The problems of the Prime Minister, Julia Gillard, turn not on her gender but, rather, on her authority.

The Lateline presenter Emma Alberici put it to the American playwright Eve Ensler that a “sexist or misogynist tone” had affected coverage of the Prime Minister’s “policies and politics”. Alberici asked whether this was “something quite particular to female leaders around the world”. Ensler said yes, and explained Hillary Clinton’s defeat in the Democratic Party primaries in 2009 as significantly due to the media’s focus on such insignificant issues as body and clothing.

This is an unproven thesis. Clinton did well in the 2008 primaries but was overcome by the superior organisation of Barack Obama’s rank-and-file supporters. Gillard looked and dressed much the same as now when she was Labor’s deputy opposition leader and deputy prime minister.

Ensler said the media throws the switch to superficial when “powerful” women are in leadership roles. There tends to be an obsession in the Western media with power. In recent years the Australian Financial Review Magazine has published an annual “Power Issue”. And now the publishers of the Crikey newsletter have set up “The Power Index”. There is a problem with word usage here. Power is most appropriately associated with authoritarian regimes and is retained by force.

In democratic societies, elected leaders possess authority, legitimised by the ballot box. Successful prime ministers or presidents exert their authority after taking account of the checks and balances on absolute rule.

Democratic leaders invariably experience problems if their authority is diminished. That’s Gillard’s problem right now. Her authority has been in decline since she succeeded Kevin Rudd as prime minister in June 2010.

There was some negative reaction when Gillard replaced an incumbent prime minister. Yet this has happened on several previous occasions: Robert Menzies was replaced by Arthur Fadden in 1941, John Gorton by Billy McMahon in 1971 and Bob Hawke by Paul Keating in 1991.

The essential problem with Gillard’s political ascension was that she and her advisers did not capitalise on her newly acquired legitimate authority. In other words, Gillard did not seem as prime ministerial as she could have. She missed a number of opportunities.

First, Gillard could have represented Australia at the G20 Summit in Toronto in June 2010 and met such world leaders as Obama but delegated the trip to her deputy, Wayne Swan. Second, Gillard could have moved immediately into the Lodge but stayed in suburban Melbourne until the election. Third, Gillard could have visited such nations as Japan, India, China and Indonesia but remained at home.

Fourth, Gillard could have maximised her time as prime minister but called an election in mid-August.

The Prime Minister did relatively well in leading Labor to victory in 2010, albeit as head of a minority government. Labor and the Coalition were reasonably close in the post-election period. Then, in late February last year, Gillard broke her promise not to introduce a carbon tax. This substantially diminished her authority – as did her decision to appear at media conferences flanked by the Greens.

On Q&A last year, Graham Richardson said it was “appalling” that the Prime Minister was often referred to as “Julia”. On the same program last week, Senator Penny Wong used the term “Julia” on no fewer than four occasions. Wong is a Gillard supporter.

It is disgraceful that some protesters have called the Prime Minister “a bitch”. But no more so than when John Howard was depicted as Adolf Hitler in demonstrations. Successful politicians can prevail over abuse.

Gillard’s problems turn on the fact that she is de-authorised. It’s always possible to restore authority. However, it takes time.

Gerard Henderson is executive director of The Sydney Institute.