INACCURATE PCOS AND THE 2010 SENATORIAL RACE

The mock election to demonstrate the accuracy of the SMARTMATIC-provided PCOS Machines was conducted on July 24 and July 25 at the House of Representative.

Two hundred and thirteen (213) votes out of 8,295 votes that were counted by the PCOS Machine differed from the count conducted by the Manual Audit on each of the candidates of the audited elected positions.

The difference that amounts to 213 votes resulted in an error rating of 2.56781% or an accuracy rating of 97.43219%.

On May 10, 2010, the national election for the Philippine senators was held. Out of the 61 candidates for the senatorial race, twelve will be proclaimed as winners. On May 15, 2010 nine senatorial candidates who were leading the race were proclaimed as winners. Three days after on May 18, 2010, the last three remaining senatorial slots were filled up with the proclamation of the last three winning candidates.

The total number of votes counted by the PCOS Machines in the senatorial race was 297,036,114 votes. However, the actual number of voters who voted for the senatorial race was 38,149,371. Hence, on the average each voter voted for about 8 out of the 12 available slots for the senatorial race.

Since a voter is required to vote for 12 or less unique candidates, it follows that a senatorial candidate received one or no vote from each voter.

Thus, the margin of error of the PCOS COUNT is based on the number of voters who actually voted for the senatorial race. Hence, the PCOS Machine miscounted the votes of 2.56781% of 38,149,371 or a total miscount of 979,603 votes.

We consider in Table 1 the 11^th to 14^th Positions of the Result of the PCOS COUNT ON THE 2010 SENATORIAL CONTEST.

Table 1. May 2010 Senatorial Contest:  11th-14th Positions as Counted by the PCOS Machines
Position	Senatorial Candidate	PCOS COUNT
11	Lito Lapid	11,025,805
12	Teofisto Guingona III	10,277,352
13	Risa Hontiveros-Baraquel	9,106,112
14	Ruffy Biazon	8,626,514

The PCOS Machines counted 11,025,805 votes for the 11^th ranking senatorial candidate. If the PCOS MISCOUNT of 979,603 votes will be subtracted or added from the PCOS COUNT, the TRUE COUNT for the 11^th ranking candidate ranges from as low as 10,046,202 or as high as 12,005,408.

Doing the same procedure on the 12^th, 13^th and 14^th Positions we have Table 2.

Table 2. Subtracting or Adding the PCOS MISCOUNT of 979,603 Votes to the PCOS COUNT
Position	Senatorial Candidate	PCOS COUNT	TRUE COUNT
			LOW	HIGH
11	Lito Lapid	11,025,805	10,046,202	12,005,408
12	Teofisto Guingona III	10,277,352	9,297,749	11,256,955
13	Risa Hontiveros-Baraquel	9,106,112	8,126,509	10,085,715
14	Ruffy Biazon	8,626,514	7,646,911	9,606,117

Hence, we counted 5 possibilities for the 11^th and 12^th places after considering the PCOS MISCOUNT OF 979,603 votes. See Table 3.

Table 3. Possible Winning Combination
No.	11th PLACE	12th PLACE
1	Lito Lapid	Teofisto Guingona III
2	Lito Lapid	Risa Hontiveros-Baraquel
3	Lito Lapid	Ruffy Biazon
4	Teofisto Guingona III	Lito Lapid
5	Teofisto Guingona III	Risa Hontiveros-Baraquel

For example, we can have a Lito Lapid for the 11^th place and Risa Hontiveros-Baraquel for the 12^th place, if Lito Lapid’s TRUE COUNT is the PCOS COUNT of 11,025,805 and Risa Hontiveros-Baraquel had a HIGH TRUE COUNT of 10,085,715 while Teofisto Guingona III had a LOW TRUE COUNT of 9,297,749.

Hence, the PCOS MISCOUNT of 2.56781% of the total number of actual voters of 38,149,371 produces uncertainty at the 11^th and 12^th Places for the May 2010 Senatorial Race.

Therefore, a 100% Manual Recount must be conducted to determine the real winners for the 11^th and 12^th places of the May 2010 senatorial election.

