Labour’s leadership candidates should back sweeping reforms of the UK’s electoral system and pledge to bring in proportional representation if elected, the Green party has urged.

Siân Berry and Jonathan Bartley, co-leaders of the Green party, have written to the three candidates offering support and dialogue “in the collegiate spirit these times demand” and asking each of them to endorse a shift to a form of PR voting.

“We cannot continue to allow our democracy to be warped by a system where many are excluded, policy is not led by those whose voices should be heard, and where votes do not match seats,” they say.

Three-quarters of Labour party members support proportional representation, according to a YouGov poll conducted shortly after last December’s general election, which produced Labour’s worst showing since 1935. But the party has fought shy of wholeheartedly adopting the policy.

The Labour leadership campaign, muted in its final weeks by the coronavirus crisis, closed on Thursday and the winner among the final three candidates – frontrunner Sir Keir Starmer, the pro-Corbyn Rebecca Long-Bailey and outsider Lisa Nandy – will be announced on Saturday.

Berry told the Guardian the Covid-19 emergency had highlighted the problems with the first-past-the-post system, which is predicated on two-party dominance. She said the crisis meant voters wanted their elected representatives to work together, but the system discourages cooperation.

“Fairer political systems force politicians to move away from point-scoring rivalries and tribalism, and leads to better outcomes,” she said. “The evidence on this spans health, income inequality, quality of life, environmental protections and education, and even shows countries [with fairer electoral systems] tend to have lower levels of national debt and lower deficits.”

The climate crisis, which all three Labour candidates have promised to prioritise, was a key example of a vital issue that cut across traditional party lines, but on which cooperation had been stifled by the current system, she said. “Just like coronavirus, there is no way we are going to be able to tackle the climate emergency without working together, and the outdated first-past-the-post system is seriously hindering our ability to do that.”

All three Labour candidates have indicated support for electoral reform, without giving detailed plans. Starmer has called for a new constitutional convention to address issues including “the fact that millions of people vote in safe seats and feel their voice doesn’t count”. Long-Bailey has also backed a constitutional convention without explicitly recommending PR for the House of Commons, and Nandy has voiced some support but stopped short of full backing.

Labour voters would win as well as the Green party from a new voting system, according to Berry. Despite a 2.7% share of the vote at the last election, the Greens still managed only one MP, Caroline Lucas, in Brighton Pavilion. Under the form of proportional representation used in European parliament elections, the Greens would have taken 12 seats. Labour, with 32% of the vote, would have taken 14 more seats than its 202 tally and the Conservatives’ 80-seat majority would have evaporated.

“All voters benefit from a fairer electoral system, no matter which party they support, because if votes match seats then people’s views really matter and our democracy is strengthened,” said Berry. Support for smaller parties is artificially suppressed under first-past-the-post, as voters choose the least-worst option if they feel their preferred candidate has little chance of winning.

The experience of the coronavirus crisis will increase people’s appetite for a fairer electoral system, Berry believes, giving the next Labour leader the opportunity to make sweeping changes to the party’s approach.

She drew a parallel between workers who have often been undervalued in pay and by governments, and voters who do not feel they have much influence on politicians.

“The huge change in attitude about which workers do the jobs that really keep our society going – not just NHS staff but the teachers, supermarket workers, delivery drivers, care workers and many other jobs that were undervalued before – is a new perspective we must not forget. I hope people will keep these values in mind [after the crisis wanes],” she said.

“It is vital that the public trust their votes count and their voices will be heard.”