Negative "eeny meeny miny moe"

August 19th, 2019
kids
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:

On Polarization

weirdmaxxing as a dating strategy

via Thing of Things March 14, 2025

Frozen meals are actually great

I cook most of my meals and am pretty frugal. I do a lot of meal prep (cooking in bulk), so I don’t have to cook every day in order to have food. But sometimes I run out of my meal prep or just want something different, and don’t have energy to cook somet…

via Home March 7, 2025

Breakfast Over February Break

Over February break I made breakfast for me and Nora three days in a row. Normally, my dad makes me, Nora, and Lily breakfast, but my dad and Lily were on a trip and my mom wasn't up yet so I was basically the only one in the house who was awake and cou…

via Anna Wise's Blog Posts March 1, 2025

more     (via openring)