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Google has promised not to develop any new way of tracking individual users for adverts once it phases out its current method.
The tech giant is one of the world's largest advertising sellers and also owns the world's most popular web browser, Chrome.
But it is following other browser providers by eliminating third-party tracking cookies.
That move is already being looked at by the UK's competition authority.
The Competition and Markets Authority said in January that Google's plan to remove the cookies – which would effectively share less information with advertisers – could have a "significant impact" on the advertising market and news websites.
One group of marketers opposed to the idea claims that Google will gain an advantage by eliminating such cookies, because it has other ways of obtaining personal information from users.
What's in a cookie?
Cookies temporarily store small amounts of information about what a user is doing on a website and are an important part of the modern internet.
For example, they can "remember" things, such as what is in an online shopping basket or whether a user is logged in.
But a third-party tracking cookie can be used to "follow" a user from site to site, so a website can "know" that you were shopping around for a type of product – like clothes or shoes – and advertise those things to you elsewhere.
Those are the type that Google is phasing out, following the lead of some major competitor web browsers, including Mozilla Firefox and Apple's Safari, which already block them by default.
What does Google say?
Some critics had been concerned that Google's plan to stop these cookies would prevent its rivals from building useful catalogues of ad targeting information – but that Google itself might still be able to do so.
The company appeared to tackle that idea directly in its new announcement.
"Today, we're making explicit that once third-party cookies are phased out, we will not build [alternative] identifiers to track individuals as they browse across the web, nor will we use them in our products," the company said in a blog post.
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It said the knock-on effect was that other providers could end up offering "a level of user identity for ad tracking across the web that we will not" (although Firefox and Safari already block the offending cookies by default).
"We don't believe these solutions will meet rising consumer expectations for privacy, nor will they stand up to rapidly evolving regulatory restrictions, and therefore aren't a sustainable long-term investment," Google said.
But that portrayal has been challenged by industry group Marketers for an Open Web, who argue Google will have an unfair advantage.
Director James Rosewell said Google hasn't promised to stop personalised marketing, or gathering of data, inside its own products – which would involve changing its product terms and conditions.
Regulators still need to ensure competition, through legislation, he said, or "advertisers will have little choice as to where they spend their money".
And there are fewer privacy advantages for the average user, he argued.
"You have one large trillion-dollar company that effectively, through an unfair contract… tracks you more of the time, the only difference is you're going to be logged in, and part of their walled garden."
"How does that make people more private, or more secure, versus something that doesn't have directly identifiable information – their name, their email address – it just uses a random string of characters?"
What might happen instead?
The shift away from cookies has been prompted by years of tightening regulation and increased consumer awareness.
But stopping the use of tracking cookies does not prevent all personalised tracking, as the industry has come up with creative solutions to generate personalised data.
So-called "fingerprinting", for example, tries to use a huge range of details about your device – the type of phone or computer, browser version, language, IP address, or even what fonts you have installed – to identify the machine.
The advertiser might not know the person's name, but it can still "follow" that unique fingerprint around the web.
Google, which will continue to sell ads, argues that it and other companies need to come up with a solution that "delivers results" for advertisers.
It now says that people should not have to be tracked invasively in order to "get the benefits" of targeted advertising.
One way of doing so, Google said in its blog post, was to "hide individuals within large crowds of people with common interests", so that an individual person's browsing history would be difficult to figure out.