Analysis of UK 2010 elections – Duverger’s Law

I recently wrote about Duverger’s law which explains why a voting system
like the one in the US can lead to just two parties surviving. The ‘law’
recognises that people will vote tactically and may not vote for their
favourite party if they think that they have no chance of winning.

As some comments pointed out there are countries, such as Canada and
the UK, where more than two parties exist. I know the UK better so I
thought I would have a look at the 2010 election results to see if there is
any evidence of the sort of tactical voting predicted by the theory.

In the UK there are three main parties, the Conservatives, Labour and the
Liberal Democrats. There are also some regional parties, for example, the
Scottish National Party, the Welsh equivalent which is Plaid Cymru, and a
number of parties in Northern Ireland where the main parties do not put
forward candidates.

To keep things simple I have excluded the regions from the analysis and
just looked at England.

There are 533 constituencies in England. I have looked at which of the
constituencies have the greatest percentage of the vote shared amongst
the first and second place parties. This shows the constituencies where
Duverger’s Law is strongest and there are only two parties in with a
chance of winning the seat.

At the top of the list is Westmorland & Lonsdale, which is in the far
north-west of England. In this constituency there was a total of 51,487
votes. The Conservatives won the seat with 30,896 votes and the Liberal
Democrats were second with 18,632. The first two parties had 49,528
votes between them, or 96% of all the votes cast.

At the bottom of the list is Birmingham Hall Green where there were
48,727 votes cast. The Labour Party won the seat with 16,039 votes, and
the Respect Party (a minority party that only had 11 candidates across
the country) came second with 12,230 votes. The top two parties claimed
only 58% of the vote so this seat was the furthest from the two party
dominance predicted by Duverger.

In an average constituency the top two parties share 76% of the vote.
So, on a seat by seat basis, there does tend to be quite strong dominance
by two parties. The graph below shows the percentage of the vote going to the top two parties when the seat are put in order.

After putting all the seats in order I have then looked at the results in four
quartiles. The table below shows, within each of the quartiles, who the top
two parties were and the second table shows who the winning party was.







The first table shows some very obvious differences between the parties.

A big majority of the seats where two parties dominate (where Duverger’s
law is strongest) are contests between the Conservatives and the Liberal
Democrats. The table shows that these account for 96 of the first 133
seats. In fact they almost completely dominate the top 50 with 47 of the
first 50 being Conservative/Liberal Democrat battles.

Seats where the top two parties are the Labour Party and the Liberal
Democrats show the opposite effect. They are more likely to occur when
the vote is split across more parties and the top two have a smaller share
of the vote (where Duverger’s law is weakest).

Liberal Democrat wins are highly skewed to the top of the table, where
two parties are dominant in a seat. Labour wins are more likely to happen
in seats where the votes are spread more evenly over the parties.
Conservative wins are fairly evenly spread but less likely in seats at the
bottom of the list.

Despite the fact that the Liberal Democrats formed a coalition with the
Conservatives after the election they are politically closer to the Labour

We seem to see evidence of tactical voting, as predicted by Duverger’s
law, in seats where the Conservatives and Liberal Democrats are the main
two parties. In this situation Labour voters seem to change their vote to
the Liberal Democrats as an anti-Conservative vote. When this happens
the Liberal Democrats pick up most of their wins.

Labour and Liberal Democrat voters are more likely to vote for their
preferred party, and not vote tactically, when it is a close contest between
all the parties. We see this in the seats in the bottom line of the table.

So, in conclusion, tactical voting, as predicted by Duverger, does happen but it is harder to spot in a multi-party system. People do change their vote when they think that the party they support has no chance of winning.

If that is the case then how do more than two parties survive? More than two parties are able to survive where there are geographical differences across the country. The Liberal Democrats are particularly strong in the south-west of England. The Scottish National Party and Plaid Cymru are able to survive in Scotland and Wales respectively because they have strong support there. Without these regional differences it would be likely that two parties would come to dominate. In some countries it may be religious differences rather than regional ones that allow more than two parties to remain viable.

This entry was posted in Game theory and tagged , . Bookmark the permalink.