## More on Informals and other electoral goodies.

Posted by Possum Comitatus on January 26, 2008

One of the problems we had with the informal voting model last time that caused some consternation was the use of non-linear variables, particularly using the squared value of the proportion of the electorate that spoke English poorly or not all – the NES variable.

The reason the square of the value was used was that it explained the data generation process better than its simple value.

The big problem wasn’t only the four electorates with the highest NES proportion, but 15-20 seats that had relatively low informal votes considering their NES level.

After ferreting around the census data, if we control for the proportion of the electorate whose highest level of schooling is year 10 or less (we’ll call this variable EDUCY10), what appears to be the slight non-linearity in the relationship between the informal vote and NES disappears.

Interestingly there is a slight correlation between NES and EDUCY10, in that the higher the proportion of the electorate with a Year 10 Education or less, the proportion of people that speak English poorly or not at all tends to be (slightly) lower.

This correlation between independent variables can create a problem called collinearity, however after testing NES against the EDUCY10, the Tolerance was 0.835 and the Variance Inflation Factor was only 1.12 meaning that collinearity simply isn’t an issue here.

So after partially controlling for education and removing what looked to be a non—linear relationship between NES and the informal vote level, our new equation becomes:

We can now explain over two thirds of the variation in the informal vote, by electorate, simply as it being a function of :

– The proportion of the electorate that speaks English poorly or not at all.

– The square of the number of candidates standing in an electorate

– The proportion of an electorate that has a year 10 education or less

– Whether optional preferential voting operates at the state level for that electorate.

Using the square of the number of candidates rather than just the simple number of candidates that stood in each electorate explains the data generation process (i.e. the election) slightly better. What this means is that as the number of candidates increases on the ballot paper, the informal vote increases in a slightly disproportional way. Not much, but enough to warrant paying attention – it’s essentially a compounding informal effect for candidate numbers.

Moving right along to some more interesting results of the election that aren’t as niche as informal voting, lets have a look at the primary vote of Family First plotted against the number of candidates that stood in each electorate, and lets run a simple regression with the two:

As the number of candidates increases, generally the Family First Vote decreases. That might sound like an obvious consequence that should happen to all parties – but it actually doesn’t (except for the ALP which we’ll get to a little later on)

At first I thought this might have had a bit to do with geography, with FFP picking up some of the bible belt vote in rural electorates that have few candidates – so after controlling for population density and running the equation again we get:

Which doesn’t make a great deal of difference to the size of the ‘candidate number’ effect on the FFP vote. Putting it another way, it smells like some evidence to suggest that a lot of people only vote for Family First because they happen to have a candidate standing, when ideally a lot of those voters would prefer to vote for some other minor party or independent if given the chance.

FFP seems to have a large soft vote.

**Next up** is something to chew over for the ALP staffers and pollies that are reading.

If we test the size of the two party preferred swing to the ALP in each electorate against the size of the Green vote (telling us if there is any statistical relationship between an increasing Greens vote and an increasing ALP swing) we get:

Yikes! This is telling us that far from a high Greens vote delivering a large ALP swing, the opposite happens where the higher the Greens primary vote, the lower the two party preferred swing to the ALP – a major implication in terms of the power that each party could wield in preference negotiations. ~~However, if we do this again but control for the number of candidates in each electorate as well, we get:~~

[*I somehow managed to run a regression on a sample of the electorate results rather than the full electorate results when I controlled for CANDIDATES- yes, yes “WTF?” was what I was asking myself too. Candidate numbers have no bearing on this result once we test all 150 electorates rather than just the 16 I somehow managed. .]*

That’s a juicy figure there – for every 3% chunk of the vote that the Greens received in an electorate, the two party preferred swing to the ALP reduced by just over 1%. Food for thought for both Comrades and Greens alike.

