I've tried Brave as well but feel that paying for Kagi is better for me. The quality of the search results and the frequent updates are what did it for me. They have a good privacy policy, but you do have to trust that they are doing what they say.
You can read more about Kagi on their documentation page, which goes into more details about their privacy and security. https://help.kagi.com/kagi/why-kagi/why-pay-for-search.html
Now that you can pay via bitcoin, you can just create a fake or masked email address and not have anything even tied to your name. I personally don't really like how Brave has tokenized their browser. Seems unneeded to me. I was experimenting with all the private search engines including Brave Search and self-hosted searx and came away liking the Kagi results and customizability the best. They also are working on some AI search stuff too.
Okay I like the idea of independent search options, am pretty happy with brave search ... What's the philosophy on censorship?
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Also, there are no advertisements. Not even keyword targeted ads. I'm of the mindset that if something is free then I am somehow the product. Someone is using my information, even if de-identified to sell to someone else.
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Looks like they allow you to personalize search results and try to avoid censorship and bias (per their page here: https://help.kagi.com/kagi/search-details/search-quality.html#avoiding-censorship-and-bias). They have a 100 search trial. BTW, I have no affiliation with Kagi outside of being a user of it. I do want them to succeed though because I would hate to no longer be able to use them.
They will not go the route of Neeva by taking sponsorship and promoting various VPNs and/or password managers. I was with Neeva before this (largely because of the former Googlers who started it).
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