A friend of mine posted the following graphic to their Facebook page to show the problem with First Past the Post elections:
This shows the vote totals for three parties in the 2015 UK general election, and uses it as an example of the problems of fist-past-the-post (FPP) voting systems. In 2011, CGP Grey made a decent video explaining the problems inherent in FPP voting:
Now, the explanations in his video were effectively for national parliamentary elections, and it didn't focus on the effect of regional parties. But the 2015 British elections were heavily influenced by regional parties; the biggest shift being the sudden dominance of the SNP in Scotland.
Now, while it's true that FPP suffers from MANY MANY problems, using the above graphic is (IMO) a bit disingenuous, and let me explain why. The SNP is a regional party (as is - to some extent UKIP). SNP won no seats in England and Wales, but it also didn't front any candidates outside Scotland. Conversely, UKIP won no seats in Scotland, but although it did front some candidates in Scotland, it focused most of its efforts in England.
To put this in a different context, one might as well list Sinn Fein who won 4 seats with 0.176m votes, Plaid Cymru who won 3 seats with 0.181m votes, or the Ulster Unionists who won 2 seats with 0.115m votes. But this, too, wouldn't be an apples-to-apples comparison, since Sinn Fein, Plaid Cymru, and UUP winning of so many more seats than UKIP is less to do with FPP and more to do with regional politics and identity and the posting of candidates. Why? Because Sinn Fein, Plaid Cymru, and UUP are regional parties who have MAJOR sway in their respective non-England regions, whereas UKIP is (nominally) a national party (that has relatively little sway outside of England).
In short, comparing the dominance of non-England parties in their non-England regions against a (nominally) national party that has greater influence in England than outside of England is not really making a fair comparison, since the vote totals don't stem from the same regional elections. A far better comparison would be between UKIP, the Greens, and LibDems would have been a better comparison, since all of them are (effectively) national parties:
LibDems: 2,415,888votes, 8 seats
UKIP: 3,881,129votes, 1 seat
Greens: 1,154,562votes, 1 seat
The apparent message remains the same, and it's more consistent in the comparison.
I'm pretty sure that there are ways to normalize the impact of regional parties vs. national parties in vote counts, but I'm almost certain that straight-up vote counts isn't the way to do it. Let me attempt one possible way of normalizing the impact of regional parties on regional elections against national parties in the same constituencies.
However, let's look at comparisons within Scotland (i.e., the only place where SNP had candidates):
Looking at the election results from Scotland (which is not necessarily a perfect assessment, since I don't know if all parties ran candidates in all constituencies in Scotland):
SNP: 1.454m votes: 56 MPs
Labour: 0.707m votes: 1 MP
Conservative: 0.434m votes: 1 MP
Liberal Democrat: 0.220m votes: 1 MP
UKIP: 0.047m votes: 0 MPs
Green Party: 0.039m votes: 0 MPs
TUSC: 0.002m votes: 0 MPs
This is a better representation of the problem of FPP. Furthermore, it indicates that SNP won far more candidates than it "ought" to have, given the median voters/seat in Scotland is 69,000. If exact proportional representation were in place (and if the median value of voters/seat were consistent throughout Scotland), then the number of MPs from Scotland OUGHT to have been:
SNP: 21 MPs (-35)
Labour: 10 MPs (+9)
Conservative: 6 MPs (+5)
Liberal Democrat: 3 MPs (+2)
UKIP: 0.047m votes: 1 MP (+1)
Green Party: 1 MP (+1)
TUSC: 0.002m votes: 0 MPs (+/-0)
THIS is a better example of how FPP didn't provide proportional representation, since it's comparing election results within the region dominated by SNP. Similar examples can be run for N. Ireland and Wales (and likely England), undoubtedly showing similar results.