I don't use loyalty cards, but I don't pay more because of it. There still exist stores that don't have them, and my observation is that the regular prices on those stores are about the same as the "loyalty card discount" price at other stores.
The "discount" you're getting with a loyalty card is a sham. The regular prices were just bumped up to give the illusion of a discount.
More to the point, though, the issue I see with your analysis is that you're assuming that privacy has a single value. My privacy is worth just as much to me as a wealthy person's privacy is to them. That others value them differently is unimportant. The cost of the loss of that privacy is the same regardless of income, but only the wealthy have a way to minimize that loss without going to extreme measures.
No, privacy is not autographs. Thats not how this works.
The rich man is paying a private shopper to use the PS's face in the facial recognition system and card tracking system. the PS gets the ads, but not the rich man. The rich man's habits are still tracked (by proxy, assuming PS doesn't shop personally at same store). At best, the rich man gets his habits co-mingled with PS to get slightly higher anonymity.
> The same can be said for loyalty cards. The one who can afford not to use loyalty card will earn the shop more profit (because no discount), meaning that it can offer bigger discounts to others.
Hmm makes sense at face level, but why would stores offer discounts to their worst customers? My credit card offers discount to those who spend 10k+ on private jets presumably because those people outspend enough to justify the cost
The thing with privacy is the more wealthy you are, the more valuable it is. For example, if I want to sell something, I will want to target the wealthiest first. Same thing for scammers, and newspapers will follow celebrities. Who care about the poor, there is no money to extract from them.
So let's get back to the private shopper. A rich and famous man will want to hire a private shopper, because he knows that if he is found in a shop, he will be bothered by people who are after his money and fame. His privacy is worth a lot, to him and to others.
The private shopper is likely to be of a more modest status, he can go shopping without being bothered, he may be tracked by robots and end up with personalized ads, be part of some statistics, whatever, but no one will stop him for an autograph or some special favor.
So when the rich man pays the private shopper, with a little extra for his discretion, that's resources that go from the wealthy to the "rest of us".
The same can be said for loyalty cards. The one who can afford not to use loyalty card will earn the shop more profit (because no discount), meaning that it can offer bigger discounts to others.
It is as if a unit of privacy is proportional to your wealth. The amount of privacy a rich man will get by paying $1000, a poor man can get it for $1. In the same way that it is much cheaper to secure a penny than a gold bar, because no one will want to steal your penny.