Political Geography and Uniform Swing

On Twitter, Guardian columnist and author Owen Jones asserted — based on a uniform swing projection — the electoral system was “rigged” against Labour.

This article examines changes in British political geography over the past two decades, to explain why this predicted majority is different.

In short

Uniform national swing: The calculation is made through a uniform national swing, assuming that every constituency changes in a consistent manner;

Regional variation: There were large changes between 1997 and 2017. The rise of the SNP as the dominant force in Scotland is one such change;

No boundary changes: There have been no boundary changes since 2010. In plurality elections, winning parties are typically efficient in gaining seats.

Uniform National Swing and Projections

The Electoral Calculus website, run by Martin Baxter, works by applying a uniform national swing to every seat, and projecting which seats would change.

This is the table from Mr Jones’ post. (Source: Electoral Calculus/Martin Baxter)

In the projection Mr Jones sought (with each party having the vote shares as in 1997), this would be calculated as:

  • Conservatives: drop by 12.8 points in every seat;
  • Labour: rise by 2.2 points in every seat.

Changes in other parties will be similarly calculated. The national swing is applied uniformly to every seat.

A major reason why the majorities differ can be seen on the projected map:

In 1997, the Scottish National Party had 22.1% of the popular vote in Scotland. In 2017, the SNP had 36.9% — taking 35 of the 56 seats.

Martin Baxter’s website does allow users to enter Scottish vote shares. Inputting the 1997 General Election results in Scotland yields a predicted Labour majority of 88.

Scotland matters. (Source: Electoral Calculus/Martin Baxter)

Voting Efficiency

How national levels of support translate into seats depends on the spread of those votes. The current House of Commons is based on First Past the Post (plurality voting): it is 650 separate contests in which the candidate with the most votes wins.

We can calculate a measure of voting efficiency: how effectively does each party translate 100,000 votes into a Commons seat?

The data was drawn from the House of Commons Library.

In general elections from 1997 to 2005, Labour were vastly more efficient than the Conservatives. The latest two elections (2015 and 2017) have shown the Conservatives to be more efficient than Labour.

Single member plurality voting systems typically reward larger parties.

A major cause of Labour vote inefficiency is: in Scotland, Labour became a smaller party. In 1997, 1.3m Scottish votes for Labour yielded the party 56 seats (out of 72). In 2017, 0.7m votes garnered just seven (of 59).

The change occurred in 2015. (Data Source: House of Commons Library)

Other causes of inefficiency are the two main parties piling up votes in seats they already win, squeezing smaller parties and reducing the number of Conservative-Labour marginal constituencies.

Labour’s seat share was broadly proportional to its vote share in 2017. (Data Source: House of Commons Library)

This was clear from Prof Sir John Curtice’s analysis of the 2015 General Election results. In 1997, about 20% of seats were Conservative-Labour marginals. In 2015, that figure fell to 13%.

I calculate it rose to 17% in 2017 — still below its value in 2005.

The definition of a Conservative-Labour marginal is given. (Source: Prof Sir John Curtice, Britain Votes 2015)

We can compute how large the electorate is, on average, by the winning party in each constituency. For 2017, there were over 3,900 more registered voters in seats which elected a Conservative MP than returned a Labour one.

There is also the issue of boundary changes. Voters move from one constituency to another. The overall House has changed size. These commissions are conducted independently, but the inevitable lag means they run behind demographic change.

There have been no boundary changes for Westminster elections in England, Wales and Northern Ireland since 2010, and none in Scotland since 2005.

The last boundary change notionally reduced Labour’s seat count by seven. (Source: House of Commons Library)

The polls have closed

The political geography of the United Kingdom is changing.

All hail the cartogram. (Source: Benjamin Henning/Geographical)

The last two elections have seen Labour translate votes into seats less efficiently than the Conservatives. Conservative constituencies generally have more people and voters than those which elected Labour MPs.

The SNP wall was eroded in 2017, but has not crumbled. A large range of scenarios would fail to induce an overall majority for either main party.

Hung parliaments continue to be a risk. Variable asymmetry within a plurality electoral system is not evidence of that system being “rigged”.

The last three elections have all been fought on the same boundaries. Labour’s relative inefficiency is entirely due to the choices and diffusion of voters.

The graphs were created using an online R console. The authors’ calculations and R snippets are available online.

House of Commons Library briefing papers (CBP 7529, CBP 7979) containing all the underlying data are also available online.

This blog looks at the use of statistics in Britain and beyond. It is written by RSS Statistical Ambassador and Chartered Statistician @anthonybmasters.

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