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Bayes’ Theorem on Women in British Politics

First impression, GO: individual has long hair, excellent penmanship, watches HGTV, and studies Computer Science

Reflex reaction for most of us would probably be to lazily assume the stereotypes and guess that the individual is more likely to be female than male. However, when prompted to give more thought, we realize the under-representation of women in the computing field. The odds of picking a female studying Computer Science are notably lower than picking a male in the same area of study. But then what about those other descriptive points? Beyond making this a discussion of sexism and gender pigeonholing, to make a logical decision, we need to consider all facets of this individual and the likelihoods of the descriptions for each gender.

Where does this leave us statistically? If you were given all the time in the world, you’d probably be able to figure out some basic probabilities with Bayes’ Theorem.

The article introduces a similar example, one emphasizing the lack of female representation in British Parliament, and comments on the ease with which we may assume a Parliament individual with stereotypically female characteristics to be a woman. The author goes on to apply methods of Bayes’ Theorem to the situation.

Screen Shot 2015-11-12 at 11.22.27 PM

The formula can be broken down into layman’s terms:

  • The prior probability is the P[A] component of the fraction, which refers to our current understanding of the probability of A.
  • The posterior probability is P[A|B], what we know after developing a new understanding of the probability of A now that we know B has happened. It is the answer to the interaction of the two factors and is captured by the change from the prior probability of A to the posterior probability of A given B.

Tailored to this case:

Screen Shot 2015-11-13 at 12.32.46 AM

Note that “female” as P[A] refers to the individual actually being female, and “description” as P[B] refers to any outside information we may have about the gender distribution within British Parliament as well as the initial description we received of the individual, including his/her physical appearance, ability, and position in Parliament. As such P[female|description] is read “the probability of the individual actually being female given the initial description we received of the individual.

The application is such:

  • The prior probability is what we currently know about the ratio of men to women in Parliament, as well as any extra information we have about the sex distribution within British Parliament.
  • The posterior probability is the conviction of male or female that we ultimately decide based on calculated probabilities.

Although the article does not give us hard numbers to calculate a precise Bayes’ Theorem probability, we gesticulate that it heightens ambiguity in the sex of the individual by offering us supplementary information, so we no longer work off of baseless stereotypes. Initially seeming to be a commentary on inequality in British Parliament, the article finishes off with a high rating of Bayes’ Theorem, attributing the formula as making the expulsion of doubt possible in situations where little is certain.

Source: http://thebrainbank.scienceblog.com/2015/10/26/bayes-and-girls/

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