The candidate enters the stadium, fist pumping the air and shaking as many hands possible en route to the podium, as thousands of supporters cheer wildly. For most politicians, scenes like that are an invaluable part of the campaign, a chance to flaunt their supporters in the face of the opposition: but not so for the woman poised to become Madrid’s mayor.

“Rallies are one person going blah, blah, blah and then leaving,” Manuela Carmena tells the Observer. “I refuse to do them.” To her, rallies simply reinforce the chasm between people and their politicians. “We said no to rallies. Instead we held meetings in neighbourhoods and said, ‘We’re your candidates, tell us if what we’re doing is good or bad, ask us questions.’ We gave the word to people – we didn’t want to speak.”

Months ago, the 71-year-old retired judge was a little-known figure in Spain. But at the helm of Ahora Madrid, a leftist coalition that ran in Madrid’s recent municipal elections, the former Communist activist has become a prominent voice of the political and social transformation sweeping Spain.

The electoral campaign saw artists come together to back her campaign, flooding social networks with artwork that cast her as a symbol of change, while street artists spread her message across the city. One week before the election, polls said the 10-point gap between the conservative People’s party (PP) – which has ruled Madrid for some 20 years – and Ahora Madrid had narrowed to a virtual tie.

Last Sunday, as Spaniards cast their ballots in municipal and regional elections, the PP squeaked out a win in Madrid, but failed to secure a majority. The result means Carmena and Ahora Madrid could join forces with the Socialists, wresting power from the PP and into the hands of a group with roots in Spain’s indignado movement.

We were unknown candidates, we didn’t have any money for the campaign. I like to say we ran on the currency of hope Manuela Carmena

“It’s been really exciting,” says Carmena in an interview at the barebones offices donated to Ahora Madrid for the campaign, one street from the Madrid plaza where the indignados launched their movement in 2011. “You wonder, what just happened? Truthfully, we were unknown candidates, we didn’t have any money for the campaign. I like to say we ran on the currency of hope.”

Ahora Madrid is not a political party, she explains, but rather a coalition of leftist groups, which includes Podemos and thousands of citizens. “It’s a platform of people who have come together to change things.”

The changes they envision for the city are straightforward, ranging from doing away with home evictions when possible and providing alternative accommodations when not, to guaranteed electricity and water for households that cannot afford utilities, and developing a plan to create jobs for young people and the long-term unemployed.

The priority is to tackle the inequality that colours Madrid, says Carmena, citing neighbourhoods where nearly one in three are unemployed, compared with others where unemployment sits at 6%. As mayor, Carmena has also promised to slash her salary by more than half.

Those are the concrete aims. But starting with her first day in office, Carmena is promising a radical overhaul in how politics is carried out in the city. “I think for a long time politics established itself in very violent ways – rigid, reactive attitudes with authoritarian structures.”

The time has come, she says, to usher in “a feminine way of doing politics”, turning Madrid into an incubator of policies centred around the values of coexistence, caring and non-aggression. “To govern is to listen,” says Carmena, repeating her oft-used phrase from the campaign.

It comes as little surprise to Carmena that two of the most prominent voices leading the push for democratic regeneration in Spain belong to women – her own and that of Ada Colau, whose Barcelona En Comú movement is likely to govern Barcelona. “I think the world is increasingly realising the need to abandon vertical attitudes and move towards a deepening of democracy,” she says. “Those are values of the new feminine culture that will likely be the culture of the 22nd century.”

Her views echo the frustrations that emanated from Spain’s plazas four years ago, when hundreds of thousands of indignados rallied against a political class whose priorities were seen to be out of step with those of the people.

It is a movement primarily spawned and supported by young Spaniards, yet in Madrid its leaders include a septuagenarian, laughs Carmena, pointing to the nearly 50-year difference that exists between her and the youngest member of her team. “It’s curious. It was like all of a sudden they looked at me and said, this generation did things that were very interesting. And in me they saw – I don’t know – maybe a caring grandmother.”

She sees parallels between the indignado generation and her own. Born years after Spain’s civil war, Carmena co-founded a group of leftwing lawyers during the Franco dictatorship, and signed up to the outlawed Communist party. Her generation, she says, was able to free itself of the fear that gripped her parents’ generation, instead quietly seizing on the small openings they saw in Franco’s regime.

Conservative candidate Esperanza Aguirre sought to stoke fears about the Ahora Madrid movement Photograph: Sergio Perez/Reuters

Inspired by the May 1968 events in France, she and her friends constantly pushed the boundaries. “We questioned everything. Everything seemed like it needed to be questioned.” They ran huge risks. “We were in jail for a short while. I was arrested, they threw me out of university,” she says.

“Those were repressive acts, but they allowed us to confirm how society was changing: they gave us a lot of energy.” Tragedy struck in 1977 when five colleagues were gunned down by a far-right group at her law office in Madrid. Her voice shakes as she recounts the incident, one of the deadliest moments in Spain’s transition to democracy. “What an injustice. The rest of us grew older, we had disappointments, we had failed relationships, we had everything: children, grandchildren. Their lives just stopped that day.”

It is these experiences she draws on to lead Madrid, building bridges along the way between her generation of activists and Spain’s indignados. “It’s really interesting. I sometimes realise that my proposals are more reformist than the young people who didn’t even realise that you can do things another way.”

These days, she travels by bicycle, blogs on justice issues and has even designed a board game about judicial processes. As the prospect of taking on Madrid’s top job looms, a major task lies in overcoming the city’s political divide. Many in Madrid cast their vote for the conservative PP, whose promises to defend businesses and lower taxes espouse a different vision of the city than that put forward by Carmena and Ahora Madrid. “Our challenge is to seduce those who didn’t vote for us,” she says.

It is exacerbated by her rival, the PP’s Esperanza Aguirre, who has sought to stoke fears about Ahora Madrid. Last week Aguirre said the leftist group wanted to use the mayor’s office as “a springboard to destroy the western democratic system as we know it”. Carmena likened the remarks to the “tantrum of a spoiled child”, in an interview with broadcaster Cadena Ser.

The end of the campaign means it’s now time to end the war of words, says Carmena. “Now it is time to use the language of doing. We’re going to convince them and they’re going to say, you were right. You live better in a society that is more just and equal.”

• This article was amended on Sunday 31 May 2015 to change the headline.