Finally for today, we know there is a relationship between the ALP primary vote and the proportion of the electorate that speak English poorly or not at all:

We also know that there is a relationship between NES and the level of the informal vote because we measured it earlier, so it’s not a great leap to reach the conclusion that a reduction in the informal vote would more than likely increase the ALP primary vote in many seats. If we model the relationship between the ALP primary vote and the informal vote that best fits the data (a simple quadratic regression) we end up with a modelled Informal vs ALP Primary vote relationship like this (which explains about 30% of the variation in the informal vote):

Some of that informal relationship, particularly in seats with an ALP primary close to 50% and beyond, would be easily explained by the nonchalant way HTV cards are often distributed in ultra-safe ALP seats (which also tend to have high NES populations… ta da!). But between the 40-47% ALP primary vote level, seats where HTV cards are definitely handed out in ways that certainly aren’t so nonchalant, if the informal vote can be reduced in those seats, those marginal seats, that informal reduction looks like it would flow more to the ALP than the Coalition by a fair margin. A 1.5% reduction in the informal vote across the board would have handed the ALP at least an extra 3 or 4 seats, possibly more.

So what’s the bet that the AEC will find themselves with new funding for voter education, specifically for targeting NES demographics and people whose maximum education level is year 10 or less (which, when controlling for population density, actually tended to vote for the ALP) ?

Especially since there’s seats in it for the new government.

For anyone interested, the Parliamentary Library has just released a **Research Paper on Electoral redistributions during the 42nd Parliament** (that’s this one), which gives us a good background on a lot of what’s likely going to happen with the all important redistribution coming up before the next election.

## kwoff.com said

More on Informals and other electoral goodies. « Possums PollyticsOne of the problems we had with the informal voting model last time that caused some consternation was the use of non-linear variables, particularly using the squared value of the proportion of the electorate that spoke English poorly or not all – the …

## Enemy Combatant said

Poss, for a moment there that f-statistic on ALPCHANGE looked a bit dodgy. I had my people give the figures a quick re-crunch and whaddya know! Got things all squared away quicker than a bloke could sort a bunch of mean dependent variables.

Bottom line is; four seats is a lot, the ALP have gotta glad-handle and wise-up their communicationally challenged supporters.

Meanwhile, in the the crazy mixed-up world of modern media,

The Bully bites the dust as The Legend of The Possum grows. But one is less likely these days to have glommed it from dead tree editions.

Mark Bahnisch on ABC Online today:

“Readers consume political news and analysis differently now – there’s little loyalty to a masthead, and those with an ardent interest in politics put a premium on the relationship they have with particular commentators, and an even bigger premium on the ability to enter into a conversation about political news. Hence the success of commenters like the irreverent and very well informed Possum Comitatus in the blogosphere and on Crikey – quite properly, there’s a desire more for a democratic conversation than for being informed from on high by pompous pontificators on a permanent drip from the pollies.”

http://www.abc.net.au/news/stories/2008/01/26/2147199.htm

## HarryH said

Poss, i’m trying to get my head around what you’re saying about the correlation between Green votes and ALP swings.

Can you give it again in laymans terms of what you are getting at and how it might affect pref deals, who Labor need to keep happy etc.

thx

## Antony Green said

No, I don’t care if Candidates^2 explains more than simple Candidates or not, it is still no justification for using it. There is no doubt there is a relationship between the number of candidates and a rise in the informal vote. For each extra candidate, the probability of a voter making an error increases. But what is the mechanism in this that causes it so go up at a faster rate and justifies a Candidates^2 term? If you were talking about the number of errors per ballot paper, I’d accept it, but not the probability of a single error. After every election since 1984, the AEC has done exactly your model and always used Candidates only. You’ve decided that Candidates^2 is better. How do you know it isn’t just some artifact of the data this time?

## dany le roux said

I understand very little of what is in the red boxes but what Anthony Green says reminds me of the ancient approach to the calculation of wind resistance of a given vehicle.It went something like this: –

R = a*v + b*v^2 + c*v^3 + d*v^4 …

where v is the velocity of the vehicle and for low speeds the higher powers have little significance and all the constants are determined empirically.

Can you do the same thing for CANDIDATES so as to not need to know what sort of nonlinearity is involved?

