No, that is not what the House of Commons would look like under proportional representation

Following the 2015 United Kingdom election, a large number of news sites published projections of the result under what was described as proportional representation. Electoral reform is a frequently discussed topic in the United Kingdom (for more information on the issue, you can read my previous post on the topic), and it is usually discussed around election time. Personally, I think it is good to see discussion of electoral reform; the sort of electoral system used in the United Kingdom has a significant impact on the nation's governance.

Dec 15 in our advent calendar: Britain's 2015 election, if votes counted proportionally https://t.co/ykNSakWBcp pic.twitter.com/SwhLKRSrJT

— The Economist (@TheEconomist) December 15, 2015

However, there is an issue with these charts. The issue is that, as far as I can tell, they do not accurately represent any serious proposals made for proportional representation in the United Kingdom. These articles instead represent a national party list system as proportional representation. While this is strictly true, a national list system has a number of flaws, and no one in the electoral reform movement has supported it.

What is national list, and why is it not realistic in the UK?

National list is a very basic electoral system. It's simply the application of a party-list proportional representation system, except there is only one district, which includes the entire electorate. It can be open or closed list, although the large magnitude means that it can be hard to use open list. It's also fairly normal to have a threshold. It is used, in its purest form, in the Netherlands (with semi-open list, and a threshold of 0.67%), Fiji (open list, with a 5% threshold) and Israel (with closed list, and a threshold of 3.25%). Sweden and Denmark use an electoral system that uses districts with more open lists, and then the seats are allocated on a nationwide basis, thus making it effectively national list.

Such systems are rarely used in large countries like the United Kingdom, though. The issue with them is that it can lead to a weak connection between voters and electors, as there is no individual accountability. It would be organisationally difficult to use open lists to allocate all 650 seats, which would mean that parties would have large control over who was elected. 

The other issue with this system is that it would lead to fragmentation. One can simply look at recent elections in the Netherlands and Israel to see that proportionality, unrestricted, can lead to massive fragmentation. Certainly, thresholds could be introduced. But that would mean the end of regional parties and local independents. 

It would mean that Plaid Cymru or the SNP, for example, would not be able to win seats in many cases despite strong support in their areas. If a 5% threshold were used at this election (not an uncommon figure), the Conservatives would have 266 seats, Labour 219, UKIP 91, and the Liberal Democrats would have 56 (excluding Northern Ireland, although none of the Northern Irish parties would have any seats under this system). The SNP would have zero seats, which would surely have made the Scottish Nationalists unhappy, since they would be represented 100% by unionist parties (for more information on this, see my previous post about thresholds). This is less of an issue in smaller countries, where there is less regionalism. 

Even if a mixed-member system was used along with national lists, there would still be some of these problems. Most mixed-member systems use closed lists, so there would still be the issue of a lack of accountability. If the New Zealand-style system of allowing parties which win constituency seats to enter the list allocation was adopted, the threshold issue could be averted somewhat, but it would still be a flawed system.

What sort of systems have actually been proposed?

In its 2015 report, the Electoral Reform Society (a pro-proportional representation pressure group) published projections for the result under a variety of electoral systems.

Results exclude Northern Ireland

The 'List PR' system here is a districted system. While the Electoral Reform Society does not exactly show the districts, it appears that they are using European Parliament constituencies. This would lead to a very high average magnitude of 63. You could potentially use smaller constituencies, or use a mixed-member system (although they are large constituencies compared to Scottish and Welsh list tier districts), but this is a more realistic party list system. 

The Alternative Vote projection is self-explanatory, though I personally think the campaign would have changed if it had been in use, and the results would have been more different than that purely technical perspective, but that is obviously quite hard to model.

The other proposal is the single transferable vote. While I don't know what sort of district size would be used, this is a more likely proposal than national list; indeed, it appears to be the preferred proportional representation system of the Electoral Reform Society, despite its relatively rare use in the United Kingdom (outside Northern Ireland, only in Scottish local government). I'm not sure what the methodology is, or whether preferences 

Other proposals for electoral reform include AV+, the proposal of the Jenkins Commission into the electoral system convened (and then promptly ignored) by the Blair government. This system is similar to a mixed-member proportional system, except that there would be relatively few list seats in each district (each one of the 80 districts would only elect one or two list members), the district vote would be the alternative vote/preferential voting instead of single-member plurality, and an open list system would be used in the districts. The existence of this system was noted by the ERS, but they did not project it "on the basis that it is not used in any country and is no longer being advocated in any meaningful way".

While it is important that issues like electoral reform are discussed in the United Kingdom, it is equally important that what is presented as alternatives to single-member plurality are serious proposals. A national list system is not a serious proposal, and the projections from the ERS offer more relevant statistics of what will happen under proportional representation.