James Glover is back with another guest post, this time digging into some poll figures ahead of the postal plebiscite on same sex marriage.

Hey, there is a survey/plebiscite/referendum on, in case you haven’t heard. It’s on same sex marriage or marriage equality. Leaving aside the fact that this is a survey and not at all binding on MPs, this post is not about the rights and wrongs of SSM but about how to interpret the results of a recent Newspoll. Unlike most Western democracies voting in Australian elections is compulsory but as this is voluntary we are left with the additional problem for psephologists of determining not just how people would vote but whether they feel strongly enough to vote. The Newspoll produced two sets of results. The familiar one of whether people supported SSM or not, but also whether they intended to send in their postal surveys. Strangely enough they didn’t include information on the voting intentions of those who actually intend to vote.

So I made a spreadsheet model to try to determine some possible outcomes and what were the real drivers of the result based on what we gleaned from Newpoll but with some possibilities of one side or the other getting more people out to vote and the underlying vote being skewed towards the “Yes” vote. We know from dozens of polls going back 10 years that the majority of people, when asked, support the general notion of SSM. The results are usually in the range 60-70% in favour, 15-25% against and about 15% undecided. Newspoll has the overall level of support at 65%, about in the middle of that range. And if the ABS, who are conducting the survey, were to conduct a statistically significant poll they would almost certainly (the probability theorists technical get out statement) say a clear majority support it. Game over. Surely?

But there are other factors coming into play here. Here is a table of the Newspoll results by age, probably the most significant determinant, outside political views, of whether they support, or not, SSM.

Support for SSM by Age	18-34	35-49	50-64	65+	Overall
Yes	70	64	64	49	62
No	22	28	30	47	32
Undecided	8	8	6	4	6
AEC enrolled population	4,271,289	4,271,290	4,271,291	4,271,292	17,085,162

To determine the ”overall” figure, and what I will refer to as the “voting population”, I am using the AEC’s own figures on people enrolled to vote, as of June 2017, which is the last line.

As has been noted support for SSM decreases with age. But the number of people in each age cohort is about the same. The overall figure for support of 62% is towards the bottom end of most surveys but let’s leave it at that.

The Newspoll also provide figures on whether people actually intend to return their surveys.

Intention to vote	18-34	35-49	50-64	65+	Overall
Definitely will vote	58	64	73	76	68
Probably will	19	16	11	11	14
May or may not	12	9	8	8	9
Probably won't	4	5	3	2	3
Definitely won't	3	5	3	2	3
Uncommitted	4	1	2	1	2

One obvious thing to note is that older people, who are also more likely to vote “No” are more likely to vote. That will skew the results towards the “No” case.

But polls two months out may not reflect the final vote as happened in the recent US and UK elections, and support for the “Yes” case may soften. And the “No” case is probably doing a lot more to ensure they get as high a turnout as possible. So, in my model, on a spreadsheet of course, I included some assumptions and variable inputs which are:

1. I assume all people who say they definitely will vote is 100%.
2. “Probably will vote” is an input
3. “May or may not vote” is an input
4. Probably won’t, definitely won’t and uncommitted is set at 0%
5. Turnout for the “No vote”. Based on the polulation figures the turnout, overall should be about 83%. So one input is the turnout for “No vote” assuming they make more of an effort to get their supporters out to vote. The turnout for the “Yes” vote is then deducted from this number to match the overall turnout, 83%, by age group so higher turnout for “No” automatically leads to a lower turnout for “Yes”.
6. For people who will claim that the “Yes” poll result is exaggerated and is actually lower, or will soften closer to the closing date I have included an adjustment term. So “-5” means I have reduced the polled support for “Yes” by 5% making it 57% rather than 62%.
7. Splitting the “undecided” vote between “Yes” and “No”. “P” means I have allocated it proportionally to the level of support, but there is a parameter which splits it, say, 25% to “Yes” and therefore 75% to “No”.