You would have a function

F(CANDIDATES)= a*CANDIDATES +b*CANDIDATES^2 + ….

or would this not work because you do not know what a and b are ?

## dawson said

Didn’t work in Indi, where the ALP 2PP of 40.81% basically equals the Green vote of 7.58 + ALP primary of 32.12.

Or do things just work differently in rural electorates?

## dawson said

…or indeed nationally, where the ALP polled 43.38 on primaries and the Greens 7.79, with the 2PP being 52.7 – again, suggesting that most of the Green vote went to the ALP.

## Possum Comitatus said

Antony,

I’m not particularly concerned that the AEC always uses a linear relationship between ballot length and the informal vote – more power to them, nor am I particularly concerned whether the use of a linear candidates variable stretches back to the dawn of time itself. I’m simply following the data, and the data suggests that ballot length has slightly increasing marginal effects on the informal vote rather than constant marginal effects. While both are similar in terms of their ability to describe what happened at the election, one is slightly statistically superior and describes the data slightly more accurately – candidates^2.

There is no compelling reason why ballot length could not have, as the data suggests, slightly increasing marginal effects on the informal vote – far from it, variables having increasing marginal effects on various forms and types of human error is a widespread phenomenon in economics and social science generally (from traffic volumes and their effect on the accident rate of some urban roads, through to the number of separate duties a production worker has to do on a production line and the effect that has on the quality control rejection rate of the finished components).

Cubic polynomial terms for independent variables are another mechanism that is enjoying widespread popularity with explaining human error rates because they can accurately measure the phenomena whereby the increasing value of the independent variable leads to the value of the dependent variable (human error) initially climbing slowly before increasing more dramatically and finally returning back to a slower growth path. The consequences of incremental additions to complexity arent necessarily linear simply because people have non-linear adaptive capabilities.

At the end of the day, ballot length should always be accounted for in the way the best explains the data – if that explanation is sometimes linear and other times not – well that’s life. I’ll stick with following the data, and in this particular case the data says a squared term is not only a slightly more accurate representation of the effect of ballot length on the informal vote, but is easily explainable as well as being a common, accurate representation of human error in fields other than psephology.

Think of it this way – the difference between having 4 candidates and 5 on the ballot might lead to,on average, an extra one quarter of a percent in the informal vote. But adding another candidate, bringing it up from 5 to 6 might lead to an extra one third of a percent and so on. That non-linear increase could simply be the result of the compounding nature of the probability of making an error (the chances of accurately filling in 5 spots rather than 4 may be disproportionally greater than the chances of accurately filling out 6 spots on the ballot). The clarity threshold of illiterate voters may also be such that 3 and 4 ballot spots they can cope with, but 5 starts to become difficult, 6 extremely so etc. There’s plenty of mechanisms available to explain why the data suggests what it does.

## Possum Comitatus said

Dawson,

that bit was about the change in the ALP vote rather than the two party preferred vote. What it’s measuring is the relationship between the Green primary vote and the size of the ALP two party preferred swing in each electorate.

Dany,

that’s essentially what I did here.It started off as a*CANDIDATES+b*CANDIDATES^2+c*CANDIDATES^3 and so on, but where CANDIDATES and CANDIDATES to the power of 3 and higher were all statistically insignificant and where removed from the equation as a result.

Harry – I’ll get back to you on that, I’m trying to hunt down some data that might explain it better.

## dawson said

Poss, wondered if that data is influenced by the results in seats like Melbourne, where the final two fighting it out were ALP and the Greens.

Obviously, in this case an increase in the Green primary vote would not translate to 2PPs for Labor.

I am the first to admit to being statistically challenged, but would like a practical example, using a specific electorate, to illustrate what you are talking about.

I also wonder if the data in fact reflects not the Green influence on 2PP but that of another party, and that this distorts the true picture.

So – to use Indi as an example again – you can posit from the result that almost all of the Dems vote went back on 2PP to the Libs.

