## Guest post from Don Harding

Another guest post, this time from Don Harding, who’s looking again at the apparent conflict between betting odds on a Labor win and those in individual seats.

### Short geeks and long hacks: analysis of the 2007 Election.

Election 2007 is seeing greater attention paid to betting markets as a way of aggregating information voluntarily provided by informed but anonymous players and observers.

The implied probabilities obtained from betting markets provide important insights about the election that cannot be obtained from other sources. Extracting these insights requires more statistical sophistication than does the analysis of polls and this has meant that much attention has focused on the headline odds of a win by the ALP which is currently given as about 66 per cent by the main betting agencies.

Several commentators have observed that the 66 per cent headline probability of an ALP win seemingly stands in stark contrast to the fact that labour is odds on favourite in only 74 seats while the coalition is odds on favourite in 74 seats. This puzzle can be largely explained by three facts. First, there are seven seats where the ALP has 40 to 50 per cent chance of winning. In contrast there are only 3 seats (Solomon, Cowan and Hasluck) where the Coalition has a 40 to 50 per cent chance of winning. Second, there are there are two seats (Kennedy and New England) where independents are odds on favourites to win. This accounts for the extra two seats necessary to make up the 150 seat Parliament. Third, There are another 4 seats where independents have a better than 15 per cent chance of winning.

This difference in the seat-by-seat probabilities is illustrated graphically in Figure 1 which shows the Coalition and ALP probabilities of winning ranked from the seat where the party has the highest probability of winning to the lowest probability of winning. The probabilities of winning cross at around 74 seats and a probability of 50 per cent. But the seat-by-seat comparison shows that ALP has a much stronger base than the coalition with a much higher probability of winning each of the 74 seats in which it is odds on favourite than does the Coalition in the seats for which it is odds on favourite (the red line is above the blue line for non geeks). Moreover, in the seats where the ALP is not odds on favourite it has a higher probability of winning than does the coalition in the comparable seat in which it is not odds on favourite (again the red line is above the blue line for non geeks)

Put simply Figure 1 says that seat-by-seat lady luck is more likely to favour the ALP than the Coalition in election 2007. To understand exactly how much room there is for luck to favour the ALP we need to focus on the probability distribution of seats in the next Parliament. I obtained an approximation to this distribution by simulating 100,000 Parliaments using the seat by seat probabilities from Portlandbet. In 65.7 per cent of cases the ALP wins more than 76 seats and thus can form government in its own right. But the Coalition wins more than 76 seats in only 5.5 per cent of cases. In the remaining 28.8 per cent of cases neither party wins a majority. So there would be a minority government based on support from independents and minor parties.

Where there are minority governments the ALP holds the largest number of seats in 17.2 per cent of cases, in 2.8 per cent of cases the major parties are tied and in 8.8 per cent of cases the coalition holds the largest number of seats.

Assuming that the party with the largest number of seats forms government the probability of an ALP government is 84.3 per cent while the probability that the Coalition forms a government is 15.7 per cent. Thus, using the seat-by-seat probabilities to obtain a probability distribution over the number of seats in the next Parliament yields a much higher estimate than the headline probability of an ALP win and a much lower probability of a Coalition win than the headline odds of the main betting agencies. There are several possible reasons for this but one I favour is that the seat-by-seat probabilities accurately summarise the information of people on the ground in those seats. The headline betting market for which party forms government is likely to be less informative than the seat-by-seat market because there are relatively few people who can do the calculations necessary to translate the seat-by-seat probabilities into national win-lose probabilities. This reflects a wider problem in the media coverage of this election which is short geeks and long hacks.

The high probability of a minority government suggests that it would be invaluable if some time was spent by the media asking the major parties, the independents and the minor parties how they would act if neither of the major parties could form a government.

*Don Harding is currently a Senior Lecturer in the Economics Department at the University of Melbourne from January 2008 he will be a Professor of Economics at La Trobe University.*

This sentences strikes me as spot on:

“Put simply Figure 1 says that seat-by-seat lady luck is more likely to favour the ALP than the Coalition in election 2007.”

But the following reasoning is silly:

“To understand exactly how much room there is for luck to favour the ALP we need to focus on the probability distribution of seats in the next Parliament. I obtained an approximation to this distribution by simulating 100,000 Parliaments using the seat by seat probabilities from Portlandbet. In 65.7 per cent of cases the ALP wins more than 76 seats and thus can form government in its own right. But the Coalition wins more than 76 seats in only 5.5 per cent of cases. In the remaining 28.8 per cent of cases neither party wins a majority. So there would be a minority government based on support from independents and minor parties.”

