A crucial decision on how Welsh Labour elects its next leader- and Wales’ next first minister – will be taken by a special party conference later.
It follows months of wrangling over whether the votes of all party members should carry the same weight.
Finance Secretary Mark Drakeford and Health Secretary Vaughan Gething are in the running to succeed First Minister Carwyn Jones who is to step down
Delegates will be asked if they want to move to the one-member-one-vote system.
UK Labour leader Jeremy Corbyn was the first from the party to be elected using the method, known as Omov.
Should it be adopted in Wales, it would mean all party members – and the members of unions and affiliated groups – get an equal vote.
A second option for members at Saturday’s conference in Cardiff would be to reform Welsh Labour’s electoral college, giving half the vote to party members and half to affiliated members.
Both options emerged from a review by former Labour Party Cabinet member Lord Murphy, who was brought in after an outcry from supporters of Omov.
Labour’s ruling executive initially wanted to keep the college which splits leadership election votes three ways between members, unions and politicians.
Mr Drakeford, the Cardiff West AM, is the favourite to succeed Mr Jones as leader when he stands down in December, is a leading supporter of Omov.
Wales’ biggest union Unite is also in favour. Its regional secretary for Wales, Peter Hughes, said the “fudged option of a reformed electoral college will only extend the division”.
Mr Gething, the Cardiff South and Penarth AM, and Mr Drakeford are the only contenders with enough backing from Labour AMs to make it onto the Welsh leadership ballot paper.
Eluned Morgan, Huw Irranca-Davies and Alun Davies have also said they want to stand in the election but do not have enough backing.
Analysis by Daniel Davies, BBC Wales political correspondent
For some, it’s been a badge of honour for Welsh Labour, preserving the status of unions within the Labour Party.
Others say the electoral college has cast a shadow over Labour since devolution, frustrating the will of rank and file members.
It cost Rhodri Morgan the leadership in 1999. He couldn’t beat Alun Michael for the top job, even though Mr Morgan had more support in the party’s grassroots.
Some of those who were closest to him looked on in dismay when history repeated itself in April. His widow, Julie, lost the contest to become deputy Welsh Labour leader, despite being the favourite of rank-and-file party members.
The college splits the vote three ways: between party members, unions and affiliated groups, and politicians.
In the rest of Britain, Labour has scrapped it. Jeremy Corbyn has twice been elected leader after one-member-one-vote elections.
Either option from the Murphy review would remove politicians from the equation.
But with enthusiastic support from constituency Labour Party groups – and backing from the biggest union, Unite – today could spell the end for the electoral college altogether.