Jacqui Lambie: Just Enough Votes to Win, Not Enough Votes to Lose

Jacqui Lambie has been elected to the Australian Senate as the lead Tasmanian Senate candidate for the Palmer United Party (PUP).

However, inspecting the full AEC distribution of preferences reveals a remarkable mathematical paradox—a failure of monotonicity in Single Transferable Vote (STV):

The critical breakpoint in the Tasmanian Senate count occurred where the Australian Sex Party (ASXP) was beaten by the third ALP candidate by just 244 votes.

This leads to a counter-intuitive scenario:

If 854 informal voters had instead cast a valid vote for Jacqui Lambie (or for any of the PUP feeder groups), Jacqui Lambie would have LOST the election!

How Is That Possible?

1. Adding 854 formal votes to Palmer United Party would have increased the Statewide Senate Quota ($Q = \lfloor V_{\text{formal}} / 7 \rfloor + 1$).
2. A higher quota means that when the first two ALP candidates and first Greens candidate were elected on primary votes, their surplus transfer values to the third ALP candidate would have been smaller.
3. That slightly smaller ALP surplus would have left the third ALP candidate behind the Australian Sex Party at the key exclusion point!
4. With the third ALP candidate excluded instead of the Australian Sex Party, and following the overflow of the Australian Greens surplus, the Australian Sex Party would have continued harvesting micro-party preferences and overtaken Jacqui Lambie for the 6th and final Tasmanian Senate seat.

More votes for your own ticket causing you to lose the seat—a classic real-world demonstration of non-monotonicity in STV elimination order!