Or at least it is silly if – as I assume – that these simulations are based on independent draws. There are strong correlations in votes across seats – the nationwide swing.

Recent research estimating the correlation in outcomes – for the US – is available at: http://www.som.yale.edu/faculty/keith.chen/papers/PresElectionModel.pdf

I have a question. I genuinely don’t know the answer. Opinions please. Does the existence of probabilities (of different outcomes for a future event) fully imply indeterminism or is determinism still a real (I hesitate to use the word) possibility? To put it another way. Is having to assign probabilites to outcomes of a future event a function of imperfect knowledge (of factors leading to a future determined outcome) or a proof of indeterminism or neither?

More than one philosopher has pointed out that once events (even socio-political events) have actually happened they can strongly present to us as having being fully determined.

Most economists who think about these issues regard probability as being essentially subjective, and therefore having no bearing on determinism either way.

I would have no problem making probability judgements about past events where I did not know the outcome – for example, when the polls close next Saturday, I would be willing to give a probability for “Labor won more votes”, even though, since the votes have already been cast, the truth or otherwise of this proposition has already been determined.

But, as the philosophers you cite point out, people tend not to think that way. John Howard’s four election wins, and Labor’s five before that are taken as having been retrospectively inevitable, even though they depended heavily on chance events (the way the votes fell in 1998, Joh’s run for Canberra in 1987).

JQ, good points. I hesitate to post further about determinism and indeterminism (let alone the even more fraught issue of free will and determinism) lest it go too far off your topic. But I have no problem with the notion of giving probablities for a determined outcome where one does not yet know the outcome. That clearly falls in the “imperfect knowledge” category in my opinion. You can garner enough information to give probabilites but not enough to be certain.

I agree “chance” makes complete sense as an operational statistical concept. I was just idly wondering whether the existence of stochastic phenomena (particularly seemingly fundamental and irrudicuble stuff like that in quantum mechanics) gives any lead into the indeterminism / determinism debate. But I am very much an amatuer philosopher. I should take that question off to some philosophy blogs. ðŸ™‚

LATEST ODDS ON CENTREBET

Odds have shortened for the favourites in most seats across the country. The latest betting odds is predicting the following wins:-

WA Ã¢â‚¬â€œ ALP (6) LNP (9)

SA Ã¢â‚¬â€œ ALP (6) LNP (5)

NSW Ã¢â‚¬â€œ ALP (27) LNP (20) IND (1)

VIC Ã¢â‚¬â€œ ALP (20) LNP (16) IND (1)

TAS Ã¢â‚¬â€œ ALP (5) ***Even a 5-zip clean sweep to ALP is only paying $1.30

QLD Ã¢â‚¬â€œ ALP (11) LNP (17) IND (1)

TOTAL COUNT Ã¢â‚¬â€œ 149 SEATS (Must have missed one or no betting odds)

Will assume the missing seat is ALP, and if the punters are right, this gives a total count of ALP (80) LNP (67) IND (3) Ã¢â‚¬â€œ A 20 seat swing to ALP or 53.3% of the 2PP Vote. Not sure I agree with many of the posters on this site predicting that the ALP will 90 something seats (Unless the punters are mostly wealthy Liberals) as there are only a handful of Ã¢â‚¬ËœtightÃ¢â‚¬â„¢ seats on the betting market (Favourite in brackets), these are:-

NSW Ã¢â‚¬â€œ Robertson (ALP)

VIC Ã¢â‚¬â€œ Corangamite (LNP), La Trobe (ALP), McMillan (LNP)

QLD – Bowman (ALP), Petrie (LNP)]

WA Ã¢â‚¬â€œ Stirling (LNP)

SA Ã¢â‚¬â€œ Sturt (LNP)

If and when the election is won by Labor, I would like all those people (and there are quite a few of you) who loudly and lengthily proclaimed that betting markets are better than opinion polls to publicly retract your statements.

Wont happen of course.

Of course, the betting markets are starting to catch up to the polls, but that’s a very delayed lag time, and due to the polls themselves.

I had the same thought as Justin. I think Don’s work – probably assuming independence – gets the seat-by-seat analysis in the same ballpark as the “party that provides the PM” headline odds. The difference, then, is the effect of inter-seat correlation.

I notice the odds are quickly firming for Labor now. An 84% probability might even be right on election morning.

