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Traders are already taxed. They make money from their trades and pay income taxes on this trading. If, however, you tax the trading itself, there will be less of it, significantly less and, most likely, the total taxes collected will decrease

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This argument seems to apply equivalently to VAT/sales tax, which in my mind makes it weak. (Consumers are already taxed on their income etc)

There's no reason to believe total taxes collected will decrease. If actors still benefit from HFT post-taxation, they will still trade, and pay the tax.

Sorry but you are clueless. Taxing the trading itself will raise the cost of trading, this making it less profitable if it is less profitable people will do less of it.

VAT is paid on the difference between what you obtained a good/service for and what you sold it on at. The clue is in the name - "value added". You can even get a refund if you make a loss. A transaction tax would be charged at both ends whether or not you make a profit.

It will also harm people who have mutual funds in their 401(k) plans via higher fees.

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