The Census and what does 'rare' mean?

Episode Summary

Executive Summary: This episode examines how statistics can mislead without context, using immigration forecasts, crime headlines, and the meaning of “rare” as case studies. It also features Nassim Taleb on black swans and antifragility, and closes with playful but data-driven answers about rat populations and infinity, reinforcing the show’s theme that numbers need caveats, language, and context to be meaningful.

Main Topics: Immigration forecasts and the limits of prediction (Priority: 5/5): The program revisits 2003 forecasts for migration from EU accession countries and shows how far they were from reality, largely because the underlying data were weak and policy reactions elsewhere changed outcomes. Crime headlines and population context (Priority: 4/5): It challenges headlines implying foreigners are disproportionately represented in London crime statistics by comparing suspect shares with the share of non-UK nationals in the city population. Nassim Taleb on black swans and antifragility (Priority: 5/5): Taleb argues that rare, high-impact events are inherently hard to predict, and that the better goal is to design systems that can absorb shocks or even benefit from them. What does “rare” mean? (Priority: 5/5): A listener question about rare disease and lightning prompts an exploration of how vague probability words map onto numbers, and why rare diseases can still affect millions when aggregated. When words are better than numbers (Priority: 4/5): Psychologists explain that words like ‘rare’ or ‘frequently’ convey not only frequency but also evaluative meaning and usefulness depending on context, while raw numbers can be unhelpful without background information. How close are we to rats? (Priority: 3/5): Using expert estimates of rat populations in homes, businesses, sewers, and farms, the program estimates Britain’s total rat population and a rough upper bound on distance to a rat in urban areas. What is the number before infinity? (Priority: 3/5): A children’s question is used to explain that infinity has no predecessor because any number can always be increased by one, contrasting finite countable quantities with the infinite.

Key Arguments: The 2003 forecast of 5,000-13,000 annual net migrants from new EU countries was badly wrong because it relied on scant data and assumptions about countries with no prior migration history. Forecasts were caveated in the original research, but politicians and media remembered the headline numbers rather than the uncertainty. Migration outcomes depended on other EU states’ border policies; when Germany closed its labor market, more migration was diverted to the UK. Headlines about foreign nationals and London crime can be misleading if they ignore the fact that non-UK nationals make up a similar share of the population. Taleb’s key argument is that predicting black swans is less useful than building systems that do not collapse when they occur. Taleb distinguishes prediction from decision: people should focus on actions where they bear consequences if they are wrong. Probability words such as “rare” are not merely sloppy numbers; they also convey evaluative and contextual meaning. Rare diseases are individually uncommon but collectively affect a large share of the population because there are many distinct rare conditions. Experts often should use words rather than numbers when audiences lack the background needed to interpret raw figures. The rat calculation shows how estimates can be built from multiple surveys and assumptions to produce an approximate but useful answer. Infinity is not a largest number; any candidate for the number before infinity can always be exceeded by adding one.

Data Points: Foreign-born residents in England and Wales: 7.5 million - Census figure discussed at the start of the program Increase in foreign-born residents since 2001: nearly 3 million - Growth in England and Wales foreign-born population Share of new arrivals from post-2004 EU countries: about 1 million (one third of the 3 million increase) - Portion of foreign-born growth attributed to newer EU member states Labour government forecast for net migration from accession countries: 5,000 to 13,000 per year - 2003 estimate cited as badly underestimated Forecast total after 11 years at upper bound: 91,000 - What the forecast would have implied by the time of the episode Estimated diverted migration to the UK from Germany’s border decision: up to about 70,000 net migrants - Christian Dustmann’s explanation of diverted flows Migration Watch alternative forecast: 40,000 per year - Pressure group’s criticism of the official estimate London population that is non-UK nationals: 24% - Used to contextualize crime-headline statistics European rare disease definition: fewer than 0.05% of the population, or 1 in 2,000 - Formal threshold used by UK and EU authorities People in Europe suffering from a rare disease: 6-8% of the population - Shows how many people are affected across all rare diseases Total rare disease sufferers in Europe: about 35 million - Approximate aggregate number referenced in the discussion Meaning of ‘rarely’ in Neil Stewart’s study: about 8% chance - Typical numerical interpretation of the word rarely Meaning of ‘toss-up’: 47% chance - Example from the verbal-probability scale Meaning of ‘always’: 94% chance - Top end of the verbal-probability scale Meaning of ‘very high confidence’ in IPCC terminology: at least 9/10 chance - Example of formalized verbal probability language Meaning of ‘medium confidence’ in IPCC terminology: 5/10 chance - Another example from the IPCC lexicon Rats in dwellings inside homes: less than 0.5% of dwellings - Survey-based estimate of indoor rat presence Dwellings with rats outside: around 3% - Used to estimate rat presence around homes Rats around dwellings in Britain: about 1.5 million - Estimated total around homes Commercial premises in Britain: 1.8 million - Base number used for rat estimate in commercial settings Commercial premises with rats: around 5% - Survey result for businesses and shops Rats around commercial premises: about 200,000 - Estimated total in commercial environments Sewer area in Britain: around 16,000 square kilometres - Basis for sewer rat estimate Sewers with rats present: around 5% - Survey estimate Rats in British sewers: about 1.6 million - Estimated sewer rat population Rats in and around urban environments: around 3.1 to 3.5 million - Combined urban rat estimate Agricultural premises in Britain: around 200,000 - Base for rural rat estimate Agricultural premises with rats: around 40% - Survey figure Average rats per affected farm: around 90 - Used to compute rural rat population Rats in rural Britain: around 7 million - Estimated farm and countryside rat population Total rats in Britain: around 10.5 million - Combined urban and rural rat estimate Human population of Britain: around 60 million - Used to compare humans and rats Human-to-rat ratio: about 6:1 - Humans outnumber rats in Britain according to the estimate

Pivotal Quotes: "There are events that are very hard to predict, nearly impossible to predict, and can carry massively large consequences." — Nassim Taleb: Explaining black swans and why prediction often fails "By definition, an anti-fragile system has to use errors as fuel." — Nassim Taleb: Defining the concept of antifragility "What you really want to know is, am I going to be able to wait and still get a ticket?" — Linda Moxie: Why words like ‘plenty’ can be more useful than raw counts in context

Implications: Listeners are reminded to treat headlines and forecasts skeptically, ask what context is missing, and prefer communication that matches the audience’s knowledge. In policy, risk, and science, uncertainty and language matter as much as raw figures.