He'll wait for others to catch up, and then explain.

The key quantity needed is P(Conspiracy) / P(Ordinary), or any other quantity which determines that one, which for this example means how likely Keltham thought Conspiracy versus Ordinary was before the absent-book observation.  Say, if Keltham previously thought a Conspiracy was 10% as likely as the Ordinary world, and then he saw the no-book observation, which in Keltham's estimate was ~2.5 times as likely if there's a Conspiracy than in the Ordinary world, the result is that a Conspiracy then becomes 25% as likely as the Ordinary world.  So it goes from 'a tenth as likely' to 'a quarter as likely'.

Meritxell's observation is that Keltham also ought to take into account that Ione told him about her book powers in the first place, even though that makes it harder for Governance to control Keltham's information and potentially makes him suspicious if they try to.  Let's say that's 1/20 as likely in the Conspiracy world than in the Ordinary one - not impossible, there's weird side possibilities where that could happen because Governance wasn't on the ball there, but yeah, sure, unlikely.  So if Keltham took that argument at face value, he'd then multiply 'Conspiracy a quarter as likely as Ordinary' by 'observation a twentieth as likely on Conspiracy as Ordinary' and get 'an eightieth as likely'.

But then of course we have to consider how the three most obviously interesting-background girls, Carissa, Ione, and Pilar, all disappeared at lunch today, supposedly to copy Invisibility spells.  Since Invisibility has nothing to do with interesting backgrounds, the probability of randomly getting that set of three women selected from twelve possibilities is 12 * 11 * 10 / 3 * 2 * 1, or 220:1.  So the new odds of Conspiracy over Ordinary are 'an eightieth as likely' times '220 times as likely' or a bit less than 'three times as likely', 2.75 times as likely to be correct.

Keltham should therefore now consider himself 2.75 times as likely to be in a Dark Governance Conspiracy world than an Ordinary world.  Does that reasoning sound correct to everyone?

He'll wait for others to catch up, and then explain.

The key quantity needed is P(Conspiracy) / P(Ordinary), or any other quantity which determines that one, which for this example means how likely Keltham thought Conspiracy versus Ordinary was before the absent-book observation.  Say, if Keltham previously thought a Conspiracy was 10% as likely as the Ordinary world, and then he saw the no-book observation, which in Keltham's estimate was ~2.5 times as likely if there's a Conspiracy than in the Ordinary world, the result is that a Conspiracy then becomes 25% as likely as the Ordinary world.  So it goes from 'a tenth as likely' to 'a quarter as likely'.

Meritxell's observation is that Keltham also ought to take into account that Ione told him about her book powers in the first place, even though that makes it harder for Governance to control Keltham's information and potentially makes him suspicious if they try to.  Let's say that's 1/20 as likely in the Conspiracy world than in the Ordinary one - not impossible, there's weird side possibilities where that could happen because Governance wasn't on the ball there, but yeah, sure, unlikely.  So if Keltham took that argument at face value, he'd then multiply 'Conspiracy a quarter as likely as Ordinary' by 'observation a twentieth as likely on Conspiracy as Ordinary' and get 'an eightieth as likely'.

But then of course we have to consider how the three most obviously interesting-background girls, Carissa, Ione, and Pilar, all disappeared at lunch today, supposedly to copy Invisibility spells.  Since Invisibility has nothing to do with interesting backgrounds, the probability of randomly getting that set of three women selected from twelve possibilities is 12 * 11 * 10 / 3 * 2 * 1, or 220:1.  So the new odds of Conspiracy over Ordinary are 'an eightieth as likely' times '220 times as likely' or a bit less than 'three times as likely', 2.75 times as likely to be exact.

Keltham should therefore now consider himself 2.75 times as likely to be in a Dark Governance Conspiracy world than an Ordinary world.  Does that reasoning sound correct to everyone?

He'll wait for others to catch up, and then explain.

The key quantity needed is P(Conspiracy) / P(Ordinary), or any other quantity which determines that one, which for this example means how likely Keltham thought Conspiracy versus Ordinary was before the absent-book observation.  Say, if Keltham previously thought a Conspiracy was 10% as likely as the Ordinary world, and then he saw the no-book observation, which in Keltham's estimate was ~2.5 times as likely if there's a Conspiracy than in the Ordinary world, the result is that a Conspiracy then becomes 25% as likely as the Ordinary world.  So it goes from 'a tenth as likely' to 'a quarter as likely'.

Meritxell's observation is that Keltham also ought to take into account that Ione told him about her book powers in the first place, even though that makes it harder for Governance to control Keltham's information and potentially makes him suspicious if they try to.  Let's say that's 1/20 as likely in the Conspiracy world than in the Ordinary one - not impossible, there's weird side possibilities where that could happen because Governance wasn't on the ball there, but yeah, sure, unlikely.  So if Keltham took that argument at face value, he'd then multiply 'Conspiracy a quarter as likely as Ordinary' by 'observation a twentieth as likely on Conspiracy as Ordinary' and get 'an eightieth as likely'.

But then of course we have to consider how the three most obvious interesting-background girls, Carissa, Ione, and Pilar, all disappeared at lunch today, supposedly to copy Invisibility spells.  Since Invisibility has nothing to do with interesting backgrounds, the probability of randomly getting that set of three women selected from twelve possibilities is 12 * 11 * 10 / 3 * 2 * 1, or 220:1.  So the new odds of Conspiracy over Ordinary are 'an eightieth as likely' times '220 times as likely' or a bit less than 'three times as likely', 2.75 times as likely to be exact.

Keltham should therefore now consider himself 2.75 times as likely to be in a Dark Governance Conspiracy world than an Ordinary world.  Does that reasoning sound correct to everyone?

He'll wait for others to catch up, and then explain.

The key quantity needed is P(Conspiracy) / P(Ordinary), or any other quantity which determines that one, which for this example means how likely Keltham thought Conspiracy versus Ordinary was before the absent-book observation.  Say, if Keltham previously thought a Conspiracy was 10% as likely as the Ordinary world, and then he saw the no-book observation, which in Keltham's estimate was ~2.5 times as likely if there's a Conspiracy than in the Ordinary world, the result is that a Conspiracy then becomes 25% as likely as the Ordinary world.  So it goes from 'a tenth as likely' to 'a quarter as likely'.

Meritxell's observation is that Keltham also ought to take into account that Ione told him about her book powers in the first place, even though that makes it harder for Governance to control Keltham's information and potentially makes him suspicious if they try to.  Let's say that's 1/20 as likely in the Conspiracy world than in the Ordinary one - not impossible, there's weird side possibilities where that could happen because Governance wasn't on the ball there, but yeah, sure, unlikely.  So if Keltham took that argument at face value, he'd then multiply 'Conspiracy a quarter as likely as Ordinary' by 'observation a twentieth as likely on Conspiracy as Ordinary' and get 'an eightieth as likely'.

But then of course we have to consider how the three most obvious interesting-background girls, Carissa, Ione, and Pilar, all disappeared at lunch today, supposedly to copy Invisibility spells.  Since Invisibility has nothing to do with interesting backgrounds, the probability of randomly getting that set of three women selected from twelve possibilities is 12 * 11 * 10 / 3 * 2 * 1, or 220:1.  So the new odds of Conspiracy over Ordinary are 'an eightieth as likely' times '220 times as likely' or a bit less than 'three times as likely', 2.75 times as likely to be exact.

Keltham should therefore now consider himself 2.75 times as likely to be in a Dark Governance Conspiracy world than an Ordinary world.  Does that reasoning sound correct to everyone?