If Parties like Dems and FF are bleeding primaries from the Libs and then feeding them back as preferences, maybe this is what’s influencing the data, rather than the number of Green primaries.

I’m trying to make sense of this, because at present the scenario you outline doesn’t make much.

Another explanation might be that past Dem voters are voting Green as a protest vote on primaries but then jumping over Labor to go to the Libs, but that seems far fetched (although one can imagine that past Dem voters were gripped by cosmic angst at this election and not responsible for their actions).

If the statistics lead to a conclusion which doesn’t pass the common sense test, then one has to question the method which produced the statistic.

I’m perfectly willing to admit that my understanding of statistics is vague at best, and I have as much right to question your findings as a weasel, but humour me.

## Ronin8317 said

The Candidate ^2 is justify by the way people fill in the vote, which is O(n^2) due to the search.

Imagine the process to fill in a HTV card

1) Find Number on the HTV card to locate name

2) Find the name on the ballot

3) Fill in ballot

4) Repeat for next number.

In computing terms, the algorithm complexity is O(n^2), or proportional the the square of the number of candidates.

## Possum Comitatus said

Thanks Ronin – I was actually looking for something like that and you set me exactly on the right path. Many thanks.

For anyone else interested, I just repeated the exercise for 2004. The square of the candidates is, again, a slightly more accurate representation of the data. I would be surprised if that wasnt the case for just about every election going back to the dawn of time.

## Antony Green said

Possum @ 8, I reckon you’re data mining. And as for Ronin’s comment, I think it is only partly relevant. At the 2004 election, only 15% of informal votes were informal because of incorrect numbering. 21% were blank, 33% ‘1’ only, 9% ticks and crosses and 14% ticks and crosses. But the AEC did find that the category of incorrect numbering was the group that increased most as the number of candidates increased.

You should get the AEC data and see if the informal votes caused entirely by numbering corresponds to your squared model. It may be that when you disaggregate the data you find two relations going on, one linear and one non-linear.

See http://www.aec.gov.au/About_AEC/Publications/Strategy_Research_Analysis/paper7/page06.htm

## Antony Green said

Sorry, 14% marks and scribbles, and there was 4% with incomplete numbering.

## Possum Comitatus said

Antony,

The difference between data mining and empirical research is semantics. As long as the significant independent variables you find have a good statistical relationship with the dependent variable combined with rational explanations or hypothesis on the underlying causative nature of that relationship, they are one and the same.

Think about the way the variables in the equation carry their regression weight, and the shape of that weight.

STATEOPV will take a large chunk of the just voting 1 impact on the informal vote, but so will illiteracy (which the EDUCY10 is a quasi-instrumental variable for) as well as poor English speaking.

After controlling for EDUCY10, the non-linearity of NES disappeared because of the way the influence of those two variables were becoming entangled.

Similarly, a large part of what you might call electoral illiteracy – some of the ticks and crosses, some of the scribbles and some of the blanks would be expected to have their weight carried in the equation with NES and EDUCY10.

But some of that electoral illiteracy effect would be carried over into ballot length – the question for this component is whether that is a linear or non-linear relationship. Additionally, it’s also the remainder, the bits that aren’t at all explained by those education, background and geography variables that make up the remaining bulk of the CANDIDATES explanatory weight in the equation.

On these, we expect there to be a non linear component anyway because of the compounding probability of error involved in marginal increases in candidate numbers. We should also expect there to be non-linearity involved because that is what we observe elsewhere – we see that type of non-linear relationship between measurable human error and marginal increases in complexity in just about every other field of human endeavor.

If you look at Figure 5 in that link you provided – the AEC was incorrect in suggesting that relationship between the first difference of candidates and the first difference of the informal vote was linear.It is not, it is a 3rd order polynomial relationship, the typical type of cubic error relationship that I mentioned in the last post.

However, I also agree with you that there would likely be additional linear components related to ballot length – yet the question becomes (in the absence of additional ballot length research) which of the two competing forms of the CANDIDATES variable (linear or non-linear) overpowers the other both in terms of the behaviour of the actual data and the explanations that describe that behaviour?

