CCSearch State Space Algo

While toying with automated Fantasy Sports trading systems, I ended up designing a rapid state search algorithm that was suitable for a variety of constrained knapsack-like problems. Here is a discussion of the algorithm and a link to a reference implementation on github.

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MusingK.M. Halpern
Two-Envelope Problems

In this piece we play with two incredibly counterintuitive puzzles involving a pair of envelopes which contain unknown amounts of money. First we describe a famous fallacy when it is known that one envelope contains double the money in the other. Then we discuss an actual mechanism (probably first discovered by Thomas Cover in the 70’s) for achieving a better than 50-50 chance of picking the larger amount. This latter is one of the most stunning puzzlers in probability theory, and we dissect precisely what is going on there.

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NotesK.M. Halpern
How 22% of the Population can Rewrite the Constitution

This is a scary piece in which I analyze precisely how many voters would be required to trigger a Constitutional Convention and ratify any amendments it proposes. Because the 2/3 and 3/4 requirements in the Constitution refer to the number of States involved, the smaller States have a disproportionate effect. In Congress, the House counterbalances this – but for a Constitutional Convention, there is no such check.

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MusingK.M. Halpern
A Travel-Time Metric

Especially in urban areas, two locations may be quite close geographically but difficult to travel between. I wondered whether one could create a map where, instead of physical distances, points are arranged according to some sort of travel-time between them. This would be useful for many purposes.

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MusingK.M. Halpern
Probabilistic Sentencing

I propose adopting a sentencing mechanism based on a probabilistic assessment of guilt or innocence. This allows jurists to better express their certainty or lack thereof than does our traditional all-or-nothing verdict.

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MusingK.M. Halpern
A System for Fairness in Sentencing

We often hear of cases that offend our sense of fairness – excessive sentences, minor crimes that are punished more severely than serious crimes, or two equivalent crimes that are punished very differently. We consider the question of whether mathematically a well-intentioned individual can assign sentences in a way that seems reasonable and consistent to him.  

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MusingK.M. Halpern
Influence in Voting

Have you ever wondered what really is meant by a “deciding vote” on the Supreme Court or a “swing State” in a presidential election? These terms are bandied about by the media, but their meaning isn’t obvious. After all, every vote is equal, isn’t it?

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MusingK.M. Halpern