So the results? Well here they are:

Summary	BCS	Exp S	RWCS	WCS
% "probably will vote" who do vote	75%	75%	50%	25%
% "may or may not" who vote	50%	50%	32%	0%
"No" vote turnout	P	95%	95%	100%
undecided split to "Yes" vote	P	P	30%	0%
adjust yes vote	0	0	-5	-5
Vote Yes	66%	62%	50%	40%
Vote No	34%	38%	50%	60%
Support Yes	67%	67%	59%	57%
Support No	33%	33%	41%	43%
Overall turnout	84%	84%	78%	71%
Yes turnout	83%	78%	67%	50%
No turnout	85%	95%	95%	100%
Population Yes vote	56%	52%	39%	28%
Population No vote	28%	32%	39%	43%

There is good news, and bad news, depending on your viewpoint. My own view is a “Yes” vote is a good thing but if you feel otherwise feel free to substitute “Best” for “Worst” in the above table. So here are the 5 scenarios. Note that once you fix the “No vote” intention to vote at, say, 95%, you remove people who intend to vote “Yes” in order to keep the Newspoll and AEC derived figure of 83% intending to vote.

1. BCS – Best Case Scenario. Based on the Newspoll numbers I have split the intention to vote and undecided vote equally among “Yes” and “No” voters. I have also assumed 75% of the “Probably will vote” and 50%” of the May or may not” voters will vote. The result is a clear win 66:34 for the “Yes case”. Also the overall number of people voting “Yes” is 56% of the voting eligible population so hard to argue this isn’t a decisive result.
2. Expected – I am assuming that the people on the “No” case will be better at getting people out to vote than the “Yes” case, 95% of them. Here there is still a clear win for “Yes” at 62%. And overall that represents 52% of the population. A clear win for “Yes” on the vote and over 50% of the population vote “Yes” as well.
3. RWSC – Reasonable Worst Case Scenario. This is a term that I (and the Mule) picked up in our early days at DB to describe a scenario which assumes negative (from my point of view) parameters that could nonetheless be possible. Here I am assuming only 50% of probably wills and 33% of may or may not’s vote. Because I have fixed the “No” voting rate at 95% this leads to less “Yes” votes” to keep the overall participation rate at 83%. Here the result is a line ball at 50:50. It could go either way. The population “Yes” vote is close to 40% so people might argue that less than 50% vote “Yes” and hence conservative MPs shouldn’t take the result as definitive.
4. WCS – Worst case scenario. Only 25% of the maybe votes and none of the may or may nots vote and 100% of the “No” votes do. I’ve reduced the support for the “Yes” case by 5%. All undecideds get allocated to “No”. Despite the overall support being 57:43 in favour of “Yes” the actual vote goes 40:60 in favour of “No”. And the overall population vote is 43:28 in “No”s favour. Under these circumstances the PM has said the vote for SSM won’t come to parliament. Largely this is driven by the 100% turnout for “No” and only 50% turnout for “Yes” as well as softening of support for “Yes” and undecideds voting “No”. This is the result the “No” campaign will be, literally in some cases, praying for as it will be difficult for the Opposition and proponents of SSM to argue the issue hasn’t been settled for the time being.

My own guess? It will be 55:45 in favour of “Yes” with overall support at 65:35. That will be enough for the anti SSM lobby to say support was never as high as the “Yes” camp claimed. But a win is a win and only the most devout glitter sellers won’t be running out of stock by Xmas.

Extra: How do I think the ABS should actually conduct this poll? Not by post for a start. There are 150 electorates and one of the arguments against using results from 1,400 people is that it barely samples many of those, less than 10 people is some cases. In actual fact the mathematical 95% margin of error for sampling N people is (approximately) 1/sqrt(N) or for N=1400, 2.67%. So the overall sample size is sufficient if the result is 60:40. But to give everyone the feeling their voice and their neighbour’s voice is being heard how about sampling 150,000 people? That is 800 people in Australia’s smallest electorate, Kalgoorlie. The MoE by individual electorates would be better than +-3.5% and over the whole Australian voting population 0.25%. And it would only cost $10m. It might even become a regular thing.

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