I'm guessing the lure of free tickets to the Open on their own course probably swung it, with only misogynistic old farts voting against it.

Women will finally be able to become members of the Honourable Company of Edinburgh Golfers at Muirfield.

According to Sky News, sources have revealed the decision of an historic ballot on the admission of women members to the club.

More than 92% of members of the HCEG voted, the broadcaster reported, with 469 voting in favour of allowing women. Another 155 voted against the motion.

The result will be announced officially at 11.30am.
The first vote, held in May last year, failed to secure the two-thirds majority required to start admitting women members to the HCEG.

This decision led the R&A to immediately announce the East Lothian course would no longer be considered to host the Open Championship.

Now, with this decision reversed, the course could be reinstated in the Open rota.

Women golfers will finally be admitted to HCEG Muirfield | Metro News