Guessing Pareto Solutions: A Test

In yesterday’s post, I described a simple multiple-criterion decision problem (binary decisions, no constraints), and suggested a possible way to identify a portion of the Pareto frontier using what amounts to guesswork: randomly generate weights; use them to combine the multiple criteria into a single objective function; optimize that (trivial); repeat ad nauseam. I ran …

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Guessing Pareto Solutions

One of the challenges of multiple-criteria decision-making (MCDM) is that, in the absence of a definitive weighting or prioritization of criteria, you cannot talk meaningfully about a “best” solution. (Optimization geeks such as myself tend to find that a major turn-off.) Instead, it is common to focus on Pareto efficient solutions. We can say that …

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Can Life emerge spontaneously?

It would be nice if we knew where we came from. Sure, Darwin’s insight that we are the product of an ongoing process that creates new and meaningful solutions to surviving in complex and unpredictable environments is great and all. But it requires three sine qua non ingredients: inheritance, variation, and differential selection. Three does …

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Coin Flipping

I don’t recall the details, but in a group conversation recently someone brought up the fact that if you flip a fair coin repeatedly until you encounter a particular pattern, the expected number of tosses needed to get HH is greater than the expected number to get HT (H and T denoting head and tail …

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The Monty Hall Evolver

The Monty Hall problem is very famous (Wikipedia, NYT). It is so famous because it so easily fools almost everyone the first time they hear about it, including people with doctorate degrees in various STEM fields. There are three doors. Behind one is a big prize, a car, and behind the two others are goats. …

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Success, Ability, and all that

I came across this nice discussion at LessWrong which is similar to my old post Success vs Ability. The illustration below shows why even a strong predictor of outcome is seldom able to pick out the very top performer: e.g., taller people are on average better at basketball, but the best player in the world is …

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Wy do you believe?

If you say you believe in something, what is it that you mean by that? For example, if you say you believe you will find a hundred-dollar bill today, what is that belief built upon?I posit that what you actually believe (as opposed to what you say you believe) is really based on probabilities. Perhaps …

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Histogram Abuse

Consider the following Trellis display of histograms of a response variable (Z), conditioned on two factors (X,Y) that can each be low, medium or high: The combined sample size for the nine plots is 10,000 observations. Would you agree with the following assessments? Z seems to be normally distributed for medium values of either X …

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