Estimates for Expected Number of Seats

Update Aug. 15: I have refined things (see underlined parts below), but this is still an approximate method.

As you can see, the projected numbers of seats, which are now provided in the right-hand column, now have one digit after the decimal point, and no longer match the numbers of seats projected ahead in the left-hand column. This is because I have decided to provide approximate expected numbers of seats, which should be less subject to "artificial" factors such as a party being projected barely ahead in a disproportionate number of seats. This change should make variations in the projection less puzzling: you won't see a party suddenly gain, say, 12 seats when it goes up by a point, but only 2 seats when it goes up by another point.

How do I estimate expected seat counts, given that as I've said before, I don't want to get into doing simulations? Based on my estimates about polling and seat model inaccuracy, I've determined that the standard error in the gap between the top two parties is about 9-10%, for an election taking place around the time of the last poll. Then I simply look at how far apart the top two parties are, and assign them probabilities of winning the seat based on the normal distribution. For example, if party A is 9-10% (1 standard deviation) ahead of party B, then party A would be given an 84% chance of winning, while party B would be given a 16% chance of winning.

More specifically, I first calculate an (usually too low) estimate for the third party's chance of winning by multiplying the probability that it gets more votes than the first party with the probability that it gets more votes than the second party. (This is usually too low because the two events are usually positively correlated.) Then I apportion the remaining probability of winning between the top two parties proportionally to their probability of finishing ahead of the other.

This is not an ideal method because it ignores underestimates third and ignores fourth parties. For most seats, this is not a problem, as only one or two parties have a significant chance of winning. However, if a party is involved in disproportionately many three- or four-way races as the party ranked third or fourth, that party will be slightly underestimated.