Season 1 would be very, very different.
First of all, if Game of Thrones took place in a matriarchal society, then none of the show's events would ever have happened.
Mainly because Lyanna Stark's sexual agency in choosing Rhaegar Targaryen over Robert Baratheon would have been respected and Robert wouldn't have the backing to go to war over his hurt fee-fees. But we digress.
HBO / Via claimfame.com
Our show opens on Catelyn Stark, Lady of Winterfell, teaching her eldest daughter and heir Sansa the noble and respected art of needlework.
"Where is Arya?" asks Sansa.
"Probably with the weapon master, sullying her god-given femininity with swordfights and other brainless work," replies Catelyn.
"Oh."
HBO / Via degrassi.wikia.com
Hark! Catelyn's husband Eddard returns from the hunt with gifts for his daughters. They are to receive direwolf puppies, the care of which will prepare them for divine motherhood.
There are some puppies left over for Catelyn's boy-children, but they have to pick last.
HBO / Via pinterest.com
A page brings Lady Catelyn news that her old friend Queen Cersei is coming to Winterfell with her husband, Bob The Royal Consort.
Catelyn wonders silently why Cersei has not yet divorced Bob, seeing as the right of a wife to dispute and terminate a marriage as long as she gives notice and reason is written in the creed of the Seven Kingdoms.
HBO / Via garethrussellcidevant.blogspot.com
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If The World Of "Game Of Thrones" Were A Matriarchy