Paper: No Stratification Without Representation

One fascinating aspect of sortition is that it treats all groups in the population fairly: If a group constitutes x% of the population, the group’s share in the panel will be x% in expectation (that is, on average over many random panels). Furthermore, it is unlikely that, in a random panel, this percentage will deviate much from x%; this event becomes ever less likely the larger the panel is. Unfortunately, there are practical limits to how large sortition panels can get, which means that a certain variance remains. Had the Irish citizens’ assembly been sampled without consideration for gender, for example, a gender imbalance of at most 45 women against at least 54 men would have happened in about 15% of random panels.¹

One way around this problem is stratified sampling. For example, 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 group will get its fair share of the panel in expectation. Stratification by gender will obviously ensure accurate representation to the genders. But what happens to the representation of other groups?

My collaborators — Gerdus Benadè and Ariel Procaccia — and I studied this question in a paper that we recently presented at the ACM Conference on Economics and Computation. As Mueller, Tollison, and Willett argued as early as 1972,² stratification can greatly reduce the variance in representation for groups that highly correlate with the feature we stratified on. This is good news since correlation is everywhere; for example, stratifying by gender will help to represent opinion groups related to military intervention, gun control, and healthcare.³ We show that there is no real downside to stratification: Even in the worst case, stratification cannot increase the variance of another group by more than a negligible amount. These results hold up to very fine stratifications, where each seat is filled by a random member of a dedicated stratum. This suggests that we should indeed make extensive use of stratification. In a case study on a real-world dataset, we show that stratification can reduce the variance in an opinion group’s representation by a similar amount as an increase of panel size by multiple seats — even if the stratifier does not know the opinion in question!

The main technical difficulty in the paper is working with indivisibilities. For instance, if we split the 99 seats of the Irish citizens’ assembly proportionally by gender, women should get around 50.66 seats. To ensure that every person is still selected with equal probabilities, we need to randomly “round” the seat assignments, giving women sometimes 50 and sometimes 51 seats. This process is somewhat delicate — rounding introduces new variance, which might lead to some unfortunate group becoming much less accurately represented than without stratification. If one uses the rounding procedure suggested in our paper, this is not the case.

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The Uses and Abuses of Sortition

Given that sortition is finally beginning to be taken seriously by politicians, academics and the mainstream media, some of us on this forum have expressed concerns about potential abuse. André has drawn our attention to the risk of politicians and public intellectuals using sortition to provide a patina of legitimacy to undemocratic practices — examples include Emanuel Macron’s ‘Great Debate’ — and there has been the usual concerns about the rich ‘n powerful using sortition to paper over the cracks of the electoralist oligarchy.

My own concerns are over the willingness of sortition advocates to assume that small stratified samples, in which participation is entirely voluntary, can represent the beliefs and preferences of all citizens. Leaving aside the size issue (most statisticians insist on a minimum of several hundred or even 1,000 for a representative sample) my principal concern is that the voluntary principle will significantly over-represent activists, “progressives” and those who want to change things, as oppose to the ‘silent majority’. The decision of the 2004 British Columbia Constitutional Assembly to change the voting system was overturned in the subsequent referendum, but this might well have been anticipated as only 4% of the original random sample opted for selection, thereby generating an unrepresentative sample (Warren and Pearse, 2008). My assumption here is that the decision not to participate might well be a sign of a conservative (small ‘c’) disposition.

Extinction Rebellion (XR) is a UK climate-change group which has gained a lot of publicity recently on account of its civil disobedience campaign, which brought much of  central London to a standstill in April. Their goal is zero carbon emissions by 2025, which would mean the banning of air transport and the removal of 38 million cars (both petrol and diesel) from the roads. In addition, 26 million gas boilers would need to be disconnected in six years.
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Schulson and Bagg: Sortition needs to become part of mainstream U.S. political discourse

Michael Schulson is a journalist who has written before about sortition. Schulson and Samuel Bagg, a democratic theorist at McGill University, have a new article about sortition in Dissent magazine. Here are some excerpts.

Give Political Power to Ordinary People

To fight elite capture of the state, it’s time to consider sortition, or the assignment of political power through lotteries.

Our broken campaign finance system is a longstanding target of progressive ire. And as Republican state legislatures have made increasingly aggressive moves to entrench minority rule, many people are beginning to see a broader defense of democratic integrity as a crucial part of any left agenda. Yet most of the attention of reformers has been limited to the electoral process—perhaps because we tend to assume that getting “our people” into office will solve the problem.

It won’t. Elite capture of the state extends far beyond the influence of large donors on elections.
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Sortition in the New Yorker

Another step in the thousand mile march: Sortition is positively featured in the second paragraph of Masha Gessen’s article in the New Yorker. The oligarchical nature of elections is rather matter-of-factedly asserted:

The concept of democracy rests on the premise that any citizen is a potential member of government. The ancient Athenian choice of sortition—the selection of government by lottery—was based on the understanding that elections would inevitably favor the aristocracy, and in a democracy the government should be a mirror of the governed. The American system has proved the Athenians right. Access to our electoral system is determined by the candidates’ ability to attract financial contributions. The contest itself is rigged in favor of the white, the highly educated, and the privileged—those who reproduce the class, race, and style of their predecessors.

Criteria for the acceptability of an allotment procedure

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 10L 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.

Scotland’s opposition parties attacking the government’s citizen assembly proposal as untrustworthy

The National reports:

Citizens’ Assembly: Scotland in Union tells Scots to stay away
By Andrew Learmonth

SCOTLAND’s staunchest Unionists are trying to kibosh the Scottish Government’s plans for Citizens’ Assembly before they’ve even started.

Scotland in Union has warned Scots to stay away, saying they’ll be “misused” for independence.

Nicola Sturgeon announced the initiative back in May, saying the Government was keen to follow the example of Ireland where the assemblies were used to find consensus on reforming Ireland’s abortion laws. [Details.]

But the Tories and the LibDems have already said they don’t want to be involved, calling the assemblies a “stunt to kick-start the conversation about independence”.
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Bradatan: Today’s democracy favors the the power-hungry, arrogant, oppressively self-assertive political animal

Costica Bradatan, professor of philosophy at Texas Tech University, has a free-ranging essay about democracy in the New York Times. It is a rather incongruous mass of ideas, some more convincing than others. It does mention (approvingly? hard to tell) sortition as one of the fundamental foundations of Athenian democracy.

The institutions of democracy, its norms and mechanisms, should embody a vision of human beings as deficient, flawed and imperfect.

Ancient Athenian democracy devised two institutions that fleshed out this vision. First, sortition: the appointment of public officials by lot. Given the fundamental equality of rights that all Athenian citizens — that is, free male adults — enjoyed, the most logical means of access to positions of leadership was random selection. Indeed, for the Athenian democrats, elections would have struck at the heart of democracy: They would have allowed some people to assert themselves, arrogantly and unjustly, against the others.

The other fittingly imperfect Athenian institution was ostracization.

Bradatan notes how different is the modern system that self-describes itself as “democracy”:
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