Senator Seselja and his rivals are downplaying the advantage ahead of the May 18 federal poll, but the prime spot offers the conservative MP a share of the donkey vote that could prove a boon in a tight contest.

The Liberal senator is fighting off a challenge from centrist candidate and independent Anthony Pesec in one of the ACT's most watched contests ahead of the election.

Senator Seselja emerged as a target among candidates following his high-profile support for Peter Dutton's hard-right challenge to Malcolm Turnbull's leadership in August, and his opposition to same-sex marriage in a city that overwhelmingly supported it.

Unions are orchestrating a "Dump Zed" campaign, while the Greens are also challenging the Liberals' grip on the ACT's second seat.

Senator Seselja said his place on the ballot paper didn't matter, and voters were too smart to be influenced by the order of candidates.

"We do not take any vote for granted," he said, adding he would fight for every last vote right up to the close of polls.

Mr Pesec, placed third on the Senate ballot paper behind the Liberals' and Greens' candidates, said Canberrans were savvy voters, muting any advantage from a donkey vote.

This election had an interesting ACT Senate race that would make voters consider their choice, he said.

Senator Seselja's ballot place might have more influence than he admits, according to ANU political marketing and advertising researcher Andrew Hughes.

"Being number one, Zed Seselja would secretly be quite enthusiastic and happy about that outcome," he said.

In a close contest, it could swing results one way. The promise of more donkey voters lifted the senator's election chances from a "maybe", but he had a lot of hard work ahead, Dr Hughes said.

The order of candidates on ballot papers is determined through a public draw.

Senator Seselja and Mr Pesec are two of 17 candidates vying for the ACT's two Senate seats.

Among the territory's lower house races, the northern seat of Fenner has five candidates, voters in the electorate of Canberra will choose from six, and the southern seat of Bean has eight.

In Fenner, United Australia Party's Glen Hodgson has the top ballot-paper position, while independent Tim Bohm heads the Canberra list, where Labor's Alicia Payne is named ahead of Greens rival Tim Hollo.

Therese Faulkner for the Australian Progressives is the first name on the ballot paper for Bean.

Clive Palmer's United Australia Party is targeting the minor party vote in all ACT seats, while far-right nationalists Fraser Anning's Conservative National Party has two Senate candidates.