BlogNomic: The Ninth Dynasty of ais523

Semantic question: What does it mean to lynch someone who’s already dead (i.e. Amnistar)?

Assuming that the sample set is those villagers with known back hair, that set contains exactly two werewolves, and no one has shaved their back, I get (from Bayes’ theorem):

P( W|H)=P(H| W)P( W)/P(H) = 0.5 * (2/14)/(2/14) = 0.5
P(~W|H)=P(H|~W)P(~W)/P(H) = 0.25 * (12/14)/(2/14) = 1.5

That is, there is a 50% chance of each person with a hairy back being a werewolf and a 150% chance of them not being a werewolf.  I may be applying the theorem wrong (please correct me if so).  Otherwise, I’ll say that there is a 3 in 4 chance that each of the two people that will be lynched in this proposal are not werewolves.

this is like the salem witch hunts. hix can tell ya that the odds are very much in favor of this killing more humans then werewolves. granted at this time its only 2 people but still.

Sorry; I meant living villagers, and the the equations should have been

P( W|H)=P(H| W)P( W)/P(H) = 0.5 * (2/10)/(2/10) = 0.5
P(~W|H)=P(H|~W)P(~W)/P(H) = 0.25 * (8/10)/(2/10) = 1.0

Which is a 2 in 3 chance that each person is not a werewolf.  My vote stands.

plus how do we know you didn’t get a shave before the barber left town?

Okay, you’re right. There’s a greater chance that those who are hairy-backed are villagers than werewolves. Here’s the math:

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Let us assume that of the 16 living villagers who aren’t you, 2 are werewolves. Let’s focus on one person with a hairy back (without loss of generality, let it be Rodney)

Thus there is a 14/16 chance of Rodney being a villager, and a 2/16 chance of Rodney being a werewolf.

Now, the chance of being a werewolf who has hair is (2/16)*(1/2)=(2/32).
The chance of being a villager who has hair is (14/16)(1/4)=(7/32)

Thus, the chance that Rodney has hair is the sum of these (9/32), and given that Rodney has hair (which he does), the odds that he is a werewolf is 2/9.

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Hairy people are still more likely to be villagers than werewolves. But what’s more important is that this likelihood is decreased.

So let’s lynch both living people with hair. I say we have a success if at least one werewolf is lynched, since the ratio of villagers to werewolves increases. The odds of killing two villagers (no werewolves) is (7/9)(7/9) = 0.60.
So, the odds of killing at least one werewolf (out of two) is 40%.
If there are three hairy people, the odds of killing at least one werewolf (out of three) is 1-(7/9)(7/9)(7/9) = 53%

These percentages, however, are the lower bound, using the hypothesized lower bound of werewolves (2 werewolves).

With 3 wolves of 16, the odds of killing at least one werewolf out of two hairies increases to 53% and one werewolf out of three hairies to 68%.

With 4 wolves of 16, the odds of killing at least one werewolf out of two hairies increases to 64% and one werewolf out of three hairies to 78%.

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However, even if the chance is 1 in 3 of a hairy being a wolf, that is greater than a 1 in 5 given no information about hairy-ness.

So it comes down to this:

How much of a risk are you willing to take?

And please don’t be guilted into voting FOR or AGAINST this, but make your own decision. I won’t be offended if you voted AGAINST.

The Almighty does not condone this madness. Show reason, my fellow villagers! Only those truly discovered to be guilty shall be burned at the stake.

-Archbishop Bob

  Now this is just silly.  This is exactly the kind of random lynching we should be trying to prevent.

BTW, Elias, what are the chances that we’ll kill the werewolves if we lynch everyone with a clean back?  Greater, probably.

“Lynch” is not defined anywhere in the ruleset. This has a zero chance of killing anyone.

My thoughts exactly, Rodney.

What Rodney said.  And this is weak.

True, I’m not sure this would actually DO anything, but because it’s madness.

Erm, it appears that this wasn’t well-received. It was just an idea.

But hmm, to Oracular Rufio: No, this isn’t random at all. It’s not a “let’s roll a DICE17 and lynch that person”. It’s lynching people who have a slightly, yet statistically, higher chance of being werewolves.

You say, “BTW, Elias, what are the chances that we’ll kill the werewolves if we lynch everyone with a clean back?  Greater, probably.”

Yeah, this is true, but that’s not our goal. Our first and foremost goal is to lower the ratio of werewolves to innocents.

Taking out more than 5 innocents for every werewolf is counterproductive. However, only one or two, although it is a loss, decreases the concentration of wolfishness in our population.

However, this is not a well-formed idea. We will probably make better decisions when Kevan reveals more information to select people (Night Watchman, ghosts, etc.)

That’s Quorum.