With speculation the prime minister will declare her support for a conscience vote on same-sex marriage ahead of Labor’s December national conference, a new poll suggests the issue could enable Labor to attract support from Greens voters.

Sources close to the PM have long hinted that there’d be a shift by Julia Gillard on the issue either before or at the conference, although not all the way in favour of same-sex unions. These have been strengthened by reports in News Ltd papers today that the PM is preparing to back a conscience vote, a compromise tactic designed to head off a damaging fight over the issue between social progressives and conservatives while shifting Labor to a more liberal stance than its current “man and woman” policy.

The pro-same-sex union group Australian Marriage Equality today released polling done by Galaxy looking at the impact on voting intention of a full Labor shift to supporting same-sex unions. The poll was undertaken last weekend with a sample size of just over 1000 respondents.

The poll showed 17% of people said they’d be more likely to vote for Labor if it supported same-sex unions and 19% less likely to support Labor, with 64% saying it would not affect their vote.

However, the distribution of those who say the issue would change their vote is significant. Coalition voters are more likely to be less inclined to vote Labor — 28% — than others, while Greens voters are much more likely to be more inclined to vote Labor — 47%. That is, Labor wouldn’t lose many votes from the issue, because Coalition supporters are most likely to be negatively disposed to support for same-sex marriage, but the votes it would pick up would be from the Greens. It would also strengthen Labor’s hold on its own voters, with 23% of Labor voters saying they’d be more likely to vote Labor, compared to 10% who would be less likely.

Galaxy calculates that overall, a switch to outright support for same-sex marriage by Labor might increase its primary vote by anything up to four points. That would primarily come from the Greens, to whom Labor has bled votes over the past two years, in effect representing a recovery of lost voters. It wouldn’t help on a two-party preferred basis, however.

There are some other interesting breakdowns in the polling results. Women are far more likely to respond positively to a Labor shift on the issue than men: 22% of women were more likely to vote Labor compared to 11% of men; 25% of men were less likely to vote Labor, compared to 14% of women. Younger voters were three times more likely to respond positively — 33% of 18-24-year-olds would be more likely to vote Labor compared to 10% of over-50s (and the figure falls linearly with age).

Queensland voters are more likely than others to respond negatively — 11% would be more likely to vote Labor and 25% less likely. High income and more educated voters are also more likely to shift their support to Labor than others on the issue. However, contrary to expectations, the differences between urban and regional voters are limited: 17% of capital city voters would be more likely to support Labor compared to 15% outside capital cities; 18% in capitals would be less likely and 21% outside capitals less likely.

While the results aren’t unexpected, they provide some context for the debate within Labor about how to fight the threat of the Greens to its Left flank. Some social conservatives in the party seem happy for the Greens to poach progressive ALP members and voters. Party powerbroker and Catholic reactionary Joe De Bruyn, who has claimed gay marriage will destroy civilisation, believes supporting same-sex marriage will wreck Labor.

Hardline Catholic MP John Murphy specifically urged advocates of marriage equality to leave the party and join the Greens earlier this year. Such an exodus would obviously strengthen the control of the conservative Right within the party, but accelerate Labor’s already dire problem of shrinking membership and boost the electoral clout of the Greens, who are serious opponents for Labor in inner-urban electorates.

Labor hard-heads less interested in improving their faction’s position and more interested in a long-term future for the party, however, understand that Labor must find a way to shore up its Left flank and fight off the Greens. This is done most effectively by co-opting what Green positions it can — a strategy that worked successfully for John Howard in confronting the threat to his conservative base from One Nation.