Blogging Senate forecasts and results in the WA Senate re-election until officially declared.

Twitter: @AU_Truth_Seeker

Friday 21 March 2014

(UPDATED) Monte Carlo Simulation - who will get elected to the WA Senate?

Under the preferential model used in Australian Senate elections, the so-called "Droop Quota" ensures the quota is as low as possible while ensuring the number of candidates elected cannot exceed the number of vacancies.

Accordingly, in a half senate election, the quota becomes 14.29% of the total number of formal votes cast. Under a hypothetical scenario where the Liberal party were to poll 43%, Labor 29% and the Greens 15%, for example, the electees would be 3xLiberal, 2xLabor and 1xGreens, and no further counting would be necessary. Okay, so this is not going to happen! But it is possible that the two major parties may poll in the vicinity of these numbers, reducing the analysis to the final electee only.

I have used the following method for estimating the primary votes of each of the parties:

Step 1: Start with WA 2013 election results
LIB: 39.20%
NAT: 5.07%
ALP: 26.59%
GRN: 9.49%
PUP: 5.01%
Others: 14.64%

I think these are the recount numbers which potentially understate the Liberal vote by ~1000 votes, or almost 0.1%. But I'm going to disconsider this for the time being.

Step 2: Apply National House of Reps swings to the WA Vote
For this step I take the party swings of the "Bludgertrack", sourced from the sidebar of the Pollbludger blog:
LIB/NAT: 43.0% (= -2.6%)
ALP: 36.0% (= +2.6%)
GRN: 10.9% (= +2.4%)
PUP: 4.0% (= -1.5%)
Others: 6.1% (= -1.0%)

Step 3: Apply additional WA swing to the National HoR swing
Given the WA swing is not the same as the national swing, we need to adjust the swings to represent WA's unique figures. While I'm not sure exactly the data behind PollBludger's National BludgerTrack, I believe it is the longest running and most reputable national poll tracker and the methodology is sound. In the absence of a better methodology, I apply a positive and negative swing to the Coalition and the ALP. Given the party swings above are commensurate with a national swing of -3.4%, and WA has a -3.7% swing, the following adjustments are necessary:
LIB/NAT: -0.3%
ALP: +0.3%

Step 4: Calculate interim expected polling performance
LIB*: 36.63%
NAT*: 4.74%
ALP: 29.49%
GRN: 11.89%
PUP: 3.51%
OTH: 13.74%
Note that I have assigned the LIB and NAT swings on a proportional basis

Step 5: Remove the LibDem effect
It was widely reported that the Liberal Democrats vote was much higher in states where they appeared close to the left hand side of the ballot. In WA, they polled an amazing 3.4% - more than the combined vote of the Shooters & Fishers, Wikileaks, Family First, Katter and the Democrats.
The variation to be applied is:
LIB: +2.5%
OTH: -2.5%

Step 6: Remove the "Could not find" effect
I anticipate that this election will see parties proactively advertising their party name and group. This should be apparent in both pre-election advertising and How To Vote cards distributed by the major parties on election day. (As I'm not from WA, can anyone confirm whether pre-election advertising is inclusive of the party's group??)

The extent to which I am removing this effect is questionable. But I am modelling that two-thirds of voters who previously voted non-OTH in the House but OTH in the Senate will revert to non-OTH votes in this WA Senate election.

I am anticipating the following variations:
LIB: +1.53%
NAT: +0.19%
ALP: +1.43%
GRN: +0.29%
PUP: -
OTH: -3.43%
These are in accordance with each party's vote. Arguably, I could have also given PUP an extra +0.1% or so, but I haven't.

Step 7: Remove the Wirrpunda effect
Conventional wisdom states that where parties run popular footballers, their vote increases. That's why they keep preselecting them! This is especially true in the AFL states, but perhaps less true in the NRL states.

