::  Posts  ::  RSS  ::  ◂◂RSS  ::  Contact

Negative "eeny meeny miny moe"

August 19th, 2019
kids  [html]
As a kid, I learned the rhyme as:
Eeny, meeny, miny, moe,
Catch a tiger by the toe.
If he hollers, let him go,
Out goes Y, O, U!
Since kids can't predict where it will end, and adults are not supposed to try, it's a reasonably fair way of drawing lots.

At times I've heard versions where the selected person wins instead of loses, and while with two kids it doesn't matter, with three or more it matters a lot!

Let's model each kid having a choice at each stage between "accept" and "protest". While protesting probably doesn't work, if enough of you protest it might. If you do the positive version, where the selected kid wins, the winner accepts but the others may choose to protest. This isn't good: everyone has reason to protest except the single winner.

On the other hand, with the negative version, where one kid is eliminated at once, it's the other way around. When the first kid is eliminated they may protest, but the other kids all accept because then they retain their chance to win. With each successive round the dynamic is the same, plus the already-eliminated kids all choose accept out of a desire for fairness. Even with the last elimination there's still only one person choosing protest.

The iterative process is O(n) instead of O(1), but it also works much better because it keeps a majority for "accept" at each stage.

(If you have a very large group of kids, then I could imagine a O(log(n)) version being worth the added complexity. Divide the kids into three groups, and do negative eeny meeny miny moe on the groups. A third of the kids may protest, but you've still got two thirds accepting. Then redivide those remaining two thirds into three groups, and keep going.)

Comment via: facebook, lesswrong

Recent posts on blogs I like:

Pieces of time

My friend used to have two ‘days’ each day, with a nap between—in the afternoon, he would get up and plan his day with optimism, whatever happened a few hours before washed away. Another friend recently suggested to me thinking … Continue reading →

via Meteuphoric November 11, 2019

Mauerfall

The Berlin Wall fell 30 years ago. I feel weird about where I’m writing this post from. I was expecting to be writing this from Berlin, after visiting the commemorations. But I’m visiting Boston (and New York) right now and the connotation of talking abou…

via Pedestrian Observations November 10, 2019

Wild animal welfare in Hans Christian Andersen

Continuing the theme of wild animal suffering in children’s lit… Hans Christian Andersen’s stories involve a lot of suffering of both human and animal varieties. “The Ugly Duckling” takes a brief detour from describing the duckling’s repeated social humil…

via The whole sky November 7, 2019

more     (via openring)

More Posts:


  ::  Posts  ::  RSS  ::  ◂◂RSS  ::  Contact