Transition Model

This page first posted 8 July 2004

The model has been modified on 28 October 2007 to become the Strong Transition Model. Click on the link for more details.

Since 8 July 2004, predictions have been based on a new model of voter movement. This new model is quite similar in effect to the simple additive Uniform National Swing model, but has two major advantages:

Under the additive model, both of these features could theoretically happen and the first often happened in practice.

The new model avoids these problems, whilst retaining the good properties of the old model, and making very similar predictions for which party will actually win each seat. Backtesting each model against the last four elections showed quite good performance from both, with the Transition Model being slightly, but not significantly, more accurate.

Below is a technical description of both models, plus the results of Backtesting, for those who may be interested.

Sections

  1. Introduction and Notation
  2. Additive Model
  3. Transition Model
  4. Comparison and Backtesting

1. Introduction and Notation

Suppose we have parties i = 1,...,n, and seats k = 1,...,N. We measure all party votes as a percentage of turnout, so support values are real numbers between zero and one.

Let us define our observables as

Our aim to estimate the unknown variable of current support for each party in each seat: There is no way we can be certain of this figure (without holding an election now), but we can estimate it in a variety of ways.

2. Additive Model

The simplest model is that of additive Uniform National Swing. It says that if a party is up 3% nationally, that it will be up 3% in each seat. In symbols,

A(i,k) = C(i,k) + P(i) - E(i).

This model, although simple, is quite robust, easy to implement, and seems to work well in practice. One problem with the model is that the prediction A(i,k) can be higher than 100% or (more commonly) negative. Whilst this may not alter who wins the seat, it is an unattractive feature.

For example, suppose Labour's support has dropped by 6% nationally, but in a particular seat their support at the last election was only 4%. Then their predicted vote in that seat will be -2% which is obvious nonsense.

3. Transition Model

The Transition Model aims to get around this problem, without moving too far from the overall behaviour of the Additive Model.

The general idea is to categorise parties into those whose support has increased and those whose support has decreased. The two groups of parties are handled separately.

Note that this is not a simple multiplicative model for the increasing parties. They only increase votes in any one seat to the extent that the declining parties have lost votes.

To express the model in symbols we need to define two quantities. They are

  1. Share(i) is the relative national share of gains made by party i relative to all the gaining parties:

    Share(i) = max{ P(i) - E(i), 0 } / Σ max{ P(j) - E(j), 0 }.

  2. SwingVoters(k) is the fraction of voters in seat k who have changed parties

    SwingVoters(k) = Σ C(j,k).max{ 1 - P(j)/E(j), 0 }.
Both the sums above are taken over all parties j = 1,...,n.

The predicted support levels are now

It is called a transition model, because we are modelling the transition of each voter from their vote at the election to their vote now. Probabilistically, we are saying that a voter from party i

This is not fully perfect, as defectors from a particular party may be more likely to vote for some parties rather than others, but it does eliminate the problems of the Additive Model.

4. Comparison and Backtesting

To test the two models, they were each run over the last four elections. In each case the model was told the full results of the previous election, plus the total votes received for each party at the new election, and asked to predict the detailed results of the new election. The results were:

Seats WrongAve Vote Error
ElectionAdditiveTransitionAdditiveTransition
200131302.9%2.8%
199750423.1%3.1%
199249512.9%3.1%
198740403.1%3.2%

The table shows the number of seats in each election which were wrongly predicted by each model, and the average major party vote share estimation error of each model.

Apart from the better performance of the Transition Model over the Additive Model in 1997, both models behave very similarly. There is no significant difference between their predictions.

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