The WA National vote was the highest since 1987, and they also got 30% more vote than they got in the House of Reps (5.1% vs 3.9%)

I am modelling the following variations:
LIB: +1.00%
NAT: -1.00%

Step 8: Add it up
Doing the sums, I end up with the following estimated votes

LIB: 41.7%(+2.5%)
NAT: 3.9%(-1.1%)
ALP: 30.9%(+4.3%)
GRN: 12.2%(+2.7%)
PUP: 3.5%(-1.5%)
OTH: 7.8%(-6.8%)

Step 9: Assign OTH vote
The biggest swing above is the sharp decline in the OTH vote - but given the fact parties will be able to advertise group numbers and the intense focus on the parlous nature of voting for the flying aliens party (or similar), I think this is reasonable. So I started by unilaterally assigning votes to the first few groups, recognising Donkey or partial Donkey voting patters that will apply to parties like Wikileaks (Group A). I have then estimated vote for the remaining parties using common sense and previous polling performance, and then I returned and ratioed down estimations to ensure the vote is 100%. I assigned party votes in groups, rather than attempting to precisely estimate each party's individual vote. (I have not used this method to increase the Group B Nationals)

After ratioing down the minor party votes, I end up with the following estimated primaries:
0.77%: Wikileaks, Sex
0.58%: Shooters&Fishers, LibDems
0.42%: Family First
0.31%: Fishing&Lifestyle
0.27%: Animal Justice, Motoring Enthusiasts, Democrats, DLP, Christians, HEMP, Woolf&Verity, Katter, Pirates
0.19%: Freedom&Prosperity, Outdoor Recreation, Rise Up, Smokers, Sport, Sustainable Population, Voluntary Euthanasia
0.10%: Building, Mutual, Republicans, Socialists, Secular, Voice

Sure, these are low. Looking at a lot of these parties, you might think these numbers are low. Please tell me where precisely you think in comments, but please also tell me how my methodology for the low OTH vote is also obtained, or which party's vote should be correspondingly lower.


At this point, I have applied the methodology as previously posted here.

Applying variance
In order to undertake any Monte Carlo Analysis, I need to estimate variance for each party's vote. I have used the following linear vote variations:
ALP & LIB: +/- 15% (That is, ALP vote varies within the range of 30.9% +/- 4.6%)
GRN: +/- 30% (That is GRN vote varies within the range 12.2% +/-3.6%
All others: +/- 50% (so FF would vary in the range of 0.42% +/-0.21% or between 0.21% to 0.63%)

These ranges are quite wide, necessarily. If a party's vote is within its variance and there are no Monte Carlo simulations that elect that party, it is extremely unlikely it will actually be elected!

If you've made it this far, you probably want to know the estimated results.
Firstly, you can check any given "point estimate" of votes by using Antony Green's Senate Calculator. But the importance of the Monte Carlo Analysis is that it enables us to easily identify where outcomes will be different for small/feasible variations in parties' primary votes. For example, run AG's calculator using default votes. Then run it again, but increasing NAT's vote from 5.07 to 5.2%. Spot the difference? In the latter case, the NAT candidate gets elected instead of the PUP candidate. But also note the default values do not incorporate latest polling, whereas the numbers above do.

Very likely senators: (>90% probability)
LIB: 3 (3rd senator with 95% likelihood)
ALP: 2 (2nd senator with 99.7% likelihood)

Other senators:
GRN: 88%
NAT: 9%
ALP (3rd): 4%
LIB (4th): 3%
PUP: 1.4%
DEM: 0.2%

So, what do you think?

UPDATED 2:30pm 21 March
I have also run some additional scenarios, with a higher percentage of votes for minors: 11.9% instead of 7.8%. Surprisingly, not much changes.
LIB: 39.8%
NAT: 3.8%
ALP: 29.6%
GRN: 11.6%
PUP: 3.4%

1.18%: Wikileaks, Sex
0.88%: Shooters&Fishers, LibDems
0.65%: Family First
0.47%: Fishing&Lifestyle
0.41%: Animal Justice, Motoring Enthusiasts, Democrats, DLP, Christians, HEMP, Woolf&Verity, Katter, Pirates
0.29%: Freedom&Prosperity, Outdoor Recreation, Rise Up, Smokers, Sport, Sustainable Population, Voluntary Euthanasia
0.15%: Building, Mutual, Republicans, Socialists, Secular, Voice

The results are as follows:

Very likely senators: (>90% probability)
LIB: 3 (3rd senator with 96% likelihood)
ALP: 2 (2nd senator with 98% likelihood)

Other senators:
GRN: 89%
NAT: 5.5%
ALP (3rd): 2.3%
LIB (4th): 0.7%
PUP: 4%
FREE: 1.3% (Yes, this is the "Freedom and Prosperity Party"
DEM: 0.8%
Voice: 0.7%
Shooters: 0.3%
Mutual: 0.3%
WIKI: 0.2%

Or, in summary - this change makes precious little difference to the 3-2-1 scenario referred to above - just slightly more scatter at the margin for one of a number of minor parties.


