Statistics: Posted by katastrofa — Yesterday, 10:38 pm

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Sewage hits dozens of beaches in England and Wales after heavy rain

https://www.bbc.com/news/science-environment-62574105

https://www.bbc.com/news/science-environment-62574105

Statistics: Posted by tagoma — Yesterday, 8:53 pm

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Monty Python only reactivates when John Cleese needs to pay for his next divorce. His words.

“The lucky, lucky bastard.”Statistics: Posted by Paul — Yesterday, 8:17 pm

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https://www.bbc.com/news/science-environment-62574105

Statistics: Posted by Cuchulainn — Yesterday, 8:01 pm

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The problem of optimal resource allocation is solved by assumption in the proof by requiring perfect information and complete markets for every conceivable future contingency. This perfect endowment means that every future contingency can be planned and hedged in a one-time (T=0) grand auction market (which sounds very ironically exactly like the work of a lone social planner!) that is so perfect (bow before its majesty!) one trades at T=0 to cover all future contingencies, and therefore there is no need for credit and even money in this marvelous capitalist world.

So, yes, there is a mathematical foundation, it is a proof determined by assuming all the issues away. Paul Samuelson's warning so long ago about the dangers of strong axioms was clearly not heeded.

Statistics: Posted by DavidJN — Yesterday, 6:28 pm

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Thanks, but I'm looking for mathematical analysis of the such optimal solutions and proofs of their existence. I went through matching problems (stable marriage/Gale-Shapley, etc.) and optimal choice theory, but they don't refer directly to Smith, Hayek and faire tales.

Did Smith think about beneficial solution in Pareto sense, or a solution in which all individuals' needs are "saturated" (loss-less compression algorithms are the kind of optimisation I have in mind)? That's the kind of questions I have on my mind, and once clarified, how I want to approach answering them (mathematically or numerically).

I doubt it can be cast as a mathematical problem.Did Smith think about beneficial solution in Pareto sense, or a solution in which all individuals' needs are "saturated" (loss-less compression algorithms are the kind of optimisation I have in mind)? That's the kind of questions I have on my mind, and once clarified, how I want to approach answering them (mathematically or numerically).

Statistics: Posted by Marsden — Yesterday, 6:10 pm

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However, "Pareto optimality" can be far from a "solution beneficial for everyone" in your OP.

For example, Elon Musk can consume all the output and that can be Pareto optimal, as taking output from him and allocating it to others may lower his utility. However, Pareto optimality seems a useful notion when there are wasted resources, barriers to competition, unnecessary regulations, etc.

I am not an economist, so I'm sure this is only part of a good answer.

Statistics: Posted by Alan — Yesterday, 4:19 pm

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It might be a bunch of basic stuff for you, but maybe some of the below might help:

- Economics: Arrow's Impossibility Theorem and this interesting paper https://ieeexplore.ieee.org/document/84 ... rs#authors

- Applied Ecology: good models survey https://www.nature.com/articles/s41559-020-01298-8#Bib1

- Complexity Theory: Porf Farmer's landing page http://www.doynefarmer.com/presentations

Rgds,

M

Statistics: Posted by Mercadian — Yesterday, 4:12 pm

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Statistics: Posted by katastrofa — Yesterday, 2:24 pm

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Statistics: Posted by tagoma — Yesterday, 11:30 am

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