The Frozen House

Methodology

This is the short version. The rules explained in depth works through each method with a small worked example, and sets out why the Alabama paradox happens rather than only that it does.

What the Tool Does

It takes a population figure for each of India's 36 states and union territories, a house size, an allocation rule and any constraints, and returns a whole number of seats for every unit that sums exactly to the house size you set, with one deliberate exception: the Delimitation Commission method is applied the way the Commission worked, and its total can miss by a few seats, which the page flags when it happens. Published projection tables usually do not sum exactly, because each state is rounded independently. The PRS annexure this tool is validated against totals 548 and 813 where it should total 543 and 815, for that reason and because a small-state exception is applied by hand to four units.

The Rules

The Alabama Paradox

The Delimitation Commission's method — one national quotient, each state rounded to the nearest seat — can never take a seat away from a state when the house grows, because a bigger house only lowers the quotient. Largest remainder can. It is a common way to build quick projections, and the defect is well documented in Balinski and Young's Fair Representation, so the list below shows what largest remainder would do on this data: numbers a projection built that way could show, but a Commission applying India's method would not produce.

Verified independently in exact integer arithmetic, with no floating point anywhere, so this is a property of the rule and the data rather than of our code. The divisor methods — Huntington-Hill, Sainte-Laguë, D'Hondt — produce no instances at all. Cube root and base-plus-proportional do, because both distribute by largest remainder. The full explanation, with a worked example.

Quota

A unit's quota is the pair of whole numbers bracketing its exact proportional entitlement. Largest remainder never leaves that bracket. Divisor methods can, and cube root and base-plus-proportional leave it almost everywhere, which is expected — neither is trying to be proportional to population.

The Data

Known Limits

• The 2016–2036 series are projections, made in 2019 and published in 2020. They predate both the 2027 Census and COVID-19 mortality.
• Projected figures are printed in thousands, so each carries up to ±500 of rounding.
• Assam was not enumerated in 1981; Jammu & Kashmir and Ladakh were not enumerated in 1991. Those cells are empty here rather than filled with an estimate, and an allocation run on those years is missing a unit.
• The historical series is on 2011 district boundaries. For 34 of 36 units that is today's map. For Andhra Pradesh and Telangana it is not: the seven Khammam mandals transferred in 2014 sit inside the historical Telangana figures. The effect is 190,304 people in 2011 and smaller amounts earlier.
• Regional groupings drive one panel and are not official. Zonal councils, used to colour the chamber, are official.
• These are seat totals per state. Nothing here says anything about constituency boundaries within a state, which is the other half of what a Delimitation Commission does.

Fuller detail than this page carries is in METHODOLOGY.md, and the repository carries the raw sources unmodified so every transformation can be re-run and checked.

Sources

SOURCES.md lists every dataset with its URL, licence, date obtained and exactly what was done to it — including the boundary sources that were rejected and why, and a wrinkle in the PRS licence terms that is recorded rather than quietly resolved.

Code MIT licensed. The PRS Legislative Research projection table is used under CC BY 4.0. Every figure here traces to a named source recorded in the data files themselves; nothing is estimated or interpolated.