The Frome Australia IRV by-election of 17 January 2009

Demonstrates some IRV election pathologies such as "non-monotonicity"

By Warren D. Smith, March 2011.

The election was triggered by the resignation of former Premier and state Liberal MHA Rob Kerin. (The seat had been retained by the Liberals in the 2006 state election by a 3.4% margin, and in the 2002 election by 11.5%. Wikipedia page on this election. Note Frome is a constituency of South Australia, i.e. not a federal house seat for full Australia, which is a point the original version of this wikipedia article confused its readers, i.e. me, about.) Instant Runoff Voting (IRV) was employed, as is usual in Australian House elections.

Top-preference counts:
CandidateVotesOther comments
Terry Boylan (Liber) 7576 Police officer.
John Rohde (Labor) 5041 Postal worker.
Geoff Brock (Indpt) 4557 Mayor of Port Pirie.
Neville Wilson (NatSA) 1267 Deputy Mayor of Port Pirie Regional Council.
Joy O'Brien (Green) 734 Former librarian and Burnside councillor.
Peter Fitzpatrick(OneNat) 134 Small business contractor.

By the 4th IRV round it was reduced to 3 candidates:

Boylan (Liber) 8215
Rohde (Labor) 5532
Brock (Indpt) 5562

whereupon Rohde was eliminated and Brock won the seat in the 5th and final IRV round [which is the "2CP" (two candidate preferred) vote in the terminology of the Australian Election Commission (AEC)]:

Brock (Indpt) 9987
Boylan (Liber) 9322

An extra chunk of data

In Australian elections, the AEC usually refuses to provide enough data to enable anybody to reconstruct the ballots or to prove the existence of various IRV election phenomena. However, in this particular election, the data the AEC published was enough to provide 100% certainty that this election was non-monotone. The key extra sliver of AEC data was the "two party preferred" pairwise vote

Boylan (Liber) 9976
Rohde (Labor) 9333

telling us how many IRV voters ranked Boylan above Rohde (or the reverse), ignoring the other 4 candidates.


If X

... > Boylan > ... > Rohde > ... > Brock > ...

voters (for any X with 31≤X≤321) had demoted Boylan to anywhere below Rohde (most simply, all the way to last place):

... > Rohde > ... > Brock > ... > Boylan

then it would have been Brock who was eliminated. Then Boylan would have won in the final round, which would have been

Boylan (Liber) 9976-X
Rohde (Labor) 9333+X

In other words: Boylan would have won if he got fewer votes. Unfortunately for him, he got too many votes, and therefore lost.

To say that again: Voters who honestly ranked Boylan top, were strategically foolish. If 31-to-321 of them had ranked him bottom, that would have made Boylan win.

That's the paradox of non-monotonicity. One of Instant Runoff Voting's flaws is that it can exhibit non-monotonicity (as this election shows). The other main kind of non-monotonicity (there are two main types) was exhibited in another IRV election (held in the same year, 2009) to choose the Mayor of Burlington Vermont, USA.

Frome 2009: Boylan loses since had too many votes Burlington 2009: Kiss wins because had too few votes
If 100 Boylan voters had dishonestly or strategically voted him as "worst," that would have made Boylan win (but as it was, Brock won because Boylan got too many votes). If 800 Wright voters had dishonestly or strategically instead voted for Kiss, that would have made Kiss lose (and Montroll win; as it was, Kiss won because he got too few votes).

A no-show paradox

If 200 new    Rohde>...>Boylan    voters had magically appeared... that would have made Boylan win. So those voters were very wise not to vote.

Other paradoxes?

There may have been other paradoxes too, but because the AEC only provided partial election data, I cannot tell.

Sources for our data

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