Variety of Documents Describing Our Prediction Market Math Graphically #388
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Other than that, I understand what is going on here. So, yay, good stuff, will approve once the changes are made. Will one of the math readmes point to this pdf? |
Will do. Currently I have everything in Overleaf in different files so as not to lose work and I will plan on merging everything together and writing descriptive language so it all flows as one paper. I will also dump all of the actual LaTeX used to generate the paper at the end as well. 
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Thank you for including the TeX file also - this really helps with readability + commentability
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I'm sorry about this but I'm authoring this document in Overleaf. So it's hard for me to intake the code from Github and copy and paste it back into Overleaf and then maintain it on Github again but I will try. What might be better is to hold off on edits until we have the final math and paper figured out, then go through a final revision. However comments along the way are appreciated and I can update the document to reflect comments, it's just that code changes are a bit harder to keep straight.
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| \section{Overview} | ||
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The 3 items are good. I think Overall Purpose and Transparency and Unit Testing can be made more concise - e.g.
This document describes how market pricing (probability) gets set and how points get distributed from a series of historical bets. It aims to be clear and provide graphical illustrations.
Pricing and distribution underpin this software. Making the full algorithm understandable is essential to writing proper unit tests and clear documentation.
Just in general, short sentences + active voice
| \section{First Transaction} | ||
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| \begin{itemize} | ||
| \item \textbf{Initial Investment:} Every market is assumed to have an initial investment of at least 1. This investment comes from a fee assessed to the market creator. This initial investment goes both in the numerator and denominator of the probability calculation. |
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What does "assessed to the market creator" mean?
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A fee is charged to the person who created the market
| \section*{Calculating Course Payouts} | ||
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| \begin{itemize} | ||
| \item \textbf{Course Payouts:} The purpose of the Course Payouts is to create a relationship between the probability, which is a float, rational positive numbers, and shares, which are of type int64, integers. We use a linear weight for each historical bet in the history of the market to create a reward factor. |
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This first item can be made clearer and more concise
| \begin{itemize} | ||
| \item \textbf{Fourth Transaction:} | ||
| \begin{itemize} | ||
| \item We can now see the effects of the course payout on scaling toward older transactions. While both Bet 2 and Bet 3 were of equal amounts, because Bet 2 was made at at a point when the YES outcome was less likely based upon the price, there is proportionally more weight given to this bet. |
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Make the second sentence clearer and split it up.
e.g. While Bet 2 and Bet 3 were the same size, Bet 2 was made at a point when the YES outcome was less likely. Therefore we assign proportionally more weight to Bet 2.
| \item \textbf{Fourth Transaction:} | ||
| \begin{itemize} | ||
| \item We can now see the effects of the course payout on scaling toward older transactions. While both Bet 2 and Bet 3 were of equal amounts, because Bet 2 was made at at a point when the YES outcome was less likely based upon the price, there is proportionally more weight given to this bet. | ||
| \item The fourth bet is a negative amount because it was a sale. Because the fourth bet occurs at the resolution price R, the Scaled Payout is zero. However in a future transaction, the Scaled Payout for this transaction could become negative, which would reduce the user's final payout, because they are no longer participating in the market at this amount. |
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This third sentence is loooooong and should be split into 2
e.g. In a future transaction, the Scaled Payout could become negative. This would reduce the user's final payout because [and then the last clause needs to be made clearer]
…om/OpenPredictionMarkets/socialpredict into doc/math-latex-graphical-overviews
| \section{Conventions} | ||
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| \item \textbf{Course Payouts Divide By Zero Condition:} When Course Payouts calculations and further calculations derived from Course Payouts may include an inf (divide by zero) condition, we will define the output as zero. This situation arises in which the Market Value is measured as zero, since everyone has exited the market. Technically the market Value is still equal to the initial investment value until the resolution has been fulfilled, so the Course Payouts, which simply represent a link between the probability and the payout at a given market condition, are not representative of the final state of the market. Thus, calling the Course Payouts and anything calculated from the Course Payouts zero makes sense. |
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Is it "Market Value" or "market value"?
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| \begin{itemize} | ||
| \item \textbf{Course Payouts:} The purpose of the Course Payouts is to create a relationship between the probability, which is a float, rational positive numbers, and shares, which are of type int64, integers. We use a linear weight for each historical bet in the history of the market to create a reward factor. | ||
| \item \textbf{Reward Factor:} Course payouts are calculated in two steps, first by calculating a reward factor \(d_i\), which is the distance from the current probability of the market \(R\), and the probability at which the bet was made \(p_i\). |
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I thought this whole section was much clearer, I really liked it
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| \section*{Normalization Factor Calculation for Third Transaction} | ||
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| \subsection*{Step Three: Calculate Normalization Factor} |
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Just in general, how many significant figures do we use for shares, probabilities and normalization factors? Should a) state these explicitly b) keep them consistent
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| where each normalized market position is represented as: | ||
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You have a text wrapping error here in the PDF and the normalized market position is unreadable
Additions to the Documentation Describing How our Math Works in Graphical / PDF Format