Measuring the strength of local parties

The Electoral Commission has reported that the Hersham Village Society received more than £200,000 left to it in a local resident’s will. Various other residents’ associations in Elmbridge must be envious of such largesse.

The Electoral Commission’s requirement that local parties are formally registered may have contributed towards their growth – although in councils such as Elmbridge, neighbouring Epsom and Ewell and elsewhere, some residents’ associations are of long-standing. 

This expression of local democracy is regarded by some as essential in mitigating the influence of national party politics. For the same reasons, the survival of Independent councillors is applauded.

Measuring the extent to which local government is diverse in its representation can be approached in various ways. One method is to measure the effective number of parties.  This can be applied by referencing either party vote shares at a given election (the notation used is Nv) or each party’s overall strength in the council chamber (Ns). 

Any measure of a party system should give more emphasis to larger parties at the expense of smaller ones. Ten parties won representation to the House of Commons in 2019 but it would be absurd to say we have a 10-party system since six of them won fewer than 10 seats.

Instead, the calculation for the effective number of parties weights each party’s proportion, in this case of seats, and derives the value of 2.4 ‘effective’ parties (see footnote, below).

For local authorities such as Barking and Dagenham in east London, where only Labour councillors were elected in 2018, Ns is equal to one.

In a hypothetical case where a council has four parties each with an equal number of councillors, Ns is four.

According to our records of council compositions, the current average value of Ns across all authorities in England and Wales is 2.2 – very close to that of the House of Commons – and lies in the range 1.9 to 2.3. This is unsurprising given our voting system is known to favour two parties.

Of course, this does not mean that councils will necessarily mirror representation in the national Parliament. Both Cheltenham and Kingston upon Thames have Ns values of 1.5 but there are no Labour councillors on either council. Liverpool and Gateshead also have a 1.5 party system but neither elects any Conservatives.

The ebb and flow of support for the Liberal Democrats, the third largest party in local government, largely explains fluctuations in the value for Ns. At the turn of the century, Ns averaged 2.3. But after the party joined David Cameron’s national coalition government and started to lose council seats, the number fell to 1.9.

There are some councils that are consistently higher than the national average. In Wales, where Plaid Cymru has pockets of strength and Independents continue, there are three and occasionally some four-party systems. 

Currently, Denbighshire (3.9), Conwy (3.8) and Vale of Glamorgan (3.5) have high values for Ns and like many such authorities are administered by coalitions.  

Conwy can lay claim to be the most diverse council. Between 2006-2007, its peak value reached 4.6, with four parties holding council seats alongside 16 Independents.

In England, Redcar and Cleveland currently has the highest value (3.8) and is consistently ranked among the largest party systems. Its 59-member council has significant representation from the three principal parties but the largest category comprises a range of Independents. 

But party systems can be dynamic, and councils may experience changes in complexity.  Swale, for example, now ranks among the most diverse party systems (3.5). But for the decade prior to the most recent elections, the effective number of parties had been two or below when the Conservatives ran the council with either Independents or Labour forming the principal opposition. 

That stability ended in 2019 when the Conservatives lost 16 seats, to a combination of Labour, the Liberal Democrats and local Independents.

Calculation of the number of effective parties 

Consider three possible seat distributions in a 100-member council.

 ABCDE
Example 15142511
Example 2512611111
Example 3403711111

At first glance we might regard each of the examples to be two-party systems since the two largest parties, A and B, have more than three-quarters of seats. 

An alternative view is that this label does not apply to examples two and three and that these are better described as ‘two and a half’ party systems.

These descriptions are somewhat arbitrary.

Instead, for Ns we allow each party’s seat shares to determine their own weights. In the first example, party A has 51 seats or a fractional share of 0.51, this being a 100-member council. In the same way, the remaining parties have fractional shares of 0.42, 0.5, 0.1 and 0.1 respectively.

The next step is to take the square of each of these values which weights the large parties relative to the smaller ones.

So, for party A in the first example, 0.51 multiplied by 0.51 is 0.26. The remaining values are: party B – 0.17; party C – 0.0025; while parties D and E are just 0.0001. 

The final step is to take the sum of these values (0.26, 0.17, 0.0025, 0.0001, 0.0001) and divide them into one.

As a result of this calculation the Ns value for the first example is 2.3, for the second 2.8 and for the third, 3.1.

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