## Can we reconcile the betting odds from the headline race and the marginals markets?

Several friends and journalists have been asking me lately about the fact thatÂ the headline betting odds have Labor a 70% chance to win, while the seat-by-seat markets have LaborÂ as favourite inÂ 77 out of 150 seatsÂ (see Simon Jackman’s site for current and past odds). As I see it, there are four possible explanations for this.

1. There are quite a few Labor seats where the odds put them a 40-49% chance of winning, and fewer such Coalition seats. Taking this into account, Simon has also been summing the probabilities to come up with an ALP expected seat count. Today, he says, “ALP Expected Seat Count: 79.7 out of 150 seats.Â … Computed as the sum of the 3-agency-average seat-by-seat ALP win probabilities.” So this answer gets us from a 2-seat majority to a 4-seat majority. That satisfies some people (eg. Tim Colebatch and John Quiggin), but not everyone I speak to is persuaded that a 70% chance of winning is consistent with a 4-seat margin.
2. The marginal seat markets are smart money, while the headline race is dumb money. So the headline odds are too optimistic for Rudd, and the marginals markets are right.
3. The headline odds are based on two factors: certainty and margin.* To understand this theory, take the analogy of a flashy sporting team and a dependable sporting team. If betting on the flashy team, you might be uncertain about whether they’ll win, but you might figure that if they win, it will be by a big margin. With the dependable team, you might be quite certain that they’ll win, but feel that it’s unlikely that they’ll win by a huge margin. So while expected margin and expected winner will typically track one another, they needn’t always do so. You might be quite confident that Rudd will form government, without necessarily expecting a landslide.
4. There’s no paradox. A 70/30 race is a pretty tight one. Unlike the pollsÂ (most of which imply that the chance of a Howard win is less than 1/10,000), the betting markets still say that this is a close race.

Of these theories, #1 is really just another way of expressing the data, and #2 doesn’t square with the literature (both theoretical and empirical) on prediction market efficiency. I’m inclined to prefer #4, though I do rather like #3.

* I owe John Quiggin for pointing this out to Justin and I when he read a pre-publication draft of our last election betting paper.

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### 24 Responses to Can we reconcile the betting odds from the headline race and the marginals markets?

1. Doug says:

the other issue is timing – the real test will be in the couple of days immediately before the election – the Jackman figures on individual seats have been slowly, consistently moving towards an increased ALP majority

2. Sinclair Davidson says:

I’m trying to understand why a four seat margin isn’t a win. The betting market is saying that there is a 70% chance the ALP will provide the prime minister. Once the ALP has a (working) majority of seats that will occur. A hung parliament with the support of independents can deliver that outcome.

I think people don’t understand what the betting market is saying; it is not saying the ALP will have a 70% share of the vote, or a 70% share of the seats.

3. Andrew Leigh says:

Sinc, no-one’s arguing that a four seat margin isnâ€™t a win. People I’ve spoken to just think that if Labor is paying \$3.20, then the expected margin ought to be more than 4 seats. But I agree with your general assessment – it could be that many people have an imperfect understanding of probabilities.

4. Vee says:

I just want to thank you for that kick back into reality.

I had started to fall for the big win propaganda. Whilst I am no psephologist or economist, my early predictions were 74 to 77 seats for the ALP or thereabouts. Most recently I had kicked the upper limit up to 87-90 based on the polls.

Time to wind it back a bit I think.

5. Steve Edney says:

Andrew, you make no mention of Simon Jackson’s simulation of outcomes, basically he seems to be running a monte carlo based on the individual seats.
http://jackman.stanford.edu/oz/Aggregate2007/bettingmarkets/currentSeatHistogram.pdf

This comes out with a 83% chance of ALP win. ie more than the headline win is showing.

6. Enemy Combatant says:

“People Iâ€™ve spoken to just think that if Labor is paying \$3.20, then the expected margin ought to be more than 4 seats.”

Close…. but no cigar.

“Unlike the polls (most of which imply that the chance of a Howard win is less than 1/10,000), the betting markets still say that this is a close race.”

“1/10,000”. Which polls so imply, Andrew? Do you think “it could be that many people have an imperfect understanding of probabilities.”?

7. Steve Edney says:

Further to my previous comment having now simulated the election from the individual seat with 100,000 paths myself, I firstly agree with Simons result that assuming independence the individual seat probabilities imply around 83% ALP victory if you assume they are independent.

As you start increasing the correlation between individual seat results the ALP victory probability decreases – 70% ALP victory assumes about a 10% correlation between seat results. as you go to 100% correlation you start coming out to the raw win/loss seat analysis. and the ALP victory comes down to around 53%.

