I use a simple system for my analysis, allocating the number of seats in Parliament on the basis of the share of the vote received. Of course, any proportional representation system cannot replicate purely the percentage figures but they tend to come close. Some systems, e.g. that of Germany, will not allow any party polling less than 5% of the total vote, to have a seat in parliament. However, I assume such a bar is not in place.
This election has seen a rise in support for both the Conservatives, who received more votes than they have done at any election since 1983, and for Labour, who saw a 10% rise in the number of people voting for them. The thing is, especially for the Conservatives, many of these votes are simply 'stacking up' in seats that they already hold safely, they are not winning additional seats, simply raising the majorities of individual MPs. Thus, whilst they are the party most opposed to proportional representation the Conservatives might actually benefit from it as they are, in many cases, firming up their hold on some constituencies especially with the departure of UKIP. Perhaps the party with the greatest stacking this time, however, are the Greens, with a single MP, but now with over a 14,000 majority. Many Green votes are not translating into seats.
While noting the stacking up, this election has also seen some very narrow majorities, the most extreme being in North-East Fife where the SNP won by just 2 votes. Such narrow margins are difficult to translate into proportional representation as simply 1 person voting differently could have changed the situation. In Kensington, Perth & North Perthshire, Newcastle-under-Lyme, Southampton Itchen, Richmond, Crewe & Nantwich, the majorities were fewer than 50 votes. In another three seats, including two in Glasgow, the winning candidate has a majority of fewer than 100 votes.
In the 2015 election there was a lot of talk about the 'shy Tory' people willing to vote for the Conservatives but unwilling to say so to people asking their opinion. This time there is talk of the 'shy Labour supporter'. In fact they are largely shy because they were under-reported by the predominantly Conservative media. Labour was having big rallies and the increase of turnout by 3% to 69% seems largely to have been young people who have not voted before, whether too young in the past or were not sufficiently engaged. There had been an assumption that UKIP supporters would simply become Conservative supporters, but it appears, especially in northern England that instead they have turned to Labour, which highlights the fact that judging the political scene in the post-referendum era and especially in the time of populist politics, on old assumptions is flawed.
Of course, if proportional representation had been before this election then the political scene would have been very different anyway which may have meant that an election would not have been called at this time. Analysis in 2015 showed the following profile for the House of Commons if proportional representation had been in place. The actual returns are in square brackets:
2015: 650 seats [Conservative Government]
- Conservatives: (36.9%); 240 seats 
- Labour (30.4%); 198 seats 
- UKIP (12.6%); 82 seats 
- Liberal Democrats (7.8%); 51 seats 
- SNP (4.7%); 31 seats 
- Green (3.8%); 25 seats 
- Plaid Cymru (0.6%); 4 seats 
- DUP (0.6%); 6 seats 
- Sinn Fein (0.6%); 5 seats 
- UUP (0.4%); 4 seats 
- SDLP (0.3%); 2 seats 
- Alliance (0.2%); 1 seat 
2017: 650 Seats [Conservative with DUP Confidence & Supply Support]
- Conservatives (42.45%): 279 seats 
- Labour (39.99%); 263 seats 
- Liberal Democrats (7.37%); 49 seats 
- SNP (3.04%); 21 seats 
- UKIP (1.84%); 13 seats 
- Green (1.63%); 12 seats 
- Plaid Cymru (0.51%); 3 seats 
- Others (0.52%); 3 seats 
- DUP (0.91%); 6 seats 
- Sinn Fein (0.74%); 5 seats 
- Independent Unionist (0.45%); 3 seats 
- SDLP (0.3%); 2 seats 
- UUP (0.26%); 2 seats 
The portrayal of Labour as so extreme and its leader Jeremy Corbyn as some revolutionary in much of the media, has overshadowed what was actually going on. The Conservatives did very well, not having polled as well as this since 1983. Labour did badly, only really as well as when Gordon Brown lost power in 2010. However, because of the incessant portrayal of Labour under Corbyn as useless, the right-wing media have made the party's modest gains appear far more significant than was in fact the case. Theresa May's arrogance in assuming she could do better than her predecessor compounded by an aloof attitude which was even greater than the snobbishness of Cameron, did her party no favours among floating voters. However, it went down very well with people who were already Conservative supporters as seen with increased majorities in safe Conservative seats. May largely talking to Conservatives rather than floating voters probably gave her a distorted view of what was happening. The assumption that almost all former UKIP voters would automatically turn to the Conservatives was also flawed.
What is apparent is that 2017 saw a polarisation back to the 2-party system characteristic of the 1940s-90s. However, there are geographical shifts with Labour picking up seats in a number of unexpected places such as Canterbury, perhaps finally benefiting from the mobilisation of university student votes, much vaunted but little seen in 2015. With so many universities in the UK and more towns having two, they may create pockets of Labour and even, in time, Green support among Conservative 'seas' of rural Britain. The Conservative return to Scotland, strongly in the South and East, in part compensated them for Labour's random gains and without which they might have even struggled to form a coalition.
Of course, Labour's chance of ever having a majority government ever again are quickly fading as boundary changes will lose them over 30 seats as parliament shrinks to 600 members. They are likely to find that they again receive fewer seats than their share of the vote as their support will stack up in small urban constituencies to a greater extent than has been the case recently.
In this alternative, there still would have been polarisation, but to a different pattern. The Liberal Democrats under proportional representation would have fallen rather than risen in the number of seats yet would have been returned to being the third party with the eclipse of UKIP. Now, if UKIP had been in a coalition with the Conservatives since 2015 they may not have been swept away; indeed there probably would have been no need for an election for Theresa May to continue with the Brexit process.
Other small parties have seen a decline, notably the Greens and Plaid Cymru. However, if the Greens had had 25 MPs in 2015 rather than 1, then people might feel a vote for them was not 'wasted' and so the fall in support might have been less in 2017 than has been the case in our system.
Labour really no longer has any need for proportional representation as its number of seats is proportionate now to the amount of the electorate supporting it. The same can be said for Plaid Cymru. The Conservatives still receive more than their 'fair' proportion of seats, getting 48.4% of the available seats. The same applies to the SNP, who got 5.4% of the seats compared to 3.04% of the votes this time even though this is a fall from 8.6% of sets in 2015 from just 4.7% of the vote. Thus, parties that win or when they are winning, large rural seats, tended to be over-represented.
Analysis that I have done on elections down the years if there had been proportional representation is that a Labour-Liberal coalition would have been the predominant form of government. In fact the more common coalitions of the 21st century under the first-past-the-post have been Conservative dominated ones as in the early to mid-20th century.
With proportional representation another Labour-Liberal Democrat coalition with probably the SNP and Greens adhering too, is likely to have appeared in 2017 with the departure of the Conservative-UKIP coalition. However, in that scenario I imagine the 'Brexit Coalition' would have continued under Theresa May and having no election until 2020.
What is interesting is that for Labour is that its vote is increasingly in line with the number of seats it receives, in contrast to the situation in the 1990s. The Liberal Democrats and the Greens, previously to a far greater extent UKIP too, are heavily under-represented for the amount of support they gain. The big winners from the first-past-the-post system are the Conservatives and SNP who effectively need a smaller number of votes to win a seat than the other parties do.