Politics of mathematics

The impeachment of Vice President Sara Duterte has taken a rousing turn with the entanglement of politics and mathematics. The politics of mathematics has taken center stage in the last two weeks at the impeachment court as math and politics have become enmeshed. Politics colliding with mathematics is knotty and messy.

Finally, the impeachment court resolved the lingering and pestering math question on the impeachment of Sara Duterte. To recall, Presiding Officer Chiz Escudero ruled at the start of the trial that the conviction threshold was 16 votes, or two-thirds of the 24 senators comprising the Senate.

Many events, however, have transpired since the start of the impeachment trial. One senator, fugitive Bato de la Rosa, did not take his oath as senator-judge since he is in hiding. Two senator-judges — Jinggoy Estrada and Rodante Marcoleta — are now detained while facing plunder charges before the anti-graft court Sandiganbayan. Senator Loren Legarda, who is facing an investigation related to alleged irregularities involving her son’s solar energy projects, is on extended medical leave abroad.

Given these developments, Senator-Judge Erwin Tulfo, on Sept. 8, 2026, filed a motion seeking to overturn Escudero’s July 6, 2026, ruling. This week, the impeachment court decided to resolve once and for all the hanging question on the voting threshold to convict or acquit Sara Duterte.

Prior to making the final decision on the math question, the impeachment court invited four respected magistrates as amici curiae to share their expert views on the issue and enlighten the senator-judges. The four amici curiae are three retired Supreme Court chief justices — Hilario Davide, Artemio Panganiban and Reynato Puno — and former Associate Justice Adolfo Azcuna. They gave their expert perspectives last week on the issue of whether 16 is a fixed number needed to convict Sara Duterte.

Davide argued that 16 is not a fixed number. “Clearly then, the basis of computing the two thirds must be the number of senators who are qualified to vote, not the twenty-four (24) in the present Senate. All those disqualified by reason of causes earlier mentioned should not be included.” As one of the commissioners who crafted the 1987 Constitution, Davide explained that “public officers facing criminal charges cannot perform official duties while in detention. Thus the two-thirds impeachment vote must be computed solely from senators qualified to vote — not all 24. Disqualified, jailed or missing members cannot be counted.”

Puno took a textual and contextual approach to the issue. He rejected the notion that 16 as the threshold for conviction is fixed and immutable. “It is inappropriate to give Article 11, Section 3 (6) a standalone, literal reading. If we give this kind of reading, … the threshold of 16 senators will be fixed and immutable. However, if that is the intent, Article 11, Section 3(6) should’ve simply stated that the number of votes to convict is 16. Period. But [it] did not say so, instead the language used [is] a fraction. It says 2/3 of all members of the Senate. By using the 2/3, the number of votes to convict will have to move depending on certain factors.”

Panganiban, on the other hand, emphasized “truth and fairness” as the basis for resolving the math question. His position is also practical and contextual. “To put it more picturesquely, Your Honor, is it truthful and fair to the parties, to our country, and to our people, to allow those abroad, those looking at the pyramids along the Nile, or shopping in fashion houses in Paris, or riding the romantic gondolas of Venice, or deliberately hiding in the dark corners of the world, while everyone here in this hall is sweating it out, listening to sometimes irrelevant and loquacious lawyers, or to humble an ancient amicus curiae like me.” In short, Panganiban is saying only those who took part in the impeachment trial should cast their vote for conviction or acquittal.

Only Azcuna deviated from the position of the three former chief justices. For him, the threshold must be “fixed and not variable,” insisting that 24 is the basis for determining the two-thirds vote, and thus 16 is the threshold for conviction.

The contentious issue is the determination of the fraction 2/3. The political future of the country hangs on this mathematical fraction. Should it be based on 24 or on the number of senators who took part in the trial and hence be variable and flexible? What should be the basis of 2/3 — 24 or the number of senators participating in the trial?

For the first time in the nation’s history, math held the nation hostage, with a fraction as the fulcrum of contestation. The politics of mathematics is on full display as the impeachment court wrestled with how to resolve a simple mathematical fraction.

Voting as an impeachment court, the Senate leaned on the views of the three former chief justices. Thirteen senator-judges voted to overturn the fixed 16-vote threshold and base the two-thirds requirement on the number of senators legally and factually capable of participating in the impeachment proceedings. If 20 senators constitute the denominator, 14 votes would be required for conviction. Four senators who are detained, at large or on medical leave may be excluded from the determination of the two-thirds threshold. Six senator-judges from the minority bloc did not take part in the voting, while Escudero cast the lone vote against the change.

The vote on the conviction threshold is a revelation. While the Cayetano siblings remained united, the Villar siblings split their votes for the first time. Voting to lower the conviction threshold, Mark Villar joined the majority, while Camille Villar stayed with the minority bloc. Mark Villar’s defection is significant, perhaps a turning point in the impeachment trial of the vice president. The solid wall that blocks Sara Duterte’s conviction is dented, if not breached. This is a chilling omen for Sara Duterte.