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.