Selecting a person from the crowd with a dice (or two).

Posted by Romain on

We use a single dice (or coin) in the current version of the method to randomly select a moderator. I employ the latter method for two reasons. Firstly,  the method is easily and practically feasible: everyone has a coin and on a lucky day one person has a dice. Secondly, the method stands midway between a list made of volunteers and an all inclusive list, since the (non-)volunteers can go sit either near or far from the coin/dice caster. The method can be easily explained and worked nicely during my previous experiments.

But, I recently thought about another method (see a former post). I called this second method the dichotomy method. The method consists in dividing the main group into subgroups. For instance, an even sized group can be divided in two, we pick the first for heads and the second for tails. You can then reiterate the process until we sort a single person. A dice enables to deal with situation for groups dividable in two or three subgroups. You face an unsolvable problem with prime numbers-sized groups as you need to have non-overlapping and equal subgroups  to guarantee that all people could be selected with the same probability.

I want in this post to introduce a third method called the enumeration method. This method works in a group with less than 36 people.  Someone casts two dices (or on die twice), of different colours one representing the unit and the other the tens (see illustration below enumerating all possibilities). We start counting from the caster (11 is the thrower then 12 up to 65, 66). If there are less than 36 people you can re-throw when you obtain a throw larger than the group size. The group might also contain 9 or 18 people, here a person respectively corresponds to three or two possible distinct throws.

One the left the prime numbers up to 2500. On the right, all the possible draws (36) with two dice. Romain Cazé CC-BY

For most situations a single dice already covers our needs. Groups of 6 are large enough for a lively discussion. A group larger than 36 becomes rapidly unmanageable.

Thank you for reading! If you have any other methods or suggestions or if you think we should only peak volunteers please comment below.

P.S.: thank you Ambre for the proof-reading.

Comment ( 1 )

  1. No thumb but a maximal time – The sortition blog
    […] To designate a new moderator we cast a dice. The nth person on the left of the caster becomes the moderator, n being the number on the dice. The person can decline this assignment any time -because everyone experiences fatigue- and before casting the thrower set a maximal time -to avoid dictatorship-. You don’t have a dice? You can use a coin then: heads, the first person on the left becomes the moderator; tails it’s the second. You are more than six and you want everybody to have the same chance to be moderator? Use two coloured dices following this method (details are here). […]