Tax distribution algorithm is a tax distribution algorithm for income tax based on my vision of what a tax distribution algorithm — and taxes — should accomplish, which runs in your command prompt.
The algorithm is based on these values:
- A person with a smaller income pays less taxes than a person with a bigger income
- A person with a bigger income pays more taxes than a person with a smaller income
- A person with a bigger income has a bigger net income than a person with a smaller income
- People with identical incomes have identical taxes; identical net incomes
The incomes are sorted from lowest to highest; a previous group of identical incomes has a smaller individual income than a current group of identical incomes and vice versa.
The incomes are grouped into groups based on identical income values — income groups.
The income groups are processed from the smallest individual income to the highest individual income.
A ratio is the result of smaller value divided by bigger value. A reverse ratio is the result of 1 - ratio.
The tax of a specific income — which will be then used as a ratio to determine the final tax — is calculated, in part, based on these factors:
- The ratio of the percentile of the start of the income group out of the percentile of the highest income group; if the last percentile is 0 the ratio is set to 1 — the last percentile is 100 only if there is only one person with the highest income
- The reverse ratio of the percentile of the previous income group to the percentile of current income group; if the current percentile is 0 the reverse ratio is set to 0
- The ratio of the individual income in the current income group to the individual income in the highest income group; if the highest individual income is 0 the ratio is set to 0
- The reverse ratio of the individual income of the previous income group to the individual income in the current income group; if the current individual income is 0 the reverse ratio is set to 0
The formula for calculating a tax for an individual income, which is then used as a ratio that is then used for calculating the actual tax = tax of an individual in a previous income group + (an average of the 4 previously listed ratios and reverse ratios * (the highest acceptable tax for an individual to still have as much net income as an individual in a previous income group - tax of an individual in a previous income group))
This tax — or more appropriately ratio, as that is how it's used — is then divided by the sum of all taxes paid by the income groups to get the ratio to all of the taxes, that were paid. That ratio is then multiplied by the total tax to be paid — which is the percentage of the sum of all incomes. This is done for all income groups.
After all these steps the algorithm is complete and the results are output to the console.
Despite me — informally — proving that this works it has very slight issues — at least they were slight in my testing — where there is very a slight overpaying or underpaying of the taxes; this is underpaying or overpaying is so small that a scientific notation is used to display its value; as far as I know — and as far as it makes sense to me — this cannot be simply solved as this is a technological limitation; the numbers use a limited part of memory that may not be sufficient, because the number may be infinite or at the very least bigger than memory in which they are held; this issue isn't addressed in the algorithm — at least so far; I don't see it as a significant enough issue for the performance trade-off as well as the potential issue of never getting to a pure 0 — even within the memory limitations; this should not be seen in the output as the output is limited to 3 numbers after the decimal separator.
Currently this program supports the following features:
- Inputting incomes — numeric values — one at a time
- Outputting the results of running the algorithm into the console
- The software has multiple releases you can use, if your release isn't listed here you can build it for you computer by following the instructions in the How to build it yourself from source code section. The available releases are:
- For 64 bit operating systems with x64 based processors:
- Linux Mint — specifically 22.3
- Windows 11.
- For 64 bit operating systems with x64 based processors:
- Get the files:
- Extract the contents of installed zip file into a folder you want; the program is portable and doesn't support or need installation.
- Check if you have gcc installed:
- For Linux: Open the terminal and type
gcc --versionandg++ --versionif it returns a text with which version you have, you have it. For best chances of success use the latest gcc version. - For Windows: Open the command prompt and type
gcc --versionandg++ --versionif it returns a text with which version you have, you have it. For best chances of success use the latest gcc version.
- For Linux: Open the terminal and type
- If you don't have it, install it by follow the instructions pointed to by these links:
- For Linux
- For Windows — note: for installing it on Windows only following the section
Installing the MinGW-w64 toolchainof the webpage pointed to by the link is necessary.
- If you pass the requirements listed above you can run the program:
- For Linux: Run the
TaxDistributionAlgorithm-Linux-x64.exefile - For Windows: Run the
TaxDistributionAlgorithm-Windows-x64.exefile
- For Linux: Run the
- Follow instructions in the program.
- Install gcc — ideally the latest version — if you don't have it.
- For Linux: follow the instructions on this webpage
- For Windows: follow the instructions on this webpage
- Navigate to
Tax distribution algorithmin your command line. - Run the command
g++ -std=c++23 ./main.cpp -o nameOfTheExecutableFile.exe. More information on the command is available here. - Your compiled program is now in the
Tax distribution algorithmfolder under the namenameOfTheExecutableFile.exeor the name you chose.
You may contact me at: martinherchel03@gmail.com.