“Theory of Moral Sentiments seem to imply that markets promote moral actions.”
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Put presure on, sure, but “promote”? I don’t see his logic.
Moral actions are free.
A classic example is with prejudice. Say a highly qualified woman wants to work at my business, but since I don't like women, I'll higher a less qualified or more expensive male. Well, she goes to my competition and now I'm losing out because I can't compete with the talent or prices my competitor has. Similar arguments happen for basketball and race. Discrimination comes at a cost in the market, so yes, in a way, markets promote morality. If I lie or cheat in a market, I may win in a few of the early stages, but eventually information in a free market gets out so that I lose in the long run. Someone who enters that is more honest will be able to take my business (or my customers just don't deal with me). In this way a market promotes honesty.
I guess you could debate with my usage of the word "promote," but I intended it to mean "to contribute to the growth of" (M-W.com) since immorality is usually punished in the market.