Equality by lot

With the increasing frequency of the application of sortition in society, it has been rightly pointed out that a lack of strict criteria for the validity of the constitutive procedure of the body would allow sortition to be misapplied and manipulated so that its democratic value is annulled. Of course, there are many aspects to constituting political bodies and they all need careful consideration and standardization if we wish to achieve well-functioning democratic decision making. Here I want to advance criteria for standardization of just one aspect – one that is unique to allotted bodies – the allotment procedure.

For an allotment procedure to be considered well designed it should have the following characteristics:

1. Public statement of n, the number of people who are going to be allotted.
2. Public statement of the allotment pool – the set of people from whom the allotted will be selected. This statement should make it easy for every person in society to know whether any other person is included in the pool or not.
3. Public definition of an equal-probability allotment mapping. An allotment mapping is a mapping of each sequence of digits of length L, for some fixed number L, to a list of n people. The mapping is publicly well-defined if it is possible for anybody putting in reasonable effort to determine with reasonable accuracy, given a sequence of numbers, the people who correspond to that sequence. The mapping is equal-probability if the number of sequences which result in a list containing each person in the pool is between N₀ and N₁ for some fixed numbers N₀ and N₁, where N₁ / N₀ < 1.01.
4. A public definition of a procedure to generate a practically-random equal-probability sequence of L digits. A procedure for generating sequences of digits is practically-random equal-probability if there is a general acceptance that as the procedure is launched as far as anyone can determine every sequence among the 10^L possible sequences is equally likely to be the outcome of the procedure.
5. The random sequence procedure should be launched after the four public statements above were made. Its launch and applications must be public so that it is applied exactly once and once it is applied, its outcome (i.e., the sequence of digits it generated) is immediately public.

Other than the first criterion, all of these criteria are non-trivial to implement. There is, of course, some similarity to a prize lottery procedure, but there are some complications associated with the fact that each person must have exactly one “winning ticket” and of course with the fact that the prize – political power – could be of much greater value than any other lottery prize ever.

In particular, making sure that the digit sequence selection procedure is practically-random equal-probability is fraught with difficulties since any physical randomization device may potentially be rigged by powerful attackers. If you have ideas for rigging-resistant randomization procedures please post them in the comments.

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