Table 4. Summary of the May 10, 2010 Philippine Senate election results
Rank	Candidate	Party	Votes	Percent Share
1	Bong Revilla	Lakas-Kampi	19,513,521	51.15%
2	Jinggoy Estrada	PMP	18,925,925	49.61%
3	Miriam Defensor Santiago	PRP	17,344,742	45.47%
4	Franklin Drilon	Liberal	15,871,117	41.60%
5	Juan Ponce Enrile	PMP	15,665,618	41.06%
6	Pia Cayetano	Nacionalista	13,679,511	35.86%
7	Ferdinand Marcos, Jr.	Nacionalista	13,169,634	34.52%
8	Ralph Recto	Liberal	12,436,960	32.60%
9	Tito Sotto	NPC	11,891,711	31.17%
10	Sergio Osmeña III	Independent	11,656,668	30.56%
11	Lito Lapid	Lakas-Kampi	11,025,805	28.90%
12	Teofisto Guingona III	Liberal	10,277,352	26.94%
13	Risa Hontiveros-Baraquel	Liberal	9,106,112	23.87%
14	Ruffy Biazon	Liberal	8,626,514	22.61%
15	Joey de Venecia	PMP	8,375,043	21.95%
16	Gilbert Remulla	Nacionalista	7,454,557	19.54%
17	Danilo Lim	Independent	7,302,784	19.14%
18	Sonia Roco	Liberal	6,774,010	17.76%
19	Ariel Querubin	Nacionalista	6,547,925	17.16%
20	Gwendolyn Pimentel	PDP-Laban	6,394,347	16.76%
21	Nereus Acosta	Liberal	5,921,111	15.52%
22	Alexander Lacson	Liberal	5,242,594	13.74%
23	Adel Tamano	Nacionalista	4,059,748	10.64%
24	Emilio Mario Osmeña	PROMDI	3,980,370	10.43%
25	Liza Maza	Independent	3,855,800	10.11%
26	Satur Ocampo	Bayan Muna	3,539,345	9.28%
27	Francisco Tatad	GAD	3,331,083	8.73%
28	Ramon Mitra III	Nacionalista	2,744,090	7.19%
29	Apolinario Lozada	PMP	2,730,279	7.16%
30	Rey Langit	Lakas-Kampi	2,694,213	7.06%
31	Silvestre Bello III	Lakas-Kampi	2,468,276	6.47%
32	Yasmin Lao	Liberal	2,081,895	5.46%
33	Imelda Papin	Bangon Pilipinas	1,972,667	5.17%
34	Susan Ople	Nacionalista	1,930,038	5.06%
35	Martin Bautista	Liberal	1,890,152	4.95%
36	Rodolfo Plaza	NPC	1,517,905	3.98%
37	JV Larion Bautista	PMP	1,415,117	3.71%
38	Ramon Guico	Lakas-Kampi	1,264,982	3.32%
39	Raul Lambino	Lakas-Kampi	1,156,294	3.03%
40	Hector Villanueva	KBL	979,708	2.57%
41	Ramoncito Ocampo	Bangon Pilipinas	944,725	2.48%
42	Kata Inocencio	Bangon Pilipinas	888,771	2.33%
43	Jovito Palparan, Jr.	Independent	825,208	2.16%
44	Alex Tinsay	Bangon Pilipinas	728,339	1.91%
45	Zafrullah Alonto	Bangon Pilipinas	712,628	1.87%
46	Reginald Tamayo	Ang Kapatiran	680,211	1.78%
47	Nanette Espinosa	KBL	607,569	1.59%
48	Regalado Maambong	KBL	545,967	1.43%
49	Shariff Ibrahim Albani	KBL	508,558	1.33%
50	Rizalito David	Ang Kapatiran	504,259	1.32%
51	Israel Virgines	Bangon Pilipinas	455,332	1.19%
52	Zosimo Paredes	Bangon Pilipinas	437,439	1.15%
53	Adrian Sison	Ang Kapatiran	418,055	1.10%
54	Reynaldo Princesa	Independent	364,245	0.95%
55	Jo Aurea Imbong	Ang Kapatiran	362,457	0.95%
56	Adz Nikabulin	Bangon Pilipinas	346,848	0.91%
57	Henry Caunan	PDP-Laban	240,676	0.63%
58	Manuel Valdehuesa, Jr.	Ang Kapatiran	201,118	0.53%
59	Hector Tarrazona	Ang Kapatiran	168,386	0.44%
60	Ma. Gracia Riñoza-Plazo	Ang Kapatiran	151,755	0.40%
61	Alma Lood	KBL	128,045	0.34%
Total turnout			38,149,371	100.00%
Total votes			297,036,114	N/A
Registered voters			51,317,073	74.34%
Source: http://en.wikipedia.org/wiki/Philippine_Senate_election,_2010

Felix P. Muga II

Associate Professor, Mathematics Department, Ateneo de Manila University (ADMU)

Senior Fellow, Center for People Empowerment in Governance (CenPEG)

Chair, Mathematical Sciences Division, National Research Council of the Philippines (NRCP)

Mathematics of Politics