PCOS COUNT on the votes of candidate Y is 10 out of 100 or 10%.

Therefore, the accuracy rating of the PCOS COUNT on the votes of candidate Y is 90% and not 100% as shown by the COMPARISON TECHNIQUE. If candidate Y is a Party List Candidate where 2% is assured of at least one party list seat, then the PCOS COUNT clearly disenfranchised the voters of candidate Y and denied the candidate of at least one seat.

The COMELEC must therefore do away with the COMPARISON TECHNIQUE and devise a mechanism to detect all types of ERRORS that a PCOS MACHINES will commit so that a reliable accuracy rating will be devised.

To determine the accuracy rating of the PCOS COUNT on the votes of all the candidates, then we have to determine the maximum number of ovals that a PCOS MACHINE will scan in an election and we have to determine the total number of FALSE POSITIVE ERRORS and FALSE NEGATIVE ERRORS committed by the PCOS COUNT on all of the ovals scanned by the PCOS MACHINE. This can be done by using the ballots, their corresponding ballot images generated by the PCOS MACHINES, and the AUDIT LOG of the PCOS MACHINES that shows how each ballot is interpreted by the PCOS MACHINE.

We assume a maximum of 500 ovals per ballot. Since we also assume a maximum of 1,000 ballots scanned per PCOS MACHINE, the maximum number of ovals shall be 500,000.

Thus, the COMELEC shall require an error rating of at most 1 error per 500,000 ovals. This is equivalent to an accuracy rating of 99.9998% for the PCOS COUNT on deciding the validity of a mark of an oval.

Felix P. Muga II

Associate Professor, Mathematics Department, Ateneo de Manila University

Senior Fellow, Center for People Empowerment in Governance

Mathematics of Politics