By Haris Aziz
“No invasions of the constitution are so fundamentally dangerous as the tricks played on their own numbers, apportionment, and other circumstances respecting themselves”
–Thomas Jefferson
As the Supreme Court case about the allocation of reserve seats in Pakistan dragged on, the fundamental mathematical principle underpinning the issue was unfortunately partially obscured by courtroom theatrics, red herrings, and election procedure technicalities. I want to discuss the issue purely from a mathematical perspective.
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The Pakistan constitution stipulates that the national and other assemblies have certain seats reserved for women and for non-Muslims. These seats are given to parties through the proportional representation system on the basis of the total number of general seats secured by each political party. The concept of proportionality dates back at least to the ancient Greeks. Euclid defined proportionality in his book Elements (Book VII) as “Numbers are proportional when the first is the same multiple, or the same part, or the same parts, of the second that the third is of the fourth.” Aristotle, emphasised proportionality as a foundational principle for fairness and representation: “equals should be treated equally and unequal unequally”.
Let us take a simple hypothetical example to explain the maths behind this issue. Suppose there are 500 seats in the Republic. Among these 500 seats, 400 are general seats that are contested via elections whereas the remaining 100 are reserved seats that are allocated to the........