  1. I think this is pretty reasonable for a starting point, my only suggestions at this point would be:

    a) We in WA have yet to see a stack of advertising (particularly from the micros) and I've not yet heard group letters be mentioned.
    b) I think reducing the LibDem effect is valid although I would hammer it down a lot less than you did. They are still a fair way ahead of the Libs on the ticket, and those who were confused last time might not be as up-to-date with the in-depth analysis as enthusiasts like us.
    c) You've removed the donkey effect from Smokers but at 0.77% I don't think this is high enough for Wikileaks.

    Other than that... this is a great start. Let the games begin!

    1. a) Please keep me posted - they'd be silly not to include their group, IMHO.
      b) Also LIB will (should) be advertising their group number, and there'll be far more focus on this effect this time. You may be right, but we'll have to see.
      c) WIKI looks low. But if it is to be higher then does the drop come from majors or minors? If minors, then we're starting to lower some groups significantly.

      I'll post a comment with new analysis below, shortly.

    2. For the donkey vote - I would simply lower all other parties by essentially the same proportion, since we're trying to model disengaged people who are not necessarily voting for any particular party anyway.

    3. Running a couple of additional scenarios (sample size = 100 to reduce my running time), I found the following when I increased WIKI's vote while proportionally decreasing all other parties' votes:
      3%: WIKI has 2% chance of election
      4%: WIKI has 10% chance of election
      5%: WIKI has 24% chance of election.

      For these scenarios, I did not apply any Monte Carlo varition to WIKI's vote, and instead just applied the MC Variation to the other parties. These figures are low because the base numbers I am assuming have ALP+GRN~=41%, and LIB+NAT~=43% - both are on the verge of 3 quotas. But still, the MC variation lowers the ALP+GRN to as low as 35% and still elects 2 ALP and 1 GRN.

    4. Thanks for that - pretty instructive. To be honest I'd be surprised if the Wiki vote exceeded 2% even with the donkey factor thrown in, so testing at 3%, 4% and 5% helps to put this issue in context.


    5. In those new scenarios, does the probability of electing GRN increase for 3% WIKI PV (compared to the base case) and then start to decrease as the WIKI PV increases (since the chance of electing WIKI is increasing)?

    6. When WIK vote gets to 5%, the probability of GRN election decreases. By my calcs at 5%, WIK has a 22% chance of election (note that this is essentially a sample (this time of 200) so you’d expect a fair margin of error for a small sample size – but not so much as to make it 40-50%, for example). At this level, GRN chance of election is 82%, but at WIK=4% or less the GRN prob is >90%, given above estimates.

      I suspect this is just statistically significant. However, if you assume the GRN vote is too high by my above analysis then these figures may change.

  2. I think this analysis is very accurate. Sportsbet are still paying $2.25 (down from $2.75) for 3 or more Liberal Senators, $1.40 for 2 ALP and $1.85 for no PUP Senators. Get on.

    1. If you failed to get on this morning, the odds have shifted.

      PUP for none at $1.73 is still good value as is 3 Liberals at $1.85.

  3. This page has already been up for several hours, why haven't we yet heard the usual tirade about the wasted slice of cake?

    1. Almost time for afternoon tea!

      I can't believe they just throw it out. Much better when the winning party gets 100% of the vote (like in North Korea) then everyone votes for a winner and no cake is wasted.

  4. I for one insist on urgently analysing who would win under a system we don't actually use. Until this important analysis is done there's simply no time for anyone to relax and have cake.

    Having said that, that doesn't mean I support cake wastage. Why would anyone divide the cake into seven slices and throw one away?

  5. Looking at these numbers I would be surprised if the green vote was as strong as you suggest. you have it up about about 2.4% points or about 28% increase. That seems excesive when you account for the fact it would have been boosted last time by disaffected labor voters. Also on a 2PP basis it would seem your numbers come in around 50/50....maybe the coalition is more on the nose in WA than I thought, i thought they had a lead still........

