::  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:

Empire State High- and Low-Speed Rail

If Swiss planners were hired to design an intercity rail network for New York State, they might propose something that looks like this: The trip times depicted on the map are a few minutes longer than intended, especially next to a terminus station like N…

via Pedestrian Observations January 27, 2020

Hedonic asymmetries

Creating really good outcomes for humanity seems hard. We get bored. If we don’t get bored, we still don’t like the idea of joy without variety. And joyful experiences only seems good if they are real and meaningful (in some sense we can’t easily pin down…

via The sideways view January 26, 2020

Live the questions now

Here’s some advice that my Godmother, Lynne Caldwell, gave me a few years ago. I found it again the other day and it struck me that at least I understand its wisdom now. She really did get my problem. It feels like he’s speaking directly to me. It’s from …

via Holly Elmore January 23, 2020

more     (via openring)

More Posts:


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