Tactical Voting Model

This page first posted 2 January 2005

This simple model of tactical voting assumes that some supporters of a party which is likely to come in third pace will change their vote to support their second-choice party. If enough voters do this, say 2% of the turnout, it can be enough to make a difference in marginal seats.

Below is a description of the tactical model used, plus the numerical evidence from the last four election results. We focus on the differences between the actual result and our basic prediction, and see how much of the difference can be explained by tactical factors.

Please bear in mind the following caveats:

1. Model description

We start by making our base (or raw) prediction as described in the transition model page. Then we restrict our attention to marginal seats, defined as those with a predicted majority of less than 10%, and discard any seats where nationalist or minor parties are significant. Next we group the seats according to which of the three major parties is predicted to come in third place.

The model is parameterised by three tactical swing numbers: Lib (to Lab); Lab (to Lib); and Con (to Lib). Non-standard swings, such as Lib (to Con) can be handled by making the swing negative.

In each group we adjust the third-place party and its second-choice party by the tactical swing. For instance, suppose the Lib (to Lab) tactical swing is 2%, Take the group of marginal seats where the Liberal Democrats are predicted to come in third place behind the Conservatives and Labour (in either order). We adjust the raw prediction for every seat in this group by adding 2% to Labour and subtracting 2% from the Liberal Democrats.

We note that this model produces predictions which no longer match the national average support figures. This is a problem, but for small tactical swings it is hopefully not significant.

Within each group, this is a simple additive model, but taken over all the seats it is a non-linear model.

We can use past elections to estimate these parameters and check the model's explanatory power.

2. Parameter estimation - residual swing

For a given previous election, we work with the groups of seats described in section 1 above. We look, in each group, at the average differences between the actual result and the raw-predicted result over the seats in that group. We call these differences the residual swings. If there is no tactical voting, these residual swings should be about zero.

For the last four elections, the actual residual swings and numbers of seats in each group are:

Residual SwingNumber of marginal seats
YearLIB to LABLAB to LIBCON to LIB weak LIBweak LABweak CON
20011.8%1.3%[-3.0%]107406
1997-1.0%1.7%[3.4%]129468
19922.9%6.9%[-0.3%]114104
1987-0.8%3.6%[1.6%]115196

We focus on the Lib (to Lab) residual swing as it represents the largest number of seats, and we will mostly ignore the Con (to Lib) column which is represents an insignificant number. The picture from the data is interesting but contains one surprise.

The 1997 result is strange and differs from the existing literature (see Evans, Curtice and Norris). This may be due to the transition model being used for the raw prediction, which shows no tactical voting by Liberal Democrats compared with the simple additive swing model of Evans et al which does (see section 5 below).

3. Seat skew tables

Another interesting set of data to examine is the seat skew table. This shows the difference in seats won between a prediction and the actual election result. For instance, the skew table for the 2001 election versus the raw prediction (no tactical voting adjustment) is:

Skew Table
2001 (Raw)
Actual seatsPredicted
Total
CONLABLIBRest
Predicted seatsCON1601070177
LAB240212407
LIB2044046
Rest210811
Actual Total1664135210641

The rows of the table correspond to the prediction, and the columns show the actual result. The sum of elements in each row is the total number of seats predicted to be won by each party (displayed in the right-hand column), and the sum of column elements is the actual number of seats won (shown in the bottom row). For instance the Conservative row shows a predicted total of 177 seats. Of these, 160 were actually won by the Conservatives. But 10 were won by Labour instead and 7 were won by the Lib Dems. On the other hand, the Conservatives actually won some seats that they were predicted to lose (2 Labour, 2 Lib Dems, and 2 minor parties), which are shown in the Conservative column. This gives the Conservatives 17 losses and 6 gains, resulting in a net total of 166 actual seats (shown in the Conservative column of the bottom row).

If the skew table only has diagonal entries, then the election has been predicted exactly. This is unlikely due to local, regional and other random factors. More realistically, we aim for the skew table to be symmetric. That is, the number of predicted Conservative seats won by Labour is similar to the number of predicted Labour seats won by the Conservatives, and so on.