    1. Poll bludger reckons 54.6-45.4... These numbers should be somewhat in alignment with that. Will investigate.

    2. Actually, I have looked at the 2nd scenario base numbers and assumed the Coalition 2PP is equivalent to:
      100% LIB
      90% NAT
      75% Right minors
      60% PUP
      50% Other minors (SMOK, VOICE, REP, BAP, MUT, VEP)
      25% GRN and Left minors
      And this equates to a Coalition 2PP of 54.2%, so it’s pretty close.

  6. will be interesting to re-run the numbers when the first WA senate opinion poll comes out.......probably a more realistic guide that your very honest attempt above....

    1. Do you know when such an opinion poll will be coming out?

  7. It's interesting that the Nationals are elected in 5.5% to 8% of simulations, especially when they might get a boost from drawing column B. I imagine that in some runs the National candidate replaces the 3rd Liberal senator, and in others he is elected in addition to the 3rd Liberal for a total of 4 Coalition senators. How often do you get 4 Coalition senators elected?

    1. When I rerun the second scenario numbers (ones that I’m actually happier – with the higher OTH vote) I end up with the coalition having an expected return of 3 members. The probabilities are as follows:
      4 Lib: 1%
      3 LIB + 1 NAT: 3%
      3 LIB: 90%
      2 LIB + 1 NAT: 2%
      2 LIB: 4%

      So in summary, when NAT gets elected, it can either replace the 3rd liberal, or provide a 4th senator with approximately 50-50 likelihood, given my numbers.

      It’s true that I’ve taken the Wirrpunda effect out but not increased the NAT vote accordingly for drawing Column B. Perhaps I should do this?

    2. It's a tough call on handling Column B - I'm not sure if or how you would model it. The high ballot position might help the Nationals take votes from the Liberals (as the Lib Dems did in September). Equally it could help the Nationals take votes from right-wing minors. Or maybe there's no significant effect.

    3. In my latest blog post, I've increased NAT and decreased LIB vote - I think you're right!
      Sorry for taking so long to respond.

  8. In the ACT 2013 Senate election the VEP - Voluntary Euthanasia Party received 1.61% of the vote compared with your estimate of 0.29% of the vote (see

    I doubt if it will affect your projections though.

    1. VEP has frequently run in ACT so has some sort of profile there. Also there's less parties that usually contest ACT so minors usually have inflated votes. In NSW it got 0.4% in a favourable group E, and 0.3% in SA.

  9. I seem to recall seeing an opinion poll re federal election voting intention with a state-by-state breakdown about a month ago.....and it had Greens support up around 12-13%. The Greens have polled at that level in earlier federal elections. Your suggested increase of 2% or so in the Greens vote over last year's result would seem reasonable in the light of the quoted opinion poll. It will be good to see a particular opinion poll done re the special WA Senate election - presumably this will be made public in the next week and some days prior to the 5 April polling day.

    1. My source for these numbers is Poll Bludger's "BludgerTrack", or more specifically the fact that national polls show that the GRN vote has increased by 2.4% since the last election.

      I have confidence in the BludgerTrack methodology, and although I think it looks "a bit odd" I've still proceeded with it as data always trumps perception. Only once in history in WA have the Greens polled this high.

      The usual trend in these situations is for the Green's vote to be overstimated by Pollsters and decline towards election day. However, given the govt won't be formed in this election, it's possible the Green support will stablise/surge.

    2. Is this the poll you were referring to?

    3. I think so. modelling a slightly higher GRN vote now, and I'm slightly less uncomfortable about its level.

  10. the figure of 12-13% in my earlier comment was for Greens support in WA.

  11. can anyone confirm whether pre-election advertising is inclusive of the party's group??)
    PUP DVD cover - no
    PUP Billboard - no
    Greens TV - no
    Greens radio - no
    Haven't seen any other than that - I'll let you know when I do

    1. Thanks.

      It doesn't make any sense to me why they're not. "Vote 1 P for Palmer" sounds great, as does D for Democrats and M for Mutual(? Ok perhaps not so great. ..)

    2. Agree - seems pretty obvious to me.I'm in Perth so I'll let you know what I see. The biggest standout so far is the lack of advertinsg.
      Libs have added slight confusion to their HTV - the 1 is sans serif so it looks like an I but you'd have to be pretty dumb to accidently vote Voluntary Euthanasia

    3. There is an ad in today's West Australian for PUP and it does mention Group P.

      That is the only ad I could find skimming the first 20 pages. I didn't read the rest.

      I concur with Shaun, there is a remarkable lack of advertising compared to the September election. I would not be too surprised to see this reflected in the turnout rate.

