Greens members will be asked how the party should choose its federal leader and what to do if it is called on to help Labor form a minority government.

For the first time in the party’s history members will be asked in two surveys if they want to have a say in the federal leadership, and whether the minor party should grant Labor only supply and confidence, enter a formal agreement or even take ministries in a Labor-Greens government.

The surveys – to be conducted this week – will give preliminary results to be discussed at the Greens national conference on 18 November, with full results to be released to members in early 2019.

Greens state and territory divisions take different approaches to forming government with Labor. It is one of the key fault-lines between moderates, who want the Greens to become a party of government and take ministries, and the party’s leftwingers who do not want to join government on Labor’s terms.

One survey will ask if the Greens’ federal leader should remain the choice of the party room. It will test the popularity of alternatives including a vote by members, either a direct election or an option with weightings for states with fewer members.

Another alternative proposes a weighted combination of votes cast by members and federal Greens parliamentarians, with members asked to nominate which should have the bigger say.

Since 2013 the federal Labor party has allowed its members a vote on the leader, with votes weighted 50% to the membership and 50% to the federal caucus.

The second survey will ask if “entering into a formal agreement is the best strategy for growing the influence of the Greens and progressing our policies” in the event Labor needs the Greens to form minority government.

The survey presents four options: remaining on the crossbench and guaranteeing only supply and confidence; adopting a formal agreement in return for particular policy outcomes, as Bob Brown did in the minority Gillard government in 2010-2013; asking for ministries in a Labor-Greens government, as it currently does in the Australian Capital Territory; or a combination of asking for both policy commitments and ministries.

In a letter to members the national convenor, Rebecca Galdies, explains that the Greens “have already clearly ruled out entering into any negotiation with a Liberal government”.

In 2015 the Greens federal leader Richard Di Natale suggested Greens could take ministries in a Labor government.

The member for Melbourne, Adam Bandt, suggested before the 2016 election the party should drive a harder bargain for policies from Labor, including threatening to send voters back to the polls if the Greens do not get their way in a hung parliament.

The shadow treasurer, Chris Bowen, argued in a book before Labor’s 2013 election defeat that Labor must “govern alone or not at all” due to perceptions an alliance with the Greens in 2010-13 hung parliament harmed Labor.

Labor currently holds 69 seats in the 150 seat House of Representatives, needing to pick up seven seats to govern in its own right.

Its current lead in opinion polls of 54% to 46% in two party preferred terms – including in the most recent Guardian Essential poll – could result in the gain of up to 25 seats if replicated on election day.

However, the crossbench of seven MPs – Bandt, Centre Alliance’s Rebekha Sharkie, Bob Katter, Cathy McGowan, Andrew Wilkie, new member for Wentworth Kerryn Phelps and rebel National Kevin Hogan – could increase the odds of a hung parliament if those MPs are returned and the margin between the major parties tightens.