Quantifying Risks

Weighing small risks without the need for big numbers

There are many broad ethical and social issues in emerging technology. The most robust approach to many of these may involve a public given access to reliable quantitative information about risks and uncertainties, and trained in how to take informed responsibility for their own choices (as both consumers and voters) therewith.

Surprisal in bits (defined by probability = 1/2#bits) might be useful to citizens in assessing risk and/or standards of evidence, because of its simple, intuitive, and testable ability to connect even very small probabilities with one's experience at tossing coins. For example, the surprisal of dying from a smallpox vaccination (one in a million) is about 19.9 bits (like 20 heads in 20 tosses), while the surprisal of dying from smallpox once you have it (one in three) is only about 1.6 bits (i.e. more likely than 2 heads in 2 tosses). Thus surprisal: (i) has meaning which is easy to remind yourself of with a few coins in your pocket, (ii) reduces huge numbers to much more intuitive size, and (iii) allows one to combine risks from independent events with addition/subtraction rather than multiplication/division. For example, from above your chance of dying is decreased by getting the vaccination, as long as the surprisal of getting smallpox without the vaccination is less than 20 - 2 ~ 18 bits. That means that vaccination is your best bet (absent other information) if your chances of being exposed to smallpox are greater than those of getting 18 heads in 18 tosses (1 out of 218~333,333).

Given the large difference between something with 2 bits of surprisal and something with 18, communications bandwidth might be better spent by newsmedia providing us with numbers on observed surprisal, rather than by reporting only that "there's a chance" of something bad (or good) happening. Saying the latter treats your audience as consumers of spin rather than information. Likewise, use of surprisals in communicating and monitoring risks to medical patients could make patient decisions about actions with a small chance of dire outcomes as informed as possible. This could reduce the costs of medical malpractice in the long run by empowering patients with tools to make informed and responsible choices, making the need for legal redress less frequent. Who knows: Some might even enjoy surprisal data on various lottery and gambling opportunities, rather than an exclusive focus on "the size of the pot".

Compare to what we have now: Journalists often leave observations (when available) out of their reports as though their audience isn't up for numbers, thus reporting mainly inferences instead. Michael Crichton, oft cited as an alarmist in such articles, for example offered a lay view of some shortcomings of the resulting consensus science (in place of tested observations) that such journalists promote. Media treatments of creationism also show that to those who treat science as "consensus about describing the world", rather than as "guidance for observers", nature's voice is irrelevant and postmodernist views of idea-hegemony actually do apply. The result: A communication network that treats its individual "nodes" as beasts that migrate from one scare to the next. It may be better to treat them as citizens, whose ability to make informed decisions from their own observations is of crucial importance.

What do you think? If such data were reliably available, some understandable tutorials (and simple web calculators) for use of data on surprisals could be quite handy for consumers. Although the probability of statistically-independent events (used in the applications of surprisal discussed above) is well understood, multiple coin tosses are also the subject of the infamous St. Petersburg game which no casino (as far as I know) has had the chutzpah to offer for an extended period in open-ended form.

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