Statistic seminar - Dr Jack Freestone - Macquarie University

A seminar by Dr Jack Freestone from Macquarie University

Title: Risk-Limiting Audits for Parliamentary Majorities

Abstract: After an election, how do we know the result is correct without recounting every ballot? A risk-limiting audit answers this by sampling ballots and accumulating statistical evidence until either the reported outcome is confirmed or a full recount is triggered –– with a guaranteed bound on the chance of certifying a wrong result.

Existing methods audit one race at a time, but parliamentary elections are different: what matters is whether a party won enough seats to form government, not whether it won every single one it claimed. This opens the door to efficiency gains — if a party won 60 out of 100 seats and only needs 51 for a majority, we just need to confirm that 51 out of the 60 were correctly won.

We formalise this idea using partial conjunction hypothesis testing and e-processes, a modern framework for accumulating sequential statistical evidence, to certify the parliamentary majority. Our methods can learn on the fly which seats are worth auditing and which to skip, redirecting effort toward the seats where more evidence is actually needed. In a case study based on the 2014 Indian general election, our best strategy certifies the parliament majority using up to 1000 times fewer ballots than a naive approach.

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