Basically I think that the two are mutually consistent, mostly for the reasons you outline in 1 under the assumption that the results are somewhat correlated.

8. Much election commentary operates with a fairly arbitrary list of ‘key marginals’ where the election will be decided. In some of these seats punters seem to be assuming that pork-barrel and personal votes will help sitting Coalition MPs defy a swing. This is the folk wisdom of 1998. Perhaps those who bet on individual seats have a different model from those who bet on the overall result. Punters are very selective in the ‘fairly safe’ seats they pay attention to.

9. Lukas says:

Along similar lines to Geoff Robinson, possibility 5 is that punters are taking a long time to understand the implications of Labor’s huge, sustained lead in the polls, paying more attention to ‘local’ factors in individual seat markets than is warranted, underplaying the national swing and falling for the same mistake as the national press of having believed that the PM has a rabbit in his hat which he can pull out to win the election.

Under this scenario, eventually (in the last days before the election) markets for an increasing number of seats will show a Labor win as the polls continue to show Labor leading. The betting markets on the last day will probably be a reasonbly good predictor of outcomes in those seats and of the overall outcome.

But it is not long ago that the markets for a majority of seats were showing a Coalition victory, despite Labor’s strong lead in the polls and despite the market for the overall outcome predicting a Labor victory (though not as strongly as now). While I find the simulation outcomes reported by Steve Edney interesting, it is pretty difficult for me to see how you can reconcile the markets of the time showing Labor winning the election but not winning a majority of seats.

If Labor wins, the betting markets for individual seats 2-3 months out from the election will turn out to be a poor predictor of the election – much poorer than the polls – even though the betting markets are designed to predict election outcomes while the polls are not!

We will see in 10 days time.

10. Steve Edney says:

is pretty difficult for me to see how you can reconcile the markets of the time showing Labor winning the election but not winning a majority of seats.

The important point is that you can expect to win a majority of seats even if you are “expected” to lose a majority on an individual basis. Turning probabilities into a win/loss outcome loses most of your information and is very misleading.

Consider this scenario. An election of 3 seats, one is giving odds of 90% ALP victory, the other two 49% ALP victory. On a straight win loss you get coalition victory 2 out of three seats.

However if you think about what is going to happen, ALP has one seat essentially won at 90%. They then only need 1 more of the two seats which are almost 50/50 bets. Just under 75% of the time they will win at least one of those two and win the election.

Their chance of ALP winning this 3 seat hypothetical election is actually 69%.

A better way to compare the individual markets and the overall is by summing the probabilities (ie getting an expected number of seats) gives you a better estimate than looking at the individual seats on a win/loss- in this case ALP gets 1.88 of 3 seats available.

11. Lukas says:

I see your logic Steve, but are you reallly saying that, a few weeks ago, when the markets were showing Labor as underdogs in the majority of seats, the sum of their individual win probabilities would have given Labor a better than even chance of winning?

And would the sum of their win probabilities be predicting a comprehensive Labor victory, which is (in my humble opinion) the scenario we are looking at for 24 Nov? Of course, the relevance or otherwise of this last question will only be known on election night.

12. Andrew Leigh says:

EC, the answer to your question comes from combining this with this.

13. Bring Back CL's blog says:

andrew,

people who bet on the national vote have the polls to assist them.

People who vote on individual seats do not. The parties do NOT poll individual seats but rather poll various ‘marginals’ to see how things are going.

I suspect ssome individual seat polling is going on in both Wentworth and Bennelong but I doubt either party is paying for it.

If the polls stay as they are and have been all year then the individual seat markets will change as time closes in.

14. Sinclair Davidson says:

Picking up on Homer’s point; the question is whether the individual seat markets are more or less informatioally efficient than the overall market. This really is an empirical question, because I can think of reasons both for and against.

The question of which leads the other, polls or betting is unclear this time around. The polls have shown the ALP to be clear winners all year, while the betting market osillated a bit (not much). Late time round, however, the polls got it wrong while the betting market got it right. Despite the naysayers, I think the markets are more likely to be correct than the polls.

15. Steve Edney says:

Lukas,

Can’t find the historic situation, but certainly if you look at the current market there are 26 seats with probabilities of ALP win in the range 0.3-0.7
7 are greater than 0.5 ALP win and 19 are here shows that a 53% poll result based on say 500 people polled represents a 91% chance of winning.

Based on Andrew’s table pretty much all those seats in the range 0.3 to 0.7 probability should be polling at or very close to 50%. Looked at in this way you would think you can split them evenly and rather a 7-19 split you get a 13 – 13 split.

16. Steve Edney says:

Wow, I really mangled that comment somehow trying to use html.

