In looking at the probabilities, I have had to deal with a well known problem: bookmaker odds typically over-estimate the likelihood of long-shot events. This is known as the long-shot bias. Typically in an election campaign, the highest odds a bookmaker offers for an unlikely winner is around $151. Ignoring the bookmaker's over-round for a moment, this equates to a 0.00662 probability of this candidate winning a seat. (Note: if I accounted for the bookmaker's over-round, the probability would be higher).
Because we have 150 seats, and if we assume each has a candidate with a similar probability (ie. 0.00662), what is the likelihood that one of these candidates gets up? In probability, the likelihood that one of k independent events occurring, given the probability α for each of those events is:
If the bookmaker odds accurately reflected the probability of an unlikely outcome (rather than being subject to the long-shot bias), we would expect to see a previously unheard of candidate from a fringe party get up in the House of Representatives in two out of every three elections. It just does not happen.
Okay, now that we have had the long digression on the long-shot bias, we can return to the probabilities from the individual seats.
Rather than tallying favourites, a more accurate way of estimating the likely party distribution of seats from the bookmaker's individual seats odds is to sum the probabilities from each seat. To manage the book-maker's long-shot bias, I have excluded each candidate with a probability of less than 10 per cent. I have normalised the remaining candidates such that the probabilities for each seat sums to one. And then for each day under analysis, I have summed the the 150 seats to get the most likely election outcome as assessed by punters on that day.
For much of the election campaign, this approach has predicted a hung parliament (albeit with the Coalition ahead); as can be seen in the next chart.
In tabular form, the data for the above chart follows. The critical figure is 76 seats, which a party needs to govern in its own right.
| Any Other | Coalition | Green | Independent | Katter | Labor | NXT | |
|---|---|---|---|---|---|---|---|
| 2016-05-12 | 0.0 | 74.468745 | 2.938078 | 1.897020 | 0.784416 | 68.599665 | 1.312077 |
| 2016-05-13 | 0.0 | 74.468745 | 2.938078 | 1.897020 | 0.784416 | 68.599665 | 1.312077 |
| 2016-05-14 | 0.0 | 74.468745 | 2.938078 | 1.897020 | 0.784416 | 68.599665 | 1.312077 |
| 2016-05-15 | 0.0 | 74.394052 | 2.938091 | 1.897028 | 0.784419 | 68.674327 | 1.312083 |
| 2016-05-16 | 0.0 | 74.649053 | 2.938203 | 1.897101 | 0.784449 | 68.551374 | 1.179819 |
| 2016-05-17 | 0.0 | 74.919578 | 2.938197 | 1.897096 | 0.784448 | 68.280865 | 1.179816 |
| 2016-05-18 | 0.0 | 74.951657 | 2.937508 | 1.991990 | 0.784264 | 68.155041 | 1.179540 |
| 2016-05-19 | 0.0 | 74.912952 | 2.945767 | 1.997590 | 0.786469 | 68.174365 | 1.182856 |
| 2016-05-20 | 0.0 | 74.779872 | 2.946194 | 1.997880 | 0.786583 | 68.306444 | 1.183028 |
| 2016-05-21 | 0.0 | 74.729046 | 2.944697 | 1.958591 | 0.786183 | 68.399056 | 1.182427 |
| 2016-05-22 | 0.0 | 74.777564 | 2.943944 | 1.958090 | 0.785982 | 68.352296 | 1.182124 |
| 2016-05-23 | 0.0 | 74.806434 | 2.943884 | 1.958050 | 0.785966 | 68.323565 | 1.182100 |
| 2016-05-24 | 0.0 | 74.984144 | 2.941717 | 1.956609 | 0.785387 | 68.150913 | 1.181230 |
| 2016-05-25 | 0.0 | 75.042677 | 2.941714 | 1.956607 | 0.785387 | 68.092386 | 1.181229 |
| 2016-05-26 | 0.0 | 75.045152 | 3.164480 | 1.956672 | 0.785413 | 67.867015 | 1.181268 |
| 2016-05-27 | 0.0 | 75.302236 | 3.270579 | 1.991936 | 0.785128 | 67.516947 | 1.133174 |
| 2016-05-28 | 0.0 | 75.370120 | 3.267782 | 1.958420 | 0.785212 | 67.485170 | 1.133296 |
| 2016-05-29 | 0.0 | 75.529159 | 3.267473 | 1.958235 | 0.785138 | 67.326807 | 1.133189 |
| 2016-05-30 | 0.0 | 75.529159 | 3.267473 | 1.958235 | 0.785138 | 67.326807 | 1.133189 |
| 2016-05-31 | 0.0 | 75.546244 | 3.262639 | 1.956012 | 0.784246 | 67.206329 | 1.244530 |
| 2016-06-01 | 0.0 | 75.723402 | 3.265761 | 1.957883 | 0.784997 | 66.998857 | 1.269100 |
| 2016-06-02 | 0.0 | 75.421845 | 3.208630 | 1.956630 | 0.924229 | 67.173650 | 1.315016 |
| 2016-06-03 | 0.0 | 75.460929 | 2.944299 | 1.939280 | 0.944448 | 67.396525 | 1.314520 |
| 2016-06-04 | 0.0 | 75.738862 | 2.879525 | 2.016399 | 0.931730 | 67.214227 | 1.219256 |
| 2016-06-05 | 0.0 | 75.738862 | 2.879525 | 2.016399 | 0.931730 | 67.214227 | 1.219256 |
| 2016-06-06 | 0.0 | 75.738862 | 2.879525 | 2.016399 | 0.931730 | 67.214227 | 1.219256 |
| 2016-06-07 | 0.0 | 75.729243 | 2.824903 | 2.042580 | 0.931514 | 67.252787 | 1.218973 |
| 2016-06-08 | 0.0 | 75.775177 | 2.825329 | 2.042888 | 0.931654 | 67.078320 | 1.346633 |
| 2016-06-09 | 0.0 | 75.891196 | 2.822167 | 2.159221 | 0.932125 | 66.959233 | 1.236057 |
| 2016-06-10 | 0.0 | 76.383699 | 2.823712 | 2.117320 | 0.932635 | 66.505900 | 1.236734 |
| 2016-06-11 | 0.0 | 76.150329 | 2.819242 | 2.269215 | 0.931159 | 66.331946 | 1.498108 |
| 2016-06-12 | 0.0 | 76.150329 | 2.819242 | 2.269215 | 0.931159 | 66.331946 | 1.498108 |
| 2016-06-13 | 0.0 | 76.135327 | 2.140131 | 2.270217 | 0.931570 | 66.991438 | 1.531318 |
| 2016-06-14 | 0.0 | 76.660399 | 2.140315 | 2.270412 | 0.931650 | 66.465775 | 1.531449 |
| 2016-06-15 | 0.0 | 77.125082 | 2.054944 | 2.272520 | 0.932515 | 66.134875 | 1.480063 |
| 2016-06-16 | 0.0 | 77.118447 | 2.052858 | 2.269558 | 0.931568 | 66.150864 | 1.476704 |
| 2016-06-17 | 0.0 | 77.127473 | 1.927562 | 2.201963 | 0.946004 | 66.290524 | 1.506474 |
| 2016-06-18 | 0.0 | 77.275149 | 1.926875 | 2.201177 | 0.945667 | 66.076621 | 1.574512 |
| 2016-06-19 | 0.0 | 77.942031 | 1.927295 | 2.201657 | 0.945873 | 65.215495 | 1.767650 |
By way of contrast, the method of tallying favourites has had the Coalition in a winning position throughout the campaign.
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