Vote from Any Country for ME/FM Charity to Win $20,000!

  • REACH FOR THE RAINBOW ONTARIO 71801
  • Alberta Animal Rescue Crew Society 67913
  • MOUNTAINAIRE AVIAN RESCUE SOCIETY 29908
  • NATIONAL ME/FM ACTION NETWORK 28427
  • SALTHAVEN WILDLIFE REHABILITATION AND EDUCATION CENTRE INC.14935
Voted! Maybe they extended it a bit due to the site being down a bit yesterday.
 
Weird - I just voted too. It's 9am in the UK and 2am in Vancouver - I wonder if their tech person is in bed and hasn't switched it off!

  • REACH FOR THE RAINBOW ONTARIO71804
  • Alberta Animal Rescue Crew Society67958
  • MOUNTAINAIRE AVIAN RESCUE SOCIETY29921
  • NATIONAL ME/FM ACTION NETWORK28446
  • SALTHAVEN WILDLIFE REHABILITATION AND EDUCATION CENTRE INC.14935
 
Huh, 1/3 = 33%, so if you drop more groups out, shouldn't the percentage increase and not decrease?

GG
Removing the votes of the winners on the first two rounds does increase the percentage chance very slightly, as I've mentioned a couple of times, but I think the effect would be very small and I still haven't figured out how you would calculate that.

But the 1/3 is based on a common error in probability: simply adding 1/9 + 1/9 + 1/9 is wrong. Instead you have to combine the probability of losing on the first draw with winning on the second, and losing on the first and second with winning on the third.

So, overall probability of winning is:

p(Win on 1st Round)
OR
p(Lose on 1st Round) AND p(Win on 2nd Round)
OR
p(Lose on 1st Round) AND p(Lose on 2nd Round) AND p(Win on 3rd Round).

Which equals:

1/9
+
8/9 * 1/9
+
8/9 * 8/9 * 1/9

As mentioned, the three fractions on the right of the above need to adjust very slightly (in our favour) based on the expectation of the number of votes removed from the hat when the 1st and 2nd rounds are won. But I think that will be a very small effect, adding 0.1 or so to the overall probability.

A couple of ways to help understand/persuade people of the fallacy of calculating this as 1/9 + 1/9 + 1/9.

1. What if there were 9 draws? If this method worked, then you would have a probability of 1, i.e. certain success. So clearly it doesn't work that way.

2. Calculate the probability of not winning any of the draws: disregarding the votes removed for the winners of the first two rounds, that would be 8/9 * 8/9 * 8/9 = 70.23%. So the probability of winning one of the draws is 1 - 0.723 = 29.77%.

As I said above, you can add a little to that 29.77% for the expected size of the votes removed from the first two winners, but I don't think that would take it much above 30%. I haven't yet worked out the best way to include that effect in the calculation, but I think it must be based on the known probability distribution of the votes for the remaining charities.
 
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