Mathematical Structure of Probability Space — 1

0. Motivation

Honestly, I find the ubiquitousness of differences in probabilities (“… led to a 3.5% point increase …”) — in news media, Social Sciences and Data Science — an indication of thoughtlessness. I’ve had people tell me to add probabilities for event sets that do not belong to a partition.

1. Why do we need to compare probabilities?

Is the “algebra” of probabilities worth understanding?

Here are some questions that arise frequently:

  1. When is a dollar not a dollar? When is the same quantitative change not of the same “value”? E.g., if I, with say a 6 figure wealth, give a dollar to an indigent in Redwood City with possibly single figure wealth, do we both perceive the same change? Why not? How is this related to income or wealth distribution?

I hope that the above simple examples sufficiently motivate the need to understand probabilities and have provided some food for thought.

See later for more complex examples.

I stop to miau to cats.

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