This post on the election outcome in Indi is a little beyond my usual area of expertise, but it is a nice example of simple modelling. I’m going to tackle the question of whether Sophie Mirabella or Cathy McGowan will win the seat of Indi in the Australian Federal Election of 2013.
So, who do I think will win, and why? The summary: given swings in Indi so far and the expected number of postal, prepoll and absent votes, McGowan will win by approximately 800 votes.
Update (7:00 p.m., Saturday 21 September): It looks like the counting has ceased. Many of the remaining ballots were not valid it seems, so McGowan’s lead was never really threatened. She finished
437 439 votes (based on the result published on the AEC website on 2 October) ahead of Mirabella, to take the seat with a margin of 0.25%. It was a narrow win for McGowan, and quite amazing that Mirabella lost after getting almost 45% of first preferences. Here are the final swings for the different booths and votes.
Update (10:30 p.m., Monday 16 September): I’m not sure when the AEC website was updated, but it looks like almost all of the issued early votes have been received now (only 64 missing). With most absent votes in, the major uncertainty lies in the number of postal votes that will be received. On current projections, McGowan will win by 200-350 depending on how many postal votes are received. If the uncounted votes turn in favour of Mirabella (set at the upper 95% limit), McGowan will win by 140-315. If the remaining votes turn in McGowan’s favour, the range is 270-400.
So I’m calling it for McGowan! Not that anyone should listen to me. My initial projection of McGowan winning by 800 was an overestimate, because the swing against Mirabella was less for the declaration votes than the
early ordinary votes.
Update (3:30 p.m., Monday 16 September): It was a good result for McGowan today; she did better than previously on all declaration votes. Here are the updated swings, with early votes moving away Mirabella compared with previously. Despite the move, the swing for early votes is considerably less than for PPVCs, and less than all booths >500 in size.
Update (11:45 a.m., Monday 16 September): A quick update on the swings after Sunday and Monday Morning counting, showing McGowan doing better on absent and postal votes than previously, and Mirabella’s improvement on early votes. Early votes remain the key; more of these counted this afternoon. Mirabella needs a large improvement on those (and many more to come in) to win it from here. The projection is for McGowan to win by ~300 votes.
Update (8:30 p.m., Sunday 15 September): McGowan did better than previously on postal votes today (she won over 46% of them), but Mirabella improved on the early votes (she won almost 59% of them). Early votes are critical because these have the most uncounted. However, McGowan is still in a winning position. If no more votes are received, McGowan will win by ~250 votes (at the current rate). If all issued postal votes are received, McGowan is projected to win by ~100 votes. If more early votes come in, it will be even closer.
So Mirabella still needs to achieve better results on the remaining votes to win. The estimates of the 2CP percentages for the different declaration votes are more precise now. Mirabella will want more postal and early votes to be returned, and will need an early vote rate over 60% (near the upper 95% limit of the estimate) for those that are uncounted. This seems very unlikely, but again it is not quite over.
Others modelling the outcome include Kevin Bonham (including some of the other close races), Michael Murray, @TomAnderson62 and @Gus_Barnes (among others) on Twitter. Please add a comment if you are also modelling the outcome.
Update (7:40 p.m., Saturday 14 September): McGowan will win even if all issued envelopes are received, provided that the uncounted votes have the same distribution as the counted votes (57.5% for postals, 45.5% for absents, 56.5% for early) and the proportion that are formal remains unchanged. If all issued envelopes are received, then McGowan will win by ~70 votes. If no more votes are received, McGowan will win by ~300 votes.
So Mirabella needs a better outcome on the uncounted votes than she has so far achieved. This might be possible. The early votes are critical – more than 3,000 early votes remain to be counted. Further, only 700 have been counted, so using the outcome of these to estimate the results for the uncounted votes is relatively uncertain.
Uncertainty in the estimate can be expressed as a confidence interval; the 95% interval for the early votes is [52.7, 60.3]. This is perhaps unrealistically wide given the large swings against Mirabella – a value of 60.3% would be a very small swing against her in the context of the results so far. However, if 20% of the outstanding issued envelopes were received, and Mirabella achieved 60.3% for the uncounted early votes, she would win by 10 votes if the current outcome for the absents and prepolls remained on the same track as they are now. The upshot: the likely result remains a McGowan win, but Mirabella is not completely out of it. However, she will need to be particularly lucky.
Edit: The updated graph of the swings is below, with early and absent votes included, showing the slightly lower swings against Mirabella for the declaration votes (green) compared with PPVC and ordinary votes.
Update (2:15 p.m., Saturday 14 September): Given a slightly higher informal vote in the postals now than earlier, and fewer postals and early votes coming in, the forecast numbers of these votes might be too high – 9,200 and 4,100 might be closer to the mark; these lower numbers would favour McGowan (a win by ~250), but it remains very close.