    4. Perhaps the limited advertising is due to the numbers: What business case exists to increase the likelihood of election of:
      Labor (2)
      Liberal (3)

      Whereas Greens may need to advertise a little to ensure their vote holds? It the 3rd liberal was genuinely in the balance then you'd expect them to be advertising more perhaps

    5. I haven't seen any advertising at all for any of the micro parties - not that I have been actively looking, but it is the advertiser's job to come to me, isn't it?

      Mind you we don't see a lot of advertising for micros in a general election anyway.

      What we have seen over the last few weeks is a few prominent stories in The West that are quite critical of the micros, particularly when candidates do not come from WA. For example, there was an article on the #2 candidate from the Outdoor Recreation Party that seemed quite critical of his choice to not even come to WA to campaign!

    6. I flipped though every page of The West today. No ads at all (or if there were any, they were easily missed) and one more story critical of interstate candidates.

      TS, I think you may be right. Both LIB and ALP would probably benefit more from not stirring the pot than anything else.

  12. There seems to be some concern in the media that HEMP might get a seat. True, they seem to get a better run than most of the others (for whatever reason) but I expect they'd need a decent kick-start to get going.

    On the assumptions above, HEMP never get a seat in any scenarios you've tested so far.

    My challenge for today is therefore... what sort of head start do they need before they are really in the game?

    1. I can’t understand why TruthSeeker’s “ratioing down” of minor party votes leaves HEMP with about a third as many votes as the Sex Party, including in the scenario where he reinstates some of the minor party vote (0.41% vs 1.18%) when the 2013 result was 1.08% vs 1.49%.

      Also not clear how HEMP end up behind Family First and a few others and equal to Animal Justice when they beat them 1.08% to 0.74% in 2013.

      Among the eliminations HEMP needs to survive to get elected are against the Sex Party and Animal Justice.

      I’m also not completely sold on the “could not find” effect, apart from the mistaken identity situation with the Liberal Democrats and even there I don’t think it will be completely eliminated given they’re still to the left of the Liberals and a lot of people refuse to take a “how to vote”.

      However there could be a “can’t be bothered” effect to the extent that part of the minor party vote is from those disillusioned with the whole thing and potentially overrepresented among those who don’t turn out for a by-election.

      I’ve been running my own simulations using slightly different Monte Carlo parameters to Truth Seeker’s (a similar overall approach whereby the smaller parties vary proportionally more than major, although I don’t swing the majors quite as much) and I get HEMP with chances in the range of 15-40% depending on the exact assumptions for other parties and minor parties overall.

      As an example, with base votes of:

      LIB 38.8%
      NAT 4.3%
      ALP 30.3%
      GRN 11.5%
      PUP 3.9%
      OTH 11.3% (including 0.86% for HMP)

      I get HEMP winning a seat in 41% of cases.

    2. You have PUP way too low in this analysis. They polled more than that in 2013 and current polling has them sitting around 8%-10%.

      PUP is too big for HEMP to get past them so they don't get elected on PUP preferences.

    3. What current polling has PUP on 8-10%?

    4. I was following TruthSeeker's lead in my numbers above - loosely applying BluderTrack swings to the PUP vote.

      I agree that if PUP get something like 8%, HEMP can't win.

      However if I re-run with them at a baseline of 6.0% (drawn proportionally from all other parties) for base votes of:

      LIB 37.9%
      NAT 4.2%
      ALP 29.6%
      GRN 11.2%
      PUP 6.0%
      OTH 11.0% (including 0.84% for HMP)

      I still get HEMP winning a seat in 18% of simulations, including a few with a PUP vote as high as 6.6%.

    5. Internal party polling has PUP sitting around 8%-10% with most of their growth coming off the Libs and the Nats.

    6. Great - I'm glad I've inspired others to undertake their own Monte Carlo analysis. As for PUP - I think the most appropriate link is from my favourite Tasmanian blogger - Kevin Bonham

  13. Anon 10:38, can you point to any actual readable poll data that puts PUP that high?

    In the last Morgan blurb there was a passing mention to a PUP vote of 10.5% in WA but this is from a very small sample size, the questions name PUP but no specific micros, and it isn't a Senate poll.

    I'm not dismissing what you are saying but curious to read further detail if it is available.

    1. I've seen something more credible - check my latest post