At ten minutes after 10am yesterday morning I was sitting on the edge of my couch watching ABC News 24, shedding quiet tears of relief.

Of course I was relieved the yes case had prevailed and felt a profound sense of love and solidarity for friends, family and colleagues in the firing line of the marriage equality campaign.

But there was also an immense sense of professional satisfaction. The final national result of 61.6% for yes mirrored very closely (well within the margin of error) all the reputable national polling on this issue.

At the beginning of the postal survey process The Essential Report reviewed all the polling done on the issue of same-sex marriage; at that time 61% of those surveyed said they would support marriage equality. Other publicly available polling had similarly put the percentage of support hovering just above the 60% mark. There is a lot of rot spoken publicly and privately about the accuracy of polling, as if the errors in other countries around national voters for presidents and membership of the European Union are automatically relevant to what we do here in this country. The reality is, as chief pollster for Galaxy David Briggs has pointed out many times, Australian polls have a far better track record for accuracy when it comes to national election results. And now for national survey results too.

At the beginning of the survey process, before most of the surveys had hit the nation’s mail boxes, the Essential Report posed the question: do you intend to participate in the same-sex marriage survey? Around 62% indicated they would definitely vote, 12% said maybe and 9% that they had already, amounting to 83%. I was optimistic about these numbers at the time, albeit a little sceptical about people’s reported intentions.

In the end the participation rate of close to 80%, with very little differences across age groups, was astounding. It throws serious doubt on the easy clichés that young people don’t care about democracy. That Australians are apathetic and disengaged. Interestingly the Essential Report found that at the beginning of the survey process only about half of those surveyed believed a national yes vote would prevail. Hopefully we are more positive about the community now this awful process is over than we were when we started. We want to dance the night away with Magda Szubanski instead of Lyle Shelton.

Former prime minister John Howard has declared that that the high participation rate in the survey reflects the wisdom of the government. I don’t think so. It reflects, by and large, the quality of the Australian people. There was no public consensus about how to manage the same-sex marriage issue. There was divided opinion around all the options on the table – parliamentary vote, referendum, plebiscite and the survey. The survey was designed to maximise the chance of a no result. The architects of the survey were cynically relying on the idea that Australians wouldn’t participate in a process that wasn’t compulsory and that young people (statistically more likely to support the issue) wouldn’t care enough to check their electoral roll status, check the mailbox and find a post box. Their cynicism was rewarded with resounding defeat, especially in the electorates where the most vocal no parliamentarians reside. Another reason for tears of relief. There was no majority of Australians calling for this mechanism for a decision on same-sex marriage and yet they embraced it anyway, a welcome sign of life in our demoralised political climate.

Finally, another cause for relief was that when the yes case based on the language of equality clashed with the no case based on arguments about freedom, equality prevailed. One of the great strengths of our society and our democracy – a defining difference in comparison to the United States – is that it is (mostly) rooted in notions of fairness rather than freedom. When the yes case offered a simple proposition based on treating people equally as well as a pragmatic proposition (same-sex couples are already in committed relationships and raising families), all the no case could offer was freedom for bakers not having to pound out royal icing for gay weddings.

In a recent column for the Guardian, David Marr observed that in Australia, any progress in the area of social reform is always hard fought. This battle has been won. I wonder what energy we might still have for the battles that need to be fought now, particularly around justice for Indigenous Australians and asylum seekers. How far can love and equality stretch? Can it embrace Uluru and Manus?

• Rebecca Huntley is the director of research at Essential Media