Why Does Sansa Have Littlefinger Killed?
This Is Exactly Why Sansa Makes Her Final Decision About Littlefinger
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Getting Ned Stark executed for treason
In season one, Baelish acts like he is on Ned Stark's side in King's Landing as Ned investigates Robert's children's parentage (and Robert's many bastards), but in fact Baelish is working with Cersei and Joffrey to take Ned out.
Baelish sets it up to look as though Ned is responsible for trying to get the City Watch to work against Joffrey and install Stannis Baratheon on the throne (since Joffrey, as the son of Cersei and Jaime, has no legal right to the throne). These machinations are what earn Ned an execution for treason.
