Lib Dem got 3.5mil votes and have 71 seats, Sinn Fein have 210,000 and seven seats
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The UK is not a place where seats are distributed proportionally to votes like in countries where you they used systems like mixed-member-proportional voting.
In the UK it is a first-past the post voting system.
That means seats are allocated per constituency. In each constituency different candidates compete with each other and the one that gets the most votes wins the seat for that constituency.
This means that the candidate does not have to have the majority of the vote in that constituency just more than any other candidate.
A party could theoretically win a majority of seats despite the majority of people in he UK having voted for candidates of a different party.
This system makes it very hard for small parties to succeed.
You don’t have to work towards getting a certain percentage of the overall vote, that won’t help you much. You have to work towards getting the most votes in a number of constituencies.
A party that is really popular in a few big cities and unpopular elsewhere fares better than a party that is somewhat popular everywhere.
Sinn Fein for example have all their voters concentrated in Northern Ireland and their candidates were the most popular ones in 7 constituencies there. So they got 7 seats (which they will never sit in) and it doesn’t matter how many other votes they got or didn’t get elsewhere.
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