Democracy and finance don't mix - the math involved

This all started on irc, as all good things. I think it's perhaps worthwhile to model the thing however, so here goes.

I. We will assume that the point of language is to state questions ; the point of reality to offer the basis on which those questions may be stated ; the point of thinking to propose processes through which answers may be derived from the questions and particular perceptions of reality ; the point of the passage of time to modify reality so that the correct answers to questions become apparent and finally that the point of history is to record previous questions, answering processes, and actual answers. While you could perhaps construct your own set of assumptions, I posit it as axiomatic that either it is reducible to the aforestated assumptions or else insane - in neither case the differences posing any sort of interest to the rational agent whatsoever.

II. At any point, the questions that can be stated will be noted as Q1, Q2... Qn, where the n is not finite. The corresponding possible answers will be noted as A1Qi, A2Qi.... AmQi, where m is not finite and i is a value between 1 and n. It then follows from this notation that all answers A1Qi... AmQi to a specified question i are equally likely to be the correct answer.

III. At any point, a population can be described as P1, P2... Pk, where k may be finite but doesn't really have to be.

IV. Time itself can be modelled as a succession of moments, T1, T2... Tl, where l may be finite but also doesn't really have to be. In principle T1 may be chosen as any arbitrary, convenient moment, just as long as it includes all the history of all included Ps. Obviously at various Ts different sets of AjQi may be active, but because n and m are not finite this requires no difference of notation, we'll simply keep separate track of which answers are available and to which questions at which times.

V. On any arbitrarily chosen set of Qs, an arbitrarily chosen set of Ps will recognise a certain, definite subset of As for each Q, at an arbitrary point in time T. Each individual P will further contain a history of a number of previous Ts, with an associated list of Qs and their associated As, in some cases with an actual correct answer as revealed by reality over the passage of time.

VI. At any point of time, over a sufficiently large selection of P, the graph of historical known Qs, historical known As and historical known correct As versus count of Ps will arrange itself on a Zipf curve. Very few Ps will know very many old questions, very many old answers, and very many correct old answers. Very many Ps will know very few old questions, answers and correct answers.

VII. The probability of correctly identifying the correct answer among the As for a given Q correlates with the number of known previous Qs, with the number of known previous As and with the number of known previous correct As. If further restrictions are imposed on the counted Qs and As (such as, for instance, similarities to the current sets), that correlation amplifies.

VIII. It then follows that very few Ps are likely to identify the correct A in the A1Qi, A2Qi.... AmQi set, and very many Ps are likely to pick randomly among that set.

IX. It then follows that democracy (ie, counting Ps) and finance (ie, finding the right A in the set) don't mix, and in general that democracy is antithetical to any professional endeavour, to science, and to human welfare generally.

X. If Ps are selected so only very few Ps towards the power end of the powerlaw are included, paradoxical effects may be discovered, but these are by definition not common. Furthermore, there is no guarantee they scale (ie, continue to manifest past an arbitrary count of selected Ps), nor is there any guarantee that a selection of Ps exhibiting them can be in fact made for any arbitrary Q or set of Qs and their associated As, nor is there any guarantee that there can be a selection process declared that is computable in any general case.

This is it, pretty much. Have fun.

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Category: Gandesc, deci gandesc

Wednesday, 29 January, Year 6 d.Tr.