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the fact that they are freely chosen by customers again and again suggests they are productive

Iím not entirely convinced by this argument. Take, for example, actively trading mutual funds. It has been statistically proven that such funds on average have lower returns than the index funds and that the financial expertise of the people in charge of them brings no value to their customers. Yet, people continue to invest money into them out of their own free will.

Actively traded mutual funds appear to be a swindle. They also represent a relatively small subset of the financial sector. I guess you're saying they're illustrative of the rest of the sector? My prior is still that a voluntary transaction is mutually beneficial, and I don't see the evidence that other financial activity is unproductive.
Silent Cal
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I am also reserved on the same point but on different grounds.

The productiveness here is monetay productiveness while the question asks whether there is "real value provided". Yeah it has moved money from one hands to other hands but if you were to forget the financial side of it would it have made anybodys lives better? An apple feeds a person, a hair cut looks neat. People sometimes choose to be mean but that doesn't suggest that meaness is productive. If the only value is that it allows people to play this exciting game called "economy" then it is just a glorified slot-machine.
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