Question: does anyone actually know what Microsoft do with the data that they get from Duck? Other syndication partners of Bing I have spoken to told me they are expected to pass on first three octets of IP. So with other data, for example useragent, location this could likely be used for fingerprinting.
Another syndication partner of Microsoft is far more transparent in their privacy policy than Duck: "Bing: IP address (obfuscated), user agent string, search term, and some settings like your country and language setting. We never communicate IP addresses along with search queries. We only send IP addresses to Microsoft in obfuscated form, meaning we remove parts of the IP address when we sent it."