Because we know that marginal changes in complexity (in this case ballot length) are more likely to involve increasing and subsequently decreasing changes in human error counts rather than constant constant changes, and because the data itself is slightly non-linear – the evidence suggests we should treat it non-linearly until such time that further research can justifiably remove the the need to treat it non linearly. Especially since it doesn’t appear to be a one off phenomenon of the last election.

I might seek out the AEC data for the 2007 election a little later and see if there are any linear and non-linear components that can be disentangled within the ballot length issue (although that sounds like data mining! ). But until some research like that pops up which can actually demonstrate the dominance of ballot length linearity – treating it as linear is neither the most accurate treatment, nor the most rational treatment considering that constant marginal effects resulting from increases in complexity aren’t exactly the norm of human behaviour.

## Antony Green said

Yes, well, I suppose in the end my problem was the one model you produced with a negative coefficient for candidates and a very high constant value. It fitted the data but as I said at the time, extrapolated very strangely.

I’ve approached this debate from looking at past work on the subject, and there is two decades of literature on informal voting at both state and federal levels. This is political science, not econometrics. Once you have established a relationship, for instance a linear one, the extra explanation you get by applying polynomial models does no more than repeat the finding you already had from the linear model. Yes you improved the fit, but you already had a good fit. But the policy implication on how to fix informal voting is the same, and above all, trying to get someone who doesn’t understand statistics to understand a linear model is much easier. The coeffecients are easier to explain.

I’m also wary that with you’re polynomial models you are soaking up the outliers at each end of the distribution. Sometimes in political science, it’s easier to have a simple model and highlight the outliers than have a complex model with fewer outliers.

I also had comment on the earlier models because of the value for the constant term in the equations. In all the work on this subject, the constant term tends to correspond to the minimal level of informal voting you get with the least number of candidates. Past research has always shown that 3-candidate contests have the lowest level of informal voting. 2-candidate contests, which we never see any more, always had a higher level of informal voting, easily accounted for by using a dummy variable.

The best models anchor the left side of the model at the value of the constant and match to the open end of the graph, if that makes sense. Your most recent models do this and are more useful, but at least one of the early models didn’t, which is where my original grumpiness came from.

I’ve seen many a political science paper that’s happy to get an r-squared of 0.3, which is why I get slightly amused that you have to keep going on beyond 0.5.

, I don’t think helps doesn’t get you anywhere.

## dany le roux said

“But the policy implication on how to fix informal voting is the same, and above all, trying to get someone who doesn’t understand statistics to understand a linear model is much easier.”- Anthony Green.

Who are the “someone”(s)?

The ^2 factor being drastically non linear and something which is easily understood by anyone with even a modicum of maths education should in itself be easy enough for an expert within the AEC or a political party to understand.

( “Sir, the number of informals is related to the square of the number of candidates and is a big deal if there are lots of candidates”.)

Anthony’s phrase “the policy implication on how to fix informal voting ” implies that there have been those who wanted the problem fixed in the past.

Most likely it is that the knowledge that informal votes favour the Coalition would have inhibited any policy change in the last eleven years. That is, two decades of research pointing to CANDIDATES^1 as a factor in producing informals did not have much effect on policy.

CANDIDATES^2 though is very in your face compelling and a piece of stuff which could get known far and wide, like an urban myth,as part of the democratic process.

Perhaps if the ^2 factor were known about by el Rodente’s mob they might have been satisfied with say 7 CANDIDATES in Benelong instead of 13. I am assuming of course that el R’s mob pulled out all stops for this electorate and that some of the candidates were LP stooges.

Anthony has made submissions to the AEC about electoral matters.

Will you?

## Antony Green said

Danny,

No, it’s not as simple as having a new line of argument that it is related to the square of the number of candidates. Now I don’t have the ability to do graphs here like possum, but holding all the other variables constant and using a Cands^2 variable means that on an X-Y plot of informal% versus number of candidates, he has a curved line rather than a straight line. By saying it fits better, we are saying this curved line is closer to all the dots than a straight line, using ordinary least squares regression.

