In short, Google and Facebook/Instagram (I expect more platforms to follow) are working toward using a deterministic model that removes dependence on cookies, browsers, and legislation. This measurement system will be available to all brands regardless of size and budget, which is significant because even brands with tiny marketing budgets will likely be advertising on Google, Facebook, or both.
In this model, Google and Facebook know who they’re serving ads to because those users are logged into Facebook, Instagram, or the Google product suite (think Gmail, Google Maps, Google Docs, etc.). They can also track actions like users clicking through ads to get to brand sites. Brands will likely get their email addresses when those users convert (whether for lead gen, purchase, etc.).
From there, instead of sending those email addresses, brands will hash the user data and then send it back to the advertising platforms, which can tie the data back to a conversion on your site. The sooner in the journey you can collect the email and hash it, the better, as you can then quickly connect to more upper-funnel actions that lead to conversions, think whitepaper downloads, value-driven incentives to sign up, etc.
In this model, brands will understand how many conversions they recorded, from which ads, and on which platforms, and they’ll know precisely how many users converted. (Note: this approach won’t solve multi-channel attribution since both advertising platforms will try to take the bulk of the credit when they deliver ads to the same user.) Although my opinion is that none of the advertising platforms would have chosen this direction without a groundswell of privacy-related demand, they should be happy because advertisers are now getting access to historically walled gardens in a privacy-focused way. They also get the PR boost of protecting user privacy while continuing to rake in advertising revenue.
All of this takes place without any cookies in play.