Possible explanations:
One sex knows something the other sex doesn't:Perhaps since men are treated as the default gender, women understand what it's like to be a man better than men understand what it's like to be a woman.
How to test: Turing test. Create an anonymous panel of 4 male and 1 female economists, and then let a group of males ask them questions. Afterwards, the males vote on which panelist was female. Reverse the test. Whichever sex knows something the other sex doesn't will do a better job at passing the turning test and a spotting one of their own.
Signalling Women and men are expected to have feminine and masculine traits respectively, and one of the ways they can signal having these traits is by supporting certain politics. For example, a woman might endorse social welfare programs to signal that she has compassion (a feminine trait).
How to test: Not sure.
Brain differences: Women and men have slightly different brains. Perhaps the presence of testosterone in men causes them to support riskier free market policies.
How to test Look at intra-sex differences in brains and see if you find any correlations. If, for example, men with lower levels of testosterone are more likely to support liberal policies, and women with higher testosterone support more libertarian policies, that would be evidence that the intersex differences in testosterone could be responsible for the gap.
Self-interest Bias Perhaps women are better off under liberal policies, while men are better under libertarian. Each group is rationalizing reasons support policies that protect their sex.
How to test: See how each sex reacts to a pair of questions, one specifying a female, and one specifying a male. For example "Should waiters be covered by minimum wage laws" verses "Should waitresses be covered by minimum wage laws." If one sex gives the same answer for both these questions, and the other sex gives different answers, that is evidence that the second sex is biased.
Differences between libertarian/liberal movements Perhaps the libertarian subculture isn't welcoming for women. Women become liberals because libertarians creep them out.
How to test Recruit politically inactive women at a local university. Send one group to a libertarian convention, the other to a liberal convention. Ask each about their experiences.
Other explanations/tests?
If women know something men don't, men could just ask. That seems much more relevant than testing people's play-acting skills, and we'd actually learn what it was. As in this case women could just publish it and get a paper out of it, I doubt it.
Edit: ParagonProtege has provided a link to the original study. Thank you! (^_^)
Link.
Can this be reasonably explained by self-interest? Female and male economists' views are probably coloured by gender solidarity. Government jobs may be more likeable to women than men because of their recorded greater risk aversion. Regardless of the reason government jobs are more important for women than for men. Also in the US where the study was done middle class white women benefit quit a bit from affirmative action in government hiring.
Politics is the mind-killer probably does play a role in explaining the difference.
First two points are somewhat congruent with stereotypes. Anyone who has run into the frequent iSteve commenter "Whiskey" will probably note that the third point indicates women may not hate hate HATE lower and middle class beta males in this case.
This seems plausible since politics is about applause lights after all, the tribes are what matters not the particular shape of their attire. But might value differences still be behind the gender difference? Maybe some failed utopias I recall reading aren't really failed.
Somehow I think this does not include ideological diversity.
No mystery here. (^_^)