If the skew table is not symmetric, that is consistent with the presence of tactical voting. For the 2001 table shown, Labour gains 8 more seats from the Conservatives than it loses. This suggests tactical voting from Liberal Democrat supporters to Labour. Similarly, the Lib Dems themselves gain 5 more seats than they lose which indicates tactical voting from Labour supporters to them. Both these observations are consistent with the measured residual swings of 1.8% (Lib to Lab), and 1.3% (Lab to Lib) for 2001 in section 2 above.

To quantify the success of a prediction we define its badness to be the sum of the off-diagonal elements of the skew table, plus the sum of the absolute differences between the predicted and actual seat totals for each party. For the table shown, the badness score is 51 seats (27 off-diagonal, plus 24 from the totals).

4. Testing the model

Let us perform a simple test. We take the residual swing levels for 2001 from section 2, which were 1.8% (Lib to Lab) and 1.3% (Lab to Lib), and ignore Con to Lib. Then we use those levels as the tactical swing parameters in the model described in section 1. Thus we get a revised prediction using tactical voting, and we can see the seat skew table for this prediction against the actual result.

Skew Table
2001 (+TV)
Actual seatsPredicted
Total
CONLABLIBRest
Predicted seatsCON155450164
LAB540812416
LIB4046050
Rest210811
Actual Total1664135210641

The new badness score is 32 seats (24 off-diagonal, plus 8 from the totals), compared with 51 seats for the raw prediction.

Two things stand out. Firstly, the skew table is much more symmetric. For instance, Labour gain 4 seats from the Conservatives but lose 5 other seats to them.

Secondly, the predicted totals are closer to the actual totals than the raw totals were. This means that the overall accuracy of the prediction is higher, which is the aim of the exercise.

Similar tests have been performed for earlier years and are described later in section 5.

5. Comparison with Uniform National Swing Model

We can repeat these calculations but using the original uniform national swing (UNS) model, instead of the transition model, as our raw prediction. See the transition model page for more details of both models.

The table of residual swings in marginal seats (actual versus UNS) is:

Residual SwingNumber of marginal seats
YearLIB to LABLAB to LIBCON to LIB weak LIBweak LABweak CON
20012.1%1.0%[-3.6%]105426
19974.9%3.7%[6.1%]97427
19922.3%2.9%[0.7%]108157
1987-1.1%2.0%[-0.1%]110227

These data are similar to the original table in section 2, but there are some important differences. The 1997 election is shown to have had a large tactical swing by both Labour and Liberal Democrat supporters, which is more realistic than the swing against Labour seen in section 2. Some of the other numbers are more moderate in size and vary more smoothly.

We can repeat the section 4 test for this model. We use tactical swings from the table above of Lib (to Lab) 2.1% and Lab (to Lib) 1.0%. Then the seat skew table can be calculated. As it happens, the UNS (with tactical voting) skew table has identical values to the transition model (with tactical voting). The badness score of the raw UNS model was 51 seats, which is also the same as the badness score of the raw transition model. So there is little difference between the models for the 2001 election. This makes sense, because there was not much swing between 1997 and 2001, so the models will behave similarly.

We can look at more elections to get a fuller picture.

Transition
Model
UNS
Model
 Year  Raw  +TV  Raw  +TV 
2001 51 32 51 32
1997 75 64128 60
1992100 57 88 50
1987 56 53 57 54
This table shows, for each election, the badness score of the four predictions:

Two facts leap out:

  1. In the years with small national swing (1987 and 2001), the models behave similarly, and the tactical voting adjustment improves the prediction.

  2. In the years with large national swing (1992 and 1997), the UNS model with tactical swing is the best predictor.

This leads us to re-consider whether the transition model is superior to the UNS model. When the national swing is low, the differences are small. So there is no need to worry now. But the problem will need to be investigated later.

6. Predictions

The user-defined prediction has been modified to allow input of tactical swings. These can be zero, positive (more tactical voting), or negative (unwind of tactical voting).

As at 8 April 2005, party support levels were CON 35%, LAB 37%, LIB 20%, giving a (raw) predicted Labour majority of 90. Some possible scenarios are:

Making a judgement that the most likely range for tactical swing is between 0% and 2% unwind, we can see that the effect could be around 20 seats. Different opinions can be accommodated by the user-defined prediction.

References

New Labour, New Tactical Voting? The Cause and Consequences of Tactical Voting in the 1997 British General Election. Geoffrey Evans, John Curtice and Pippa Norris. Crest working paper 64 (1998).
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