50% chance of doing X

This is a bit abstract and it follows on from this previous post about voting demographics.

Let’s say you’ve got a statistical model that predicts a person Z with Y characteristics has a 50% chance of doing X. The actual percentage doesn’t matter but 50% is a nice amount of measurable uncertainty — maximally knowing that we don’t know what person Z will do about X given the context of Y.

Empircally, the data would be looking at lots of Y people and seeing they do X 50% of the time. However, note that there’s a big and important distinction here between two extremes.

  1. Half of Y people do X and half of Y people don’t but those two halves are distinct. This implies that Y isn’t really the relevant factor here and we should be looking for some other feature of these people that better explains X behaviour.
  2. Y people do X half of the time randomly. That is Y people are essentially a coin toss with regards to X. In that case Y isn’t great for predicting whether people will do X but it is really relevant to the question (particulalry if W people behave more decisively).

In the demographic voting model and taking a figure of say 80%:20% for atheists splitting between left and right, I suspect this is a grouping where individuals have even less variability in their actual voting patterns. Some of that 20% will be Ayn Rand style atheists who are very committed to a right-wing viewpoint, rather than representing a 20% chance that a given atheist would vote Republican. However, that is not neccesarily true of other groups where the percentage may more closely represent a degree of individual variability.

 

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