One of the arguments against the validity of the Bayesian approach is that, in some cases, it’s hard to pin a precise number on a probability. When we can find good and relevant statistics to back up the assessment of a likelihood, this isn’t such an issue. But in the real world, some of the time we don’t have good numbers. Or we have the numbers on something similar to what we’re looking for – but not quite the same thing.
So what happens in those cases when we have to estimate the inputs?
One of the biggest problems we as humans have to overcome when thinking about complex problems is our set of innate cognitive biases. Evolutionarily speaking, we’ve developed a set of specific cognitive strategies to help us understand the world better and more efficiently – but they don’t come without serious trade-offs.
Buster Benson (of Better Humans) wrote a great article about the constellation of cognitive biases and categorized them according to what kind of mental problem they attempt to address. As he explains, these biases may have developed for a good reason, but they also introduce systematic mental errors into our reasoning:
Every cognitive bias is there for a reason — primarily to save our brains time or energy. If you look at them by the problem they’re trying to solve, it becomes a lot easier to understand why they exist, how they’re useful, and the trade-offs (and resulting mental errors) that they introduce.
Here’s a thought-provoking article by David J. Spiegelhalter and Hauke Riesch on how to deal with the unknown in a rational analysis—not just things we know are unknown, but deeper uncertainties.
Take, for example, the following case study:
Up to a certain point, humans have an intuitive understanding of basic probability. Toddlers can observe probabilistic patterns and grasp their meaning without any formal instruction, and we naturally use an internal process that approximates Bayesian inference to estimate physical states by combining previous knowledge with new sensory information.
Rootclaim is more objective and comprehensive than any other method of reasoning.
The Rootclaim system improves on other approaches by forcing each hypothesis to build a complete, unbroken storyline that explains all of the evidence without cherry-picking, or providing contradictory explanations to different pieces of information. By requiring each competing version of events to play out to its complete logical conclusion, Rootclaim conquers one of the most difficult weaknesses of mass mis-reasoning: allowing inconsistent, illogical, and incomplete explanations to masquerade as reasonable, coherent, and even convincing possibilities to those without the tools to break the arguments down and ensure mathematical and logical validity.
In mathematics there is a unifying language that links past discoveries and current theories. We can take a complete block of previous scholarship, plug it into a block of new scholarship, and they will fit perfectly and exactly with one another.
The beauty of mathematics as a system of knowledge is that it allows us to deal with complex problems by building on past knowledge. Once someone formalizes their findings in a proven mathematical model, the whole scientific community can seamlessly integrate it into their research and reach a better understanding of the world we live in.
For example, once Pythagoras proved that a2 + b2 = c2, other mathematicians could use that formula whenever they encountered a right triangle, without having to prove it again each time.
Today’s world is complex. To make sense of it, we have to take in – and filter out – a huge amount of information. The problem is, it’s incredibly difficult to get to the bottom line when there’s so much noise to sift through.
Reporting is often biased. Governments, politicians, businesses, news organizations and interest groups can easily cherry-pick the evidence, giving you an incomplete or inconsistent picture of reality. If a story makes splashy headlines, or advances a certain political and/or financial agenda, then you’re more likely to hear about it.
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