But the coeffecient on a Cands^2 line is 0.017, in a (slightly different) Cands model is around 0.2. On the informal vote plot, for large numbers of candidates, all of the points are above the linear trend line, and the Cands^2 model partly works better by providing a better fit to these outliers. But if you put the coefficients above into a spreadsheet, along with two columns of Cands and Cands^2 squared variables and do the multiplications and graphs, you’ve just got two different shaped lines describing the same data. Cands^2 provides a better fit to the data, but the accelerating squared term produces a much smaller coefficient which fits the data better but differently, which is why I’d be uncomfortable saying informal voting goes up as a square of the number of candidates.

As I posted earlier, most informal voting has nothing to do with mis-numbered ballot papers. I think I’ve given Possum a research project now to apply his squared model just to the category of mis-numbered ballots. I’ll mention the idea to the electoral commission if he doesn’t do it himself.

But as an example of what I’m talking about, the electorate of Wills in 1990 had 8 candidates and an informal vote of 6.4%. The 1993 Wills by- election had 22 candidates, but the informal voting was still 6.4%. The research I’ve done looking at state elections and joint elections all point to getting a lower informal vote if only one election is held, with no confusion caused by upper house ballots. The South Australian example clearly illustrates that as much as half the informal vote is simply confusion with the Senate’s ‘1’ only voting system.

I have the vague feeling I know what is going to come out of the Labor government on this, and it won’t be optional preferential voting.

The first will be a savings provision, so that if a ballot paper has some preferences, and the ballot paper would end up with a candidate whose preferences would not be distributed, then the ballot paper would be formal. So a ‘1’ only vote for Labor or Liberal would be valid, but the same vote for a Green or Family First candidate would not. A misnumbered ballot with first preference for Labor or Liberal would count, but for Greens of Famiuly First would not. On past evidence, such a provision would halve the informal vote with one legislative amendment.

A second would be the South Australian system of ticket voting, where misnumbered or ‘1’ only votes can be saved and imputed to have preferences. This method would not disadvantage minor parties as much as the suggestion in the previous paragraph, but would have to be watched closely to make sure it did not come with provisions that allow parties to advocate a ‘1’ only vote and therefore capture preferences, as occurs in the Senate.

In 1989, Western Australia trialled a lower house ballot paper that included ticket voting at two by-elections. It was a mess. One problem was that in WA to this day, there are no split tickets in group ticket votes. Each party can lodge only a single ticket. This was a problem in the lower house, as it prevented Independents, who didn’t want to lodge any ticket of preferences, from having access to the group ticket voting square.

## Antony Green said

Possum,

On a technical note, and I’m sorry it’s about the constant again, if you’re trying to measure the impact of the increasing number of candidates, there’s a problem that the data has the lowest number of candidates at 4. If you subtract 4 from the number of candidates before you do the regression, you will get a set of coeffecients that produce a constant that better measures the exogenous level of informal, and a coeffecient of the Cands^2 that better measures the increase in the number of candidates. The current model includes an extrapolation from 4 candidates back to zero candidates.

## Possum Comitatus said

Antony,

The difference between the statistics of political science and econometrics only really differs in it’s sophistication (I dont mean that in a bad way) – and then not necesarrily to a great extent. I understand that political science approaches data more on the basis of finding empirical evidence to support (often) long held views on the way elections work, whereas economists tend to approach data from the position of the data itself.

This isnt the first time that economists pissing in the patch of other fields of specialisation annoys the shit out of all and sundry – so I sympathise with your annoyance It’s like the R-sq of 30% and people being happy with it. I’d be happy with it too if that was the best representation of the data possible – that should always be the point. But the amount you can explain is a simply a function of the data combined with testing variables you believe would have a significant relationship and effect on the behaviour of the dependent variable. As long as we avoid lots of large order polynomials, only use variables that have not only a significant relationship but one of a meaningful size, and that we keep an eye on the sample size vs degrees of freedom, there isnt a problem going higher than the 30% that some others were happy with.

