Equality by lot

One of Dahl’s objections to an allotted parliament is that “as anyone familiar with the laws of probability knows”,

the chances are by no means negligible that a sample of five hundred might deviate by a considerable margin from the mean of the whole population, occasionally we might find ourselves with a highly unrepresentative legislature subject to no authority except the next lottery.

He adds: “I cannot think of a better way to discredit the idea and democracy itself.”

Joel Parker, following Peter Stone, points out that, in reality, the laws of probability show quite the opposite. In fact, when using simple random sampling, the chance that a sample of 500 people will have a majority of members from a group that makes up 45% of the population is merely 1%. If the group makes 40% of the population, that chance drops to less than 3 in a million. That group can be defined geographically, ethnically, ideologically, or by any other characteristic – it is still very unlikely to command a majority in an allotted parliament unless it has a majority in the population, or is very close to having such a majority.

Still, one could ask for more, and find one’s request fulfilled. By using a stratified sample – i.e., a sample which allocates a fixed number of seats to pre-identified groups – one can assure exact representation of those groups (that is, having their proportion in the sample be identical, up to rounding, to their proportion in the population). This can be done without giving up the requirement of equiprobability (i.e., the requirement that each person has the same chance of being picked). For example, if representation of geographical areas is considered important, the country can be divided into geographical units, each containing the same number of people, and have one person allotted from each unit. In a similar way, exact representation by any characteristic – whether objective or self-identified – can be obtained.

It is interesting to note that, unlike a majoritarian system, stratification in a sortition system is not prone to gerrymandering. No group can expect to increase its representation by changing the stratification units. The only effect of such a system is to reduce the variation along a certain characteristic of the sample – the expected proportion in the sample is always the same.

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