Recently, the Irish Government established the Citizens’ Assembly, a body of 99 citizens that will consider a number of constitutional issues. The Assembly meets on Saturday to continue its deliberations on the Eighth Amendment to the Constitution, which concerns the ban on abortion. It will report to the Oireachtas (Parliament) on this issue in June [TM106 or search for “thatsmaths” at irishtimes.com].
The assembly comprises the chairperson and 99 registered voters. Red C Research and Marketing Ltd was selected by tender to provide the representative body of 99 members. The goal was that the assembly would be broadly representative of the State’s population. More specifically, the 99 members were chosen to be representative of the Irish electorate in terms of gender, age and regional spread.
A list is available on the official website (www.citizensassembly.ie) giving the names and counties of the members. A reader of “That’s Maths” has observed that a significant number of counties are absent from this list. Of the 26 counties of the Republic, there are assembly members from just 16, with none from the remaining ten counties.
Assembly Members by County
As this seemed surprising, I asked my colleagues in the UCD School of Mathematics and Statistics, Nial Friel and Alan Benson, if they could estimate the probability of the observed assembly membership arising, assuming that the selection process was truly random; that is, if the probability of choosing someone from each county were proportional to the number of voters in that county. Their report is referenced below (Benson and Friel, 2016).
Since the boundaries of the parliamentary constituencies do not all coincide with county boundaries, the country was divided into 22 areas, each with a known number of voters. These closely correspond to counties or pairs of counties: Carlow-Kilkenny, Cavan-Monaghan, Longford-Westmeath and Sligo-Leitrim. Amongst the selected assembly members, 16 areas are represented and six are not. The six “missing areas” include ten counties, as shown on the map.
Number of Assembly members by county (November 2016). Ten counties are without any representatives.
Monte-Carlo Simulation
The outcome of simple random sampling is modelled by a probability distribution called the multivariate hypergeometric distribution. By repeatedly selecting 99 voters randomly from the electorate, an ensemble of “virtual assemblies” is generated. This is called Monte-Carlo simulation, reflecting the crucial role of chance in the procedure. The ensemble of assemblies is then analysed to estimate the probability of the spread of assembly members actually observed.
To give everyone an equal chance, 99 voters were sampled randomly from the 3.3 million electors. Then each was mapped to an area and the number of areas was recorded. The UCD statisticians generated one million sets of 99 members. From these, the probability distribution of the number of “missing areas” was calculated.
Distribution of number of areas not represented in an ensemble of 1,000,000 virtual assemblies. Probability of 6 or more is 0.0155% .[Image courtesy of Alan Benson and Nial Friel]
Only 1% of the ensemble members had five or more of the 22 areas unrepresented. Only 155 of these had six or more areas unrepresented. This gives a tiny probability – about one in six and a half thousand – of the observed pattern occurring in a truly random process.
It must be stressed that the method described here is not that used by Red C Research, which is explained in part in a document on the assembly website [ PDF ]. Red C incorporated constraints to ensure gender balance and spread amongst socio-economic groups. They appear to have employed a hybrid method with a random component but including systematic aspects in the interests of balance.
Notwithstanding this, the absence of representatives from so many counties does point towards an unintended bias.
Source
Benson, Alan and Nial Friel, 2016: Statistical analysis of the formation of the Citizens’ Assembly. UCD School of Mathematics and Statistics [ PDF ]
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That’s Maths, with 100 articles, has just been published by Gill Books. Available from
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