Update 1:30 p.m., Saturday 14 September):
Well, it has become very interesting. 700 early votes have been counted, of which Mirabella has won 57%. This is a much smaller swing away from Mirabella (only about 5%) than for the pre-poll votes from the PPVCs (Prepoll Voting Centres). If this rate remains the same, Mirabella will lead by about 600 early votes and 1,500 postal votes, and trail by 200 absent votes. With McGowan’s lead on the ordinary votes adjusted to 1961, the overall outcome would be a win to McGowan of less than 100 votes – it really is going down to the wire! Here is the updated projection:
|Type of vote||Number of formal votes||% to Mirabella||Votes to Mirabella||Votes to McGowan||Difference|
Update (5:00 p.m., Friday 13 September): Absent votes are favouring Cathy McGowan, who is getting 55% of votes after 1,000 have been counted (see tweet from Ben McGowan who noted this). My forecast below of 58% to McGowan looks a touch high, but is in the right ballpark. Postal votes are still favouring Sophie Mirabella at 57.6% with most now counted. There might be still more than 2,000 postal votes to count, but not many more. Information on the early votes is still absent, but if they are similar to postal votes, Cathy McGowan will win. Edit: if McGowan gets 55% of 2,500 absent votes, Mirabella will need approximately 60% of 4,500 early votes to win, which seems very unlikely.
This table breaks down the votes, projecting McGowan to win by 700 votes. Values in bold are based on my projections. Values in italics are estimates based on votes received to date. Values in regular font are those published on the AEC website.
|Type of vote||Number of formal votes||% to Mirabella||Votes to Mirabella||Votes to McGowan||Difference|
Original post from here on:
After the ordinary votes, Cathy McGowan leads Sophie Mirabella on a two candidate preferred basis* of 1983 votes**.
However, thousands of votes remain to be counted. From these, can Mirabella win enough to overcome this deficit of 1983 votes?
The remaining votes are absent votes, early votes (prepoll votes cast outside the electorate), postal votes, and provisional votes. Very few of the provisional votes will be counted (in 2010 only 139 were accepted), and they are likely to be roughly spread between the two candidates, so I’ll ignore those.
The postal vote outcome is reasonably clear now. Mirabella is winning 57.6% after 6000 postal votes have been counted. The total number of postal votes will be less than 10,465 (the number of envelopes issued). So far, 9,223 have been received, and over 98% of those counted have been accepted, so we might expect 10,000 valid postal votes (at the most). At the current rate, this will give Mirabella 5760 votes and McGowan 4240 votes, a difference of 1520 votes.
So after postal votes, McGowan should lead by around 443 votes (or more given there will probably be fewer than 10,000 valid postal votes).
Now, what might we expect for the absent and early votes?
In the past, early votes have favoured Mirabella against the other candidate. In 2010, she received 62.4% of the 4,443 early votes. However, this election has seen a large swing against her.
Absent votes in the past have not favoured Mirabella as much as other votes. In 2010, she received 52% of the 2,667 absent votes. With a swing of a few percentage away from Mirabella, McGowan would be expected to actually win the absent votes.
So, what swings might we expect for early and absent votes? This is the key question to determine who will win Indi (along with the number of these votes).
Below I plot the swings for Indi booths from 2010 to 2013 against the number of formal votes in 2013 for each booth. It shows swings of greater than 5% against Mirabella in all booths with more than 500 votes.
If a swing of -5% is applied to both early and absent votes, then Mirabella will win 57.4% of early votes and 47% of absent votes. If there are 2500 accepted absent votes (so far 2,662 have been received after 2,697 were issued), and 4,500 early votes (only 1,808 have been received so far, but 4,633 were issued), then Mirabella will lose by 153 on the absent votes and win by 669 votes on the early votes, a nett gain of 516 votes.
This gain of 516 votes on early and absent votes would be just sufficient for Mirabella to win the election. However, this is an unlikely outcome. If the early votes have the same swing as other prepoll votes counted so far, Mirabella will need a miracle in the absent votes to win.***
I suggest that the most likely outcome is that Mirrabella and McGowan will roughly split the early votes, with a swing of around 12% against Mirabella from 2010 (matching the approximate swing of other prepolls).
Then a swing of 10% against Mirabella in the absent votes (giving McGowan 58% of those) will see McGowan gain a further lead of 400 votes. That would see McGowan win by approximately 800 votes.
* All reference to votes in this post will be on a two candidate preferred basis. This is the vote after distribution of preferences to the leading candidates.
** 37,945 to 35,962; as recorded on the AEC site at 7:47 p.m. on Thursday 12 September. Edit for clarification: These are the numbers for ordinary votes, ignoring postal , early, absent and provisional votes.
*** Mirabella received approximately 61% of the ordinary prepoll votes in 2010, yet in 2013 she received only 49% of these.