::  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:

Circumferential Lines and Express Service

In a number of large cities with both radial and circumferential urban rail service, there is a curious observation: there is express service on the radial lines, but not the circumferential ones. These cities include New York, Paris, and Berlin, and to s…

via Pedestrian Observations September 15, 2019

Reframing the evolutionary benefit of sex

From the perspective of an organism trying to propagate its genes, sex is like a trade: I’ll put half of your DNA in my offspring if you put half of my DNA in yours. I still pass one copy of my genes onto the next generation per unit of investment in chil…

via The sideways view September 14, 2019

Bear store

A preschool game that’s been particularly popular and versatile with my kids. Materials: Pennies Collection of counting bears or any other small objects One person is the storekeeper and sets out the bears in any way they want. The other people are custom…

via The whole sky September 9, 2019

more     (via openring)

More Posts:


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