General Discussions

Cromwell and the Probabilities

Cromwell’s states that the use of prior probabilities of 0 (“the event will definitely not occur”) or 1 (“the event will definitely occur”) should be avoided, except when applied to statements that are logically true or false.

As stated in referred documents and popularly cited,

In 1650, after the Scots proclaimed Charles II as king during the English Civil War, Oliver Cromwell made a famous appeal to the Church of Scotland urging them to see the error of their royal alliance, he pleaded,

I beseech you, in the bowels of Christ, think it possible that you may be mistaken.

The Scots rejected the appeal, and Cromwell invaded Scotland in response.

What the rule means is that the statements like, “Elephant is going to talk some day”, “Sun will never rise someday”, and “Moon is made of cheese” etc should not be assigned with a probability of zero. Instead it can be a small number like 1 in a million.

This concept can be smoothly applied to e-commerce recommendations. Like we cannot say that a television set is not related to a shaving cream. They could be part of a recommendation with a weaker probability. We never know who in the universe would prefer to sit in front of TV and get the shaving done and when might that turn into to a larger trend.

However it does not mean that it has to be part of recommendation system results. It would clutter the screen with too many results. It is to convey that they can all be part of background results and the algorithms is intelligent enough to learn with time and carefully move from background result to main result while at need.

[1] Carlyle, Thomas, ed. (1855). Oliver Cromwell’s Letters and Speeches. 1. New York Harper. p. 448.
[2] Jackman, Simon (2009) Bayesian Analysis for the Social Sciences, Wiley. ISBN 978-0-470-01154-6

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