Stratified sortition

Posted on May 13, 2010 by Yoram Gat

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.

Filed under: Sortition |

7 Responses

lysias, on May 21, 2010 at 7:05 pm said:

For anybody worried about the chances that a sample of 500 may be distorted (and, as the poster points out, those chances are already very small indeed,) you just have to increase the size of the sample to, say, 1,000, and the chances become so minuscule that they can be safely ignored.

The chances of a skewed result from elections are obviously much, much greater.

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Yoram Gat, on May 21, 2010 at 7:30 pm said:

lysias,

I think there are good reasons not to let the allotted chamber grow beyond a few hundred – even 500 may be too big. Once the decision group becomes too big, the pathologies of mass politics begin to assert themselves. Pretty soon you are where you started before the allotment.

I think there are two factors of importance here:

1. The decision power of each member of the chamber must be high enough so that it serves as a good motivation for the members to invest the intellectual and emotional effort needed to arrive at informed decisions.

2. The group has to be small enough to allow personal acquaintance with the members of the group and an all-to-all mode of communication. Once most communication flows through some centralized channels, those who control those channels become a powerful elite.

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Common Lot Sortitionist, on February 10, 2014 at 7:05 pm said:

[…] exact representation by any characteristic – whether objective or self-identified – can be obtained.[…]

It seems to me that ‘self-identified’ characteristics would be problematic. There are so many multiple ways of defining oneself: ethnically, economically, ideologically, etc. Whatever box one might check would ultimately be idiosyncratic. Would it not?

Thus it would seem that only the geographic stratification would be acceptable … particularly if an allotted House of Representatives, for instance, were to replace the representatives from geographically determined Congressional districts of today.

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Jacob Richter, on February 10, 2014 at 9:47 pm said:

I’ve been a strong supporter and advocate of stratified sampling as the basis for sortition, but I think this is best served in party-political structures:

https://equalitybylot.wordpress.com/2012/08/23/party-policies/

“Policy proposals [should] be the exclusive domain of expert bodies filled by random selection, with the general body being left to vote up or down on each line of every policy proposal. In other words, I put forward stratified sampling.”

“A certain degree of expertise is required for any given policy proposal / plank / demand / etc. included in the final document. Shouldn’t that expertise be recognized formally, in the form of program committees (preferably, of course, with randomly selected memberships) having the exclusive authority to suggest any policy proposal / plank / demand / etc. while some broader organizational congress / conference / convention having mere up and down votes?”

“This does not preclude the broader membership from participation in the brainstorming of what will be submitted to the congress / conference / convention, but again this is a recognition of the expertise needed for policy proposals / planks / demands.”

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Jacob Richter, on February 10, 2014 at 10:22 pm said:

I hereby revise my Party Policies comment made on August 25, 2012 at 2:54 am:

“Qualification examinations should combine multiple-choice questions, short-answer questions (or longer questions, each consisting of a few short-answer questions), mathematical problems, and case studies.”

Should be

“Qualification examinations should combine objective format questions, short simulations (including those consisting of a few short-answer questions), mathematical problems, and case writing.”

MCs are too cheap, short simulations test what writers are able to *do* more effectively than knowledge-based short-answer questions, and case writing is a lot less hazy than generic case studies.

Also, I don’t think I organized my list of left-oriented areas above well enough. Communications is just one pervasive or soft skillset, while the other seven are knowledge skillsets. I hereby list the qualification skillsets as follows:

Political Conduct (pervasive skillsket which promotes integrity and prohibits bullying, making sexist or ethic remarks, purely self-serving activities while doing political work, etc.)

Decision-Making Process (pervasive skillset which includes problem solving)

Communication (pervasive skillset ranging from making presentations using technology to case writing ability)

Self-Management (pervasive skillset ranging from improving one’s own work to seeking help from fellow experts and other comrades)

Group Interaction (anti-bullying, anti-sexism, and other behaviour falls more under Political Conduct, while Group Interaction is the pervasive skillset of one’s ability to work with others overall, and not just in teams)

Labour law (knowledge skillset)

Labour history and/or “critical labour history” (knowledge skillset)

Labour economics and/or “critical labour economics” (knowledge skillset)

Heterodox economics (knowledge skillset that includes the MMT / Post-Keynesian school)

Political economy (knowledge skillset that critical enough of “economics,” but this is needed these days before being critical of “political economy” once more)

Democratic theory and general political science (knowledge skillset with, again, the possibility of “critical,” and one very recent work on this is Paul Lucardie’s “Democratic Extremism”)

Sociology and/or “critical sociology” (knowledge skillset)

Note that, nowhere in the above list is any mention of philosophy. Though it has relevance for the last three knowledge skillsets, the absence of philosophy is in accordance with the axiom on interpreting the world vs. changing it. Sorry, Badiou, Negri, and Zizek.

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Jacob Richter, on February 10, 2014 at 10:33 pm said:

To be qualified for selection into a policy proposal body relating to the above, individuals would have to have all three pervasive skillsets, be skills experts in labour law or labour economics (which helps with careers outside political work), be skills experts in two areas other than labour law or labour economics, and show skills breadth in all other areas.

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Paper: No Stratification Without Representation | Equality by lot, on July 24, 2019 at 4:42 pm said:

[…] one could fill half of the seats with random women and half of them with random men. As Yoram wrote in an earlier post on this blog, one can still guarantee that every person is selected with equal probability, and thus, that every […]

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