Some mathematics from the local bard
Numbers are allies to those that will use them
Though it not always easy to choose them
Should one use permutations, combinations, what should one do?
But I've got my head around it and report back to you.
Regarding the shortlisting suggestion. I need to know how many people would be on the shortlist roughly. Let us say a majority of 5 people voted for an innocent.
Now, of the 14 of us, 5 are chosen. There are 2002 different groups of 5 people that can be chosen from the group of 14. However, from the 11 villagers, there are only 465 ways in which 5 people can be chosen, so the overall chance of getting at least one wolf in the shortlist is 77%.
Compare this to the present system, where we have a 100% chance of beign able to vote for a wolf.
However, one person of the five is chosen to be killed. This is slightly more complex.
The probability that there are no wolves is 23%
The probability that there is one wolf in the 5 is 49%.
The probability that there are two wolves is 25%
The probability that all three wolves are in is 3%
Out of the five people, one is lynched at random.
If there are no wolves, there is a 0% chance of lynching one.
9.8% of the time, we will lynch the wolf when there is one.
10% of the time, we will lynch a wolf when there are two.
1.8% of the time, we will lynch a wolf when there are three.
Overall, we stand a 21.6% chance of getting a wolf in this way.
Normally, we vote for a random person out of 14. There is a 3 in 14, that is, 21.4% chance, of choosing a wolf.
Therefore, by implementing Fordim's rules, we are 0.2% more likely to lynch a wolf.
So there you go.
Last edited by the guy who be short; 06-04-2005 at 05:40 AM.
Reason: Correcting some maths
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