Let's be clear: a PR voting system would not sort out all our problems overnight. Problems like climate change and social inequality have deep and complex roots, and need concerted action on many fronts. Nevertheless, we believe that a PR voting system would facilitate solutions to many of the problems we face as a society. Here's why. The first two points relate to people having more of a stake in the electoral process:
EVERYONE COULD VOTE FOR THE PARTY THEY SUPPORT
The incentives vary slightly between the different PR systems.
EVERYONE'S VOTE WOULD COUNT
FEWER RIGHTWING GOVERNMENTS
Over the past 100 years, FPTP has given the UK about twice as many Tory as Labour governments. At some of those elections, more people voted for left-of-centre parties than for right-of-centre parties; on those occasions, a PR voting system would have given us left-of-centre coalition governments.
Research shows that on average, PR systems produce fewer rightwing governments than FPTP systems.
We can't say for certain what the outcome of a particular election would have been under a PR voting system, because many people would probably have cast their votes differently. For example, many more people would have voted for the Greens under PR, than actually voted Green under FPTP. But the experts' best guess is that the UK would have had more leftwing governments under PR.
GOVERNMENTS THAT A MAJORITY OF PEOPLE VOTED FOR
As Labour supporters, we know what it feels like to wake up on the morning after a Conservative election victory, knowing we have to put up with the Tories for another five years. There's only one thing worse, and that is waking up to a Tory government when most people in the country voted for a left-of-centre party.
If we switched to PR, rightwing governments would still be elected. But these would be governments that had gained the support of a majority of voters on election day. They would have won fairly. As Labour voters that may not be the outcome we'd want, but it's one we'd be able to live with.
In the UK, our Conservative governments tend to be very extreme, and make it a priority to axe public spending and cut taxes for the rich. Right-of-centre coalitions in countries which have PR tend to be more moderate; many European countries have been governed by rightwing coalitions which have honoured the "social contract".
BETTER REPRESENTATION FOR WOMEN AND MINORITY GROUPS
Countries that use PR tend have a much better record on diversity of representation than countries that use FPTP.
Here's why. Taking ethnicity as an example, approximately 14% of the UK population belongs to an ethnic minority. If Parliament were properly representative of the population, we'd expect about 14% of MPs to belong to minority ethnic groups.
Under FPTP, it's difficult to make this happen. In a system where each local party selects one candidate to stand in their constituency, no constituency party has individual responsibility for selecting a minority ethnic candidate - and most parties don't select minority candidates. Under 5% of MPs in the UK are from minority ethnic groups. There are possible solutions: each party could insist that some local parties select candidates from particular groups, in the way that Labour introduced all-women shortlists in 1997. But this would bring central control to a system which many people believe should be locally managed, and has always met with opposition from the Tories.
PR can and does help. In a system where some or all MPs are chosen from a party list, a list of 20 candidates of which 15 were white males would (rightly) generate an outcry. It's no surprise that PR systems do better than FPTP when it comes to diversity.
It is clearly not the case that PR would instantly solve all our problems with social inequality and with discrimination on the grounds of gender, ethnicity, disability, class, etc. However, research suggests that introducing PR would give these and other groups a bigger voice in Parliament. In addition, there is evidence that a PR voting system is associated with lower levels of income inequality, higher public spending, and a more equitable allocation of public goods. All of these things work to the benefit of traditionally less well-off groups in society.
Are you sick of seeing leaflets and posters proclaiming "Lib Dems winning here", or "Only the Lib Dems can beat the Tories here"? These captions, (often entirely untrue) are attempts to get people to vote tactically. Under PR systems, they would all but disappear.
Are you sick of Labour Party campaigns attacking parties like the Green Party and the SNP, whose policies are in many ways pretty close to Labour's own policies, rather than attacking the Tories and UKIP? This is particularly common in local campaigns, and it happens because each party has the best chance of winning if it attacks its most dangerous rival - which could be a party with a similar programme.
And are you sick of safe seats being all but ignored at election time, while all the parties' resources are poured into key marginals? In a PR system where all votes counted equally, parties would have to make their campaigns relevant to people in all parts of the country and to all demographic groups.
In STV or AV systems, the parties know that it's not only first preferences that matter; second preferences matter too. As well as winning first preferences, each party tries to gain second preference votes from parties with similar programmes. Vicious attacks on other parties' programmes will alienate voters and lose second preference votes.
In all PR systems, parties campaign in the knowledge that they may be seeking to form a coalition after the election. Of course there will be robust exchanges during an election campaign; but a party that has behaved honourably and respectfully towards other parties is more likely to be able to successfully broker a coalition.