Royal Troon, which is on the west coast of Scotland, has hosted the British Open on eight previous occasions, most recently in 2004.

But Cheyne said the club had reviewed more than the issue of women’s membership in recent months. “The focus was on all categories of membership and how we could become more involved in promoting golf, a sport which is currently declining: declining in male, female and junior membership,” he said. “What we did tonight was focus on the single issue of women’s members, but we need to focus on how we can encourage young people to play this game.”

In 2014, the Royal and Ancient Golf Club of St. Andrews voted to end its male-only membership policy, which had been in place for 260 years. In 2015, another Open venue — Royal St. George’s Golf Club in Kent, England — also voted to allow female members.

And on Monday, the Honourable Company of Edinburgh Golfers announced that it had called a special meeting to seek approval to organize a second vote later this year on Muirfield’s male-only membership policy

It was unclear when Royal Troon would welcome its first female member. “I think what will happen is that when applications come in, they will be treated the same way as men,” Cheyne said. “There will be no fast-tracking women as members. Equality does mean equality.”

That is in part because Royal Troon already has an affiliated women’s club: Ladies Golf Club, Troon. Its clubhouse is a short walk from Royal Troon’s clubhouse, and the two clubs will work together to stage the British Open.

“We were a mixed club until the 1890s, when the ladies elected to leave and build their own clubhouse,” Cheyne said. “We have had a very harmonious relationship for 138 years, and the ladies have always been able to come play the Old Course free of charge any day of the week and enjoy our clubhouse.”