UK Election

6 different firms have completed polls following last Thursday's historic debate. Doing a straight arithmetic average of the polls gives:

CON - 32.2%
LD - 31.2% 30.3%
LAB - 26.8%

However, according to UK Polling Report, assuming a uniform swing gives the following distribution of the 632 British seats (18 more are allocated to Northern Ireland - none of them are expected to go for any of the three major parties):

LAB - 261 265
CON - 242 243
LD - 116 111
Other - 13

(The BBC's calculator gives the same result for each party, +/- 3 seats.)

If the popular vote pattern stays stable (which is of course a huge 'if', given the tremendous shift due to the debate), these seat projections are likely to be too pessimistic for the Lib Dems. The reason is that when a small party's support increases, assuming that the increase is uniform disadvantages it in a first-past-the-post system. Consider the following stylized example:

Before the surge
Seat A: Lab 40, Con 30, LD 20
Seat B: Lab 40, Con 30, LD 20
Seat C: Lab 35, Con 35, LD 20
Seat D: Con 40, Lab 30, LD 20
Seat E: Con 45, LD 25, Lab 20
Total: Con 36%, Lab 33%, LD 21% (Con 2.5 seats, Lab 2.5 seats, LD 0 seats)

After an uniform surge (+10 LD, -5 Con, -5 Lab)
Seat A: Lab 35, LD 30, Con 25
Seat B: Lab 35, LD 30, Con 25
Seat C: Lab 30, Con 30, LD 30
Seat D: Con 35, LD 30, Lab 25
Seat E: Con 40, LD 35, Lab 15
Total: Con 31%, LD 31%, Lab 28% (Con 2.33 seats, Lab 2.33 seats, LD 0.33 seats)

A uniform rise in Lib Dem fortunes allows them to finish second in ridings A, B, D and E, which were Labour or Tory strongholds. This of course doesn't give the Lib Dems any seats, so all they can hope for is that the 3-way race for seat C goes their way.

However, as we saw with the Conservatives in Québec during the 2006 general election, rising fortunes may well be distributed unevenly. Suppose the Lib Dems' support doesn't change in seats B and D, but their surge doubles in seats A and E. Then we get:

After a skewed surge
Seat A: LD 40, Lab 30, Con 20
Seat B: Lab 40, Con 30, LD 20
Seat C: Lab 30, Con 30, LD 30
Seat D: Con 40, Lab 30, LD 20
Seat E: LD 45, Con 35, Lab 10
Total: Con 31%, LD 31%, Lab 28% (LD 2.33 seats, Con 1.33 seats, Lab 1.33 seats)

In reality, the Lib Dem's increase in popularity is unlikely to be nearly as uneven as in the above example: if their popular vote stays where it is, they will likely end up with the most 2nd place finishes (and the fewest wins). However, it also probably wouldn't be as bad as the standard uniform swing model predicts.

With 2 debates left, this will be an interesting election to follow!