You are correct that if you are compelled by the government to do something it's not a free market. But if coca-cola convinces you to try a new flavor through a marketing campaign, it does not eliminate the free market. It was your choice the whole time.
I don't think you can compress the issue down to a "government" vs "corporation" binary.
There are some powerful benefits of free markets over command economies, such as decentralized self-organization, tendency towards the maximization of total surplus, and dynamic adaptation to changing conditions.
But those benefits are conditional on, for one thing, the rational behaviour of individuals.
There are ways to "hack" people such that they stop behaving rationally (with respect to the economy). The threat of violence or incarceration (maybe one you are equating with government intervention) is one of them.
But there are plenty of others: chemical addictions (e.g. cigarettes), systems that prey on the susceptibility of our dopamine-reward pathways (like slot machines, or your perhaps your facebook feed), etc.
Good policies in a free market economy are ones that make it more difficult to disrupt the beneficial aspects of a free market. I'd say good policy-making actually increases the free market-ness of markets in a messy, imperfect world.
Historically, our society has drawn a distinction between force (things like direct threats of violence or incarceration), which makes things done under such conditions involuntary, and things that are addictive but which people still voluntarily choose to do.
In some cases, such as smoking, we have ended up still imposing penalties on companies that purvey such products, but the basis for such penalties has not been the addictiveness of the thing, but the physical harms it causes, such as lung cancer. Addictive things that do not cause harms of the same sort, such as slot machines, have not been treated the same.
IMO that distinction is a good one: addiction does have a voluntary aspect that is not present in cases of simple threat by force. Treating addictions as though they simply override the agency of the person is not, IMO, a good idea. And I think a similar distinction can, and should, be drawn between simple threat by force and "persuasive technologies"; there is a voluntary aspect to the latter--people have to choose to believe what they are being told--just as there is with addiction.
Of course we also draw a distinction between acceptable persuasion and fraud or manipulation, which are unacceptable and punishable. That distinction is also a good one, and I think it can help to deal with "persuasive technologies" in a reasonable way.
> if coca-cola convinces you to try a new flavor through a marketing campaign, it does not eliminate the free market.
If the marketing campaign is open, and I'm aware that that's what it is, and it doesn't make any actual false claims (puffery is another matter--that's basically unavoidable), then yes, it's my choice whether or not to be convinced.
If the "marketing campaign" is really efforts behind the scenes to present me with misleading information and to disguise the motives behind it, that's something different.
It is true that efforts of the latter sort are not new. What impact new "persuasive technologies" have on the frequency or success rate of such nefarious tactics is, I think, an open question.
