What chance for an LNP government in Qld?

As of end of counting Election Night, there were still about 600,000 pre-poll votes to count, out of a total of 2.7million (no reference - just something I heard a couple of times).  That's more than 22% still to go, plus any postal votes not yet in (as of 8pm Sunday night, ABC states that 75.1% are counted)  Is that significant?  Could they make a difference to the overall outcome?

And while the result has been awful for the LNP relative to their last outing, the actual voting so far is pretty even, effectively a 2PP of 50%.  In theory, this should mean that either party should be in with a chance to form government, given the support of the independents.  In reality, all the independents took a No Asset Sales position into the election, and so it seems unlikely that they would support the LNP without some serious policy backflips (which, from politicians, we couldn't rule out).

Assumptions

All that aside, I'm a little curious as to what chance the LNP still have of forming government in their own right.  So let's have a bit of a look at it mathematically.  First, some assumptions.

• No independent supports the LNP, so they need 45 seats in their own right.
• The LNP keeps any seat in which they currently lead (might look at this later)
• To win each extra seat in which the LNP is currently just behind, LNP needs 50.01% of the total vote (votes already counted plus pre poll votes)
• Each electorate is treated as a 2 candidate competition, so the voter's choice is simply LNP or ALP.  This is effectively the case in most seats as the 2PP is LNP v ALP in almost all cases.
• There are still 6,742 (600,000 divided by 89 seats) votes still to count in each electorate, which could make a difference to the outcome. This is probably the weakest assumption as this will vary from seat to seat, but will do for a first attempt.

 Again, as of 8pm tonight, the ABC election website gives the LNP 39 seats, and the ALP 43.  So this means that the LNP need another 6 extra seats in their own right in order to keep government. 

Methodology

What I intend to do is to look at the 6 most marginal seats currently trending to the ALP, and determine the likelihood of the remaining 6,742 flowing adequately to the LNP to allow them to win each of those seats, given the assumptions above.

The Maths

I'm going to use a little bit of binomial statistics to determine the likelihood of the LNP getting enough votes in the prepolls to make a difference.  I'll explain how this works in more detail in another post, but binomial statistics is really just high school stats.  Nothing too fancy.  In fact, we can use an online calculator to do the grunt work for us.  We just need to know three values first.

• The first is n, the number of trials in each test.  In this case, we'll make n = 6,742, the number of extra votes that we're going to count.
• The second is p, the likelihood of success in each trial, or in this case, the likelihood of a vote for the LNP.  In our assumption we stated that we need a success of 50.01%, or in decimal, p = 0.5001
• The third is x, the number of successes that we are looking for for an LNP win.  This will vary from seat to seat.  I will calculate this as 3,362 (half of the remaining 6742 votes) plus the number of votes the LNP is behind.

Plugging these three numbers into the online calculator mentioned above will give us a calculation for the likelihood of the LNP winning the seat from the current situation.

The Seats

It shouldn't come as a surprise that there are actually quite a few seats currently given to the ALP that are reasonably marginal.  I've also calculated the Vote Deficit, ie, how many extra votes the LNP candidate would need on a 2PP basis to overtake the ALP candidate. The eight most marginal seats are, in order

Seat                  Margin (to ALP)    Vote Deficit (from ABC election website)
Ferny Grove     1.3%                           578
Springwood      1.6%                           785
Bundaberg        1.9%                           816
Pumicestone     2.0%                          1063
Mt Coo-tha       2.9%                          1149
Mundingburra   2.9%                         1170
Maryborough    3.0%                         1200
Barron River     3.2%                         1757

Throwing the n, p & x values for each seat at the online calculator gives

Seat                  x (3362+Vote Deficit)   Cumulative Probability (P (X >=x))
Ferny Grove     3940                              <0.000001, or < 0.0001%

Obviously for the other seats there is less chance than this.  So unless there is some mechanism that makes pre-poll voters more likely to vote LNP than other voters, then it's pretty clear the LNP is unlikely to get any more seats .

Using the same mathematics, you can show that Whitsundays is now pretty safe for the LNP, even with a lead of only 84 votes.  With the votes left to count, there is only a 5% chance that it could swing to the ALP.