I use the banal-ometer. The side with the shortest and most banal catchphrase will win. The nominations from elections past are;

1. It’s Time (Gough Whitlam)

2. Can-do Newman (Campbell Newman Lord Mayor Bris)

but the winner is…

“Kevin 07!” Labor will win.

Here’s my question.

I bet $100 on the US election result now; the result will become known in 12 months. The bookie can take my $100 and obtain a return of 5% (say) and have $105 risk free by the time she has (potentially) to pay up. The bookie therefore has an incentive to get me to bet as early as possible and should be willing to pay a small premium (in the form of higher odds) to get me to commit early.

My question is: do betting markets reflect this? If not, why not?

Short priced favourites have a higher probability of loosing than winning. It is good for bookies.

A hung parliament, what did he say were the odds for that?

Two observations:

Predictions about election results based on punters’ behaviour are fun but have no serious meaning. You can use all the stats. you like but they are not a real sample. If their beliefs are meant to be analogous to opinions polls, it is a very skewed at best. Know many rich punters?

Talking about odds on favourites in a two horse race is misleading. 6/4 on in a ten horse race has some meaning. 10/9 on in two horse race is virtually even.

Has anyone done rigorous research on the reliability of various markets in past elections at different stages of the electoral cycle?

There seems to be a dose of bird-cage flu affecting people’s judgment lately. Too many free drinks perhaps. I recommend a good examination of the entrails as an alternative to massaging the odds to find some wisdom.

I was listening to the bookies this week, strong backing for the ALP, $70k bets was mentioned.

One thing for sure, the track always wins.

“10/9 on in two horse race is virtually even.”

Labour @ $1.25 Libs @ $ 3.85

Does $ 3.85 for an even chance represent good value?

Simon Jackman models monte-carlo’s the election betting, and I re-create his models as a way of learning the R stats language.

He makes the point that straight MC of the odds assumes that each seat result is independent of each other, an unrealistic assumption. If one seat is swinging, then it is very likely others are too.

Difficult to model…

is luck going to affect this process? i thought the electors of oz were participating in ‘democracy’, with australian characteristics.

each is delivering his/her measured judgement on which party is offering the best lollies, and is more likely to pay off for favor received.

perhaps you believe a certain percentage of the electorate is making this judgement by flipping a coin? well, several coins at once perhaps, followed by consulting the yi jing.

The 10/9 reference was to individual seats not the odds for an ALP victory overeall. It refers to: “it is odds on favourite (the red line is above the blue line for non geeks)”. That term has a very different meaning in a larger field.

A quick response to Justin Wolfers. First, thanks for commenting.

Yes I did need to assume something akin to independence.

But no I don’t feel this is silly. Essentially, what I need to assume for my approach to be exactly valid is that the odds on betting markets can be completely explained by observable variables such as past voting patterns, census data and other observable features of electorates, candidates and parties. Clearly this assumption only holds approximately. But my feeling is that it is a reasonably good approximation for Australia.

You are incorrect to say that my approach is compromised by state or national swings. It is not they are controlled for. But what it is potentially compromised by is the variation about the means of the common factors that underpin national and state swings. My initial peek at the data says that this variation is sufficently small not to be a problem but I have yet to write this up formally.

So I stand by what I wrote and the approach taken.

The main thing that I would change in what I wrote relates to the independents and minor parties – I now think that the standard way of obtaining probabilities from beting odds overstates the probability that longshots will win. Correcting for this will change my prediction about the number of independents in the new Parliament.

The betting markets for individual seats are largely a nonsense. The opening prices are set by the bookies on the advice of consultants who are supposed to be experts. Inevitably, however, they have little idea which seats in particular are going to change hands and so they make the incumbents the favourites, often strong favourites.

Now you might think that the odds will subsequently reflect information about each seat, but the problem is hardly any money is bet on each seat. There’s 150 of ’em, and the markets are very thin, except in special cases like Bennelong. The amount bet on each seat is not not normally known but it is on Betfair, and that amount is half of two thirds of buggar all.

The individual seat betting was systematically biased to the incumbents in the last WA state election. There may be other examples.

The beeting on the overall outcome is a different matter altogether. The market isn’t thin, and the punters backing Labor don’t have to guess which seats Labor will win. They just have to be confident that Labor will at least 16 of them.

It’s like backing Tiger Woods to win a golf tournament. You can be confident that he will be birdie a large number of holes, but you don’t know which ones and you don’t have to know in order to back him to win the tournament.