SEATS IN PARLIAMENT DON'T MATCH VOTES CAST
Sometimes, the system works so badly that a party can "win" the election despite losing the popular vote.
MILLIONS OF VOTES ARE WASTED
In the UK, estimates suggest that as many as 12-15% of people aren't registered to vote. Of those who are registered, about 30% don't turn out on polling day. It's no surprise that levels of apathy are so high in a system where so many votes count for nothing. Research shows that turnout is higher under PR systems.
Of the people who do go out to vote, about 20% vote tactically for a party they don't support, and about 30% vote for a losing candidate in a safe seat (some of these are the same people).
Surely it's not too much to ask that people should be able to go to vote on polling day, able to vote for the party they prefer, knowing that their vote will make a difference.
THE PLAYING FIELD ISN'T LEVEL
When an election is called, we like to think that all parties have a fair crack at the whip. However, FPTP does not treat all parties equally.
In the 2015 election, the SNP got 1.5 million votes, and 56 MPs. UKIP got nearly 4 million votes, and only one MP.
We disagree with everything UKIP (and later, the Brexit Party) stands for - but this result is simply not fair.
Some people have suggested that FPTP is a good system because it keeps extreme parties, such as UKIP/the Brexit Party, out of Parliament. But despite being almost entirely unrepresented in Parliament, these far-right parties have driven the Tory party agenda, culminating in the prospect of a no-deal Brexit that very few people ever wanted.
Good politics needs a fair voting system that doesn't leave large swathes of people feeling that they don't have a voice.
FPTP MESSES UP POLITICS
Under FPTP, a party that splits risks being wiped off the political map, even if it splits into two sections which jointly remain as popular as the original party. In the 1980s, a group of centrist Labour MPs split from Labour to form the SDP; although support for the SDP and for Labour together remained high, the split kept the Conservatives in power for years.
The Brexit fiasco, which looks likely to culminate in a no-deal Brexit that hardly anybody ever wanted, is arguably attributable to the efforts of successive Conservative prime ministers to keep the Conservative Party together, and avoid the risk of the right wing of the party splitting off.
A good case can be made that under a PR system, none of this would have happened. Under PR, if some of a party's supporters shift their support to another party, the worst that will happen is that the original party will lose some of their seats at the next election. Under FPTP, a party that loses a relatively small number of supporters can risk total annihilation at the polls.
Party splits do not pose a significant threat under PR systems, because each of the resulting parties can stand in future elections and win seats in proportion to their support. Then, the two parties could form a governing coalition - perhaps with other smaller parties.
Although FPTP has delivered coalitions in two of the last three elections, many British people see coalitions as unstable and undesirable, because FPTP only results in coalition government when one party has "failed" to win a majority.
However, the vast majority of developed countries hold elections under PR, and many of them are governed by coalitions. These coalition governments have several advantages: they represent over half the electorate, they tend to make consensus-based decisions, and they do not allow a single party to implement extreme policies without wider support.
FPTP favours the Conservative Party in elections, because so many Labour votes are wasted in safe Labour seats.
In addition, FPTP breeds apathy, which leads to lower levels of voter registration and turnout. People who aren't registered to vote, or who don't vote, tend to be young, to live in rented accommodation, and to be less affluent... and these are groups that historically favour the Labour party.
FPTP also favours a right-wing agenda in other, more subtle, ways. Research shows that PR systems tend to produce societies with lower levels of inequality, higher levels of public spending, and a fairer distribution of public goods.
It's not hard to see how this comes about. Although PR systems do produce right-of-centre governments, these governments tend to be broadly-based and to operate with a degree of consensus. Because of this, they find it difficult to launch attacks on the welfare state such as we regularly see from Conservative governments in the UK.
Some people support FPTP because they look forward to the day when the Labour Party wins an overall majority in Parliament on a minority of the vote, and introduces a socialist programme.
The problem here is that with an FPTP system, the Tories will eventually win again - and will dismantle all the gains of the Labour years. Tory governments have sold off council houses built under Labour; they are dismantling the NHS; and their attacks on the welfare state have reversed Labour's reductions in child poverty and seen thousands of families relying on food banks.
Broad-based governments elected under proportional representation could introduce Labour's programme of reforms, most of which is extremely popular with the electorate. And Tory governments, when they eventually come along, would find it difficult to dismantle them.