Equality by lot

I would rather be governed by the first two thousand people in the Boston telephone directory than by the two thousand people on the faculty of Harvard University.

— William F. Buckley, Jr., 1965

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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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Posted as a comment by Ronald Mercer (coach1640280)

Narrative description:

Time: Not too distant future.
Setting: America after the second democratic revolution.
America has undergone a second democratic revolution where the constitution was significantly altered to adjust to new global economic, climate, and security (terrorism) conditions.
A constitutional convention was held. A new congress was formed, among other things, keeping the basic congressional house structure and reforming the senate by making it a chamber of 300 sortitioned senators serving 5 year terms.
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In his 1970 book, After the Revolution?, Robert A. Dahl suggests appointing by lot advisory committees for the president of the U.S., for congresspeople, for state governors and for large city mayors^[1]:

Let us imagine that the membership of each advisory council were to consist of several hundred constituents picked by the same procedures used to ensure randomness in modern sample surveys; that the citizen selected would be required to serve […]; that suitable provisions would insure against hardships arising from the obligation to serve – for example, the citizen selected would not only have all relevant expenses taken care of but if he (or she) were poor or unemployed he (or she) might receive a stipend, while an employed person would continue to receive his (or her) regular pay; that one would serve for a year and be ineligible for a second term; that a council might meet at intervals for a total of several weeks in the course of a year; that it would have its own presiding officer (and a professional parliamentarian); that it would invite the elected official to meet with it, to answer questions, hear the debate and discussion…

A timid thinker would have focused on making the argument supporting such an idea against “conventional critics” who would argue that “the proposal goes too far”. Dahl, however, dismisses those critics with one paragraph, and spends the rest of the discussion (pp. 150-153) arguing against “a less conventional critic” who argues that the proposal “does not go far enough” because it does not suggest using the lot to replace elections for selecting government officials.

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