Basically I was trying to say that if you look at the odds you get 7 marginal ALP leaning and 19 lib leaning marginals (between 0.3- 0.7) if you calculate the expected outcome it is a lot close to 13-13 than a simple win/loss will suggests.

The other thing I think there is confusion between what a 53% probability represents and a 53% poll result. A 53% poll result 500 respondents is equivalent to a 91% probability, according to Andrews table (his second link in comment above).

All these seats with odds in the 0.3-0.7 range should be polling 49-51%. which we would normally regard as being pretty much going either way.

17. charles says:

The single seat market is thin. To get the wisdom of a crowd you first need a crowd.

18. David says:

It is quite an interesting topic to consider. There is however a whole body of literature by Kahnerman etc, which explores how and why humans systematically behave in ways which do not conform to conventional notions of economic rationality. Perhaps the people who bet on local electoral results do in fact systematically form different perceptions than those who chose to bet on national results. There is lots of scope for speculation.

Perhaps for example, a natural experiment of sorts exists. Given that there are far more national polls published than local ones and given that the polls are suspected of driving the betting odds, could it be market is getting better information on the national result than is available for any one local electorate. If the final result falls in line with the national market then a win for the â€˜Pollsâ€™ if more in line with the local market then a win for the those who advocate interpreting the betting odds.

19. John Quiggin says:

I think you should qualify the statement about the poll odds. They apply only if you assume
(i) No change between now and the election
(ii) Win on 2PP = win in the election
(iii) No non-sampling error

(In fact, following the link in your response to EC, I see you have most of these points there).

20. Rocket says:

I think that the real story is that most people bet on the overall result taking the polls into account – this is a big pool of money and most people back Labor. The individual seats are much smaller pools of money, and susceptible to candidates, who might be worried about losing their seats, backing themselves with a few thousand dollars and skewing the odds. (Which would mean if they lost they would also be losing money to any opponents who bet against them!)

21. Andrew Leigh says:

John, they’re certainly important points. I think that (i) applies for any forecasting tool, and we wrote a bit about (iii) in our Economic Record piece. But one I didn’t twig to until I read this piece by Simon Jackman is that Labor systematically have to get 51-52% of the 2pp vote to get over the line. If we move the breakpoint up a bit, a 55% Newspoll might actually suggest that the chances of a Howard victory are as high as 1 in 1000 or (gasp!) 1 in 100. Nonetheless, I’ll stand by the substantive point: the betting markets say this is a much closer race than do the polls.

David, Justin and I comparedÂ marginal seat polling and betting in our papers on the 2001 and 2004 elections – both available here if you’re interested.

22. Peter Brent says:

First, a niggling point about terminology. Labor winning 77 seats would generally be called a 4 seat majority – 77 to Labor, 73 to everyone else. 79 seats is an 8 seat majority. This is what we mean by Howard enjoying a 24 seat majority currently.

More substantially: I think the punters are having trouble envisioning Labor taking seats they have never won before, or not for a long time. They favour Labor in Dobell, for example, because it was recently held by Labor, but not in Bennelong, because it never has been. I actually think their chances are about the same in each.

Demographics have changed a bloody lot in the 14 and a half years since Labor last got a winning vote. In fact, they look set to get their biggest vote since about 1943. We should expect the unexpected.

Every “big” change of government includes some “ohmygod ididn’t expect that seat to fall” results. I’m sure the odds on, say, Hughes would have been long for a Liberal win in 1996. Today it is as Liberal as can be and certain to remain so this year.

Corangamite is a seat whose Labor odds are under-valued, simply in my opinion, because Labor hasn’t held it since the 1930s.

For this reason I’ve put dosh on it (and Wentworth).

23. Chris Mayer says:

As charles said, *surely* the seat-by-seat market is just too thin for a valid comparison againt the overall market.

24. EconoMan says:

So much restraint you show Peter Brent? I just know you want to say the betting markets are just sheep following poll results… But I completely agree with both your substantial points: there’ll be ‘ohmygod’ results if there’s a 54-46 TPP; and your analysis of ‘haven’t recently held’ seats.

I also agree that thin markets is an issue. Or to be more accurate, it was last time I checked betfair. Only bennelong had any significant money matched, and still 1/10th of the National market. I’m sure they’re thicker now, but thick enough to satisfy the ‘marginal rational voter’ assumption?

But the key here IMO is what Jackman has well and truly covered. The Monte Carlo probability of 76+ is still higher than the national market 3-agency average. Has been equal or above for a while.

Personally, I believe both national and individual seat markets are slightly conservative: Labor should be >90%, and closer in seats like Bennelong, Boothby, Sturt (though I think Pyne might hold), Leichardt, Ryan, some Vic seats, maybe even Greenway?