Having promised a while ago to try and explain some concepts from political science, I think it’s time to make a start. The first few posts on this are going to be about parties and party competition, partly because that’s an area I’ve been studying recently, and partly because I think it’ll be of most interest to a lot of you.

One thing we often here in discussions about politics is what type of party system a country has, specifically how many parties. For instance, the USA is generally referred to as a two-party system, Belgium is a multi-party system and the UK can be a two-party, three-party or multi-party system depending on who’s defining it and which election they’re looking at.

Wouldn’t it be good if there was a way to make a direct comparison across systems as to the relative number of parties? Luckily for us, and especially for this post – the Effective Number of Parties concept of Laakso and Taagepera. This is a relatively simple calculation that gives us the numbe rof parties in a system, calculated either in terms of their share of the vote (effective number of electoral parties, or ENEP) or share of the seats won (effective number of parliamentary parties, or ENPP).

(And now seems a good time to make this disclaimer – most concepts in political science are not universally applicable or universally accepted. Like many concepts, there are many critiques and refinements of Laakso-Taagepera, but as an introductory and explanatory tool it’s very good.)

enpThis is Laakso and Taagepera’s formula, and I can already see the furrowed brows of many of you as you try and work out what it means. What it means is that the effective number of parties in a system is calculated by taking the fraction of votes or seats won by each party, adding up the sum of the squares of those numbers and dividing 1 by that result to give the result. A couple of examples might make it clearer:

Suppose there are two parties, each getting 50% of the votes/seats. That means we have two shares of 0.5 and 0.5. 0.5 squared equals 0.25, so the total of the squares is 0.25+0.25=0.5. 1 divided by 0.5 is 2, and we thus have a two party system. The same calculation works for any system where the vote is divided equally between the parties. Four parties each with 25% will give an ENP of 4, 10 each with 10% will give an ENP of 10 and so on.

So far, so obvious and so unlikely to occur in reality. What happens when we apply it to the real world? Let’s take the 2010 general election result. In terms of votes, and only using parties who got 1% of the vote or more, we have the Conservatives on 36.1%, Labour on 29%, Lib Dems on 23%, UKIP on 3.1%, BNP on 1.9%, SNP on 1.7% and Greens at 1%. Adding the squares of all those up and dividing it into 1 gives us an ENEP of 3.72. In terms of seats, the Tories got 47.1%, Labour 39.7%, Lib Dems 8.8% and DUP 1.2% and this results in an ENPP of 2.58. (I cut off at 1% because shares below that make very little difference to the final result)

What does all this mean? Does it mean that we can now say Britain has an almost-four-party-system electorally but only a two-and-a-half-party-system in Parliament? Much as it might be tempting to use the figures in those way, that would be a simplistic view. The main use of ENEP and ENPP figures is a comparative one, allowing us to see trends across time and across countries. Luckily, I don’t now have to go through and do the ENP calculations for every British election, as here’s one someone else made earlier, and we can also find comparative ENEP and ENPP figures for other European countries.

The key point about ENEP and ENPP figures is that while they might make for vaguely interesting numbers when calculated for one election, their real use is in making those comparisons over time or between countries. For instance, the British series shows us that the trend in Parliamentary elections is for both to increase, while the European data shows that while the numbers are increasing, we’re still below the European average. However, what they also show is that ENEP and ENPP tend to be closer in other countries than they are in the UK (and France), which helps illustrate the different effects of proportional and majoritarian voting systems.

Party systems and the way parties compete in them is a very complicated field, but I hope this has given a bit of an introduction to one part of it. As I said, there are other ways to examine and calculate the number of parties (as well as amendments to Laakso-Taagepera) but the original calculation of ENP is an easy one to explain and create some useful initial data with. It’s also a good way of showing trends across time and letting us see if there has been a long-term change in voting patterns. One interesting use of ENP data in a UK context has been to compare UK-wide figures with voting patterns in Scotland, Wales and Northern Ireland, especially comparing Westminster voting patterns to voting for the devolved governments.

If you want to read more on this, I’d recommend Alistair Clark’s Political Parties in the UK or (if you can find it) Paul Webb’s The Modern British Party System (Clark was published in 2012 so is more up to date, Webb is older but has more theoretical background).