On the polynomials vs linear bit, polynomials are helpful not **JUST** because they can explain human behaviour slightly more accuratetly (via their simulation of non-constant marginal effects), but their other benefit is the way they affect the size of the residuals in each seat. They can provide a more accurate estimation of the size of the unexplained informal vote, as well as a more accurate estimate of the distribution of that unexplained informal vote in each electorate. Often the difference in explanatory power between a polynomial representation of a variable and a linear representation of the same variable will be relatively small (often making us wonder why we would bother), but the way it affects the distribution of the residuals, in this case seat by seat, can be quite profound.

That’s pretty important if we want to do any further research on such things.

The outliers are a tricky question – “are they really outliers to begin with?” being the key thing here. The fact that most of the outliers tend to be either clustered together at the ends, as well as being on the expected side of the value threshold suggests to me at least that its more likely than not that they arent actually outliers in the true sense of the word, or even at all. If we had a thousand electorates in an election we could easily get to the bottom of it. Unfortunately combining election results to increase our sample also gives us temporal effects that pollute the data. I’ve played around using panel data to try and remove them but it doesnt really make any difference (the results still suggest in my mind that they arent outliers in the true sense), and we just add more uncertainty in the process.

On the constant, I still dont think that it’s wise to give the constant any actual interpretive meaning. Because there cannot be zero candidates, as you say, it throws out the interpretive value. But even if we subtract 4 from the candidates series, while that allows for the possibility of zero in the adjusted series, it also leaves us with the problem of there never being seats with zero value for NES, nor additionally in my case zero people with a maximum education of Year 10 or less. So unless we also adjust those other series values, the constant will continue to have no real intepretive value as a result. But we can’t really adjust those other values while simultaneously maintaining the integrity of the data.

The constant will (obviously) simply be the average of all the things the equation doesnt explain, but whose value would be expected to be swamped by the magnitude of the residuals for any given seat anyway.

So rather than treat the constant as interpretive, we should probably treat it as merely a mechanism to give us unbiased errors (which in my experience in other fields tends to be the norm anyway – it’s more usual for constants to have no inherent meaning in complicated cross-sectional data than actually containing real interpretive meaning) and allows us to simply focus on the expected changes involved in informal voting that are associated with marginal changes in the actual values of the independent variables themselves.

I appreciate that it’s not “neat”. And I appreciate the difficulty that arises when trying to explain the results of very “un-neat things” to people with little or no statistical background. But neatness is really a two edged sword – to make something neat (for the sake of easy explanation) will often sacrifice the accuracy of what you are trying to explain in the first place.

## dany le roux said

I dug out a book – “Mathematical Methods for Physics and Engineering” which has a big chapter on statistics I did not need to look at before.

The TAFE College of Wikipedia tends to spread the subject “statistics” out over many Wiki entries and a coherent overview of the subject is impossible.

I am giving myself a month to get on top of it all.

Very few contributors apart from Possum and Anthony Green talk statistics here and I would hope others do a short course as well because many preface their comments with stuff like ” don’t understand a word you are saying Possum…”

One Wiki entry even says that “statistics” is not really mathematics at all.

I hope to find out if this is really true.

## Antony Green said

Danny, a chapter on statistics in a book on physics or engineering might not be very helpful. The sorts of statistics used varies amazingly in differents academic fields. Medical research statistics requires vast knowledge of small sample maths that no-one else bothers with. Econometrics spends a lot of time with time series analysis, which brings in subjects us lagged variables and heteroskedasticity which no political scientist would ever come across. Political scientists like to use census data which causes everyone to get obsessed about ecological fallacy. Possum and I are coming at informal voting from different directions which is why we differ on interpretation.

## caf said

I agree with Antony that you need to have a plausible mechanism before you start pulling in variables, but I also agree that Ronin has provided such a plausible mechanism for informals to be proportional to Candidates^2.