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Why does Google need to keep all of this data, when they could just classify (cluster) people based on their searches, and keep only that information? That approach would anonymize the data to a great extent.

EDIT: In fact, perhaps users should be enabled to specify the amount of dimensions in the "cluster space" that Google is permitted to store.

Or, alternatively, specify the "uniqueness" of the data. So, for example, if I specify that I want my data to be 100% unique, Google will retain all of my information. But if I specify that I want my data to be 1% unique, Google will only remember that I'm a programmer that likes Japanese movies (and not the details, such as specific programming languages I use and specific movies I watch).

In fact, this could be enforced by allowing Google to only store N bits of information about me, where N is a user-defined constant.

And this would not only be useful from the viewpoint of privacy, but also from the perspective of not getting trapped in a filter bubble. [1]

[1] http://en.wikipedia.org/wiki/Filter_bubble

> when they could just classify (cluster) people based on their searches, and keep only that information? That approach would anonymize the data to a great extent.

Well I'm glad you've solved it. Better get on to Goog's Engineers to let them know!

> Why does Google need to keep all of this data, when they could just classify (cluster) people based on their searches, and keep only that information?

That assumes you can take a pre-generated cluster and add information to it without having to recompute with all the original information.

It also assumes there's nothing you can do with personal search histories to either target adverts more effectively or add features, which would absolutely amaze me.

Good point. Please see my note about the uniqueness of the data that I just added to my comment.
I disabled web search history on my account a while ago, but they have re-enabled without notifying me.
You might have accidentally clicked on one of the nag screens Google throws at you (in Google Now for example). I turned my search history off a long time ago and it's still disabled.
I don't click 'accidentally' on anything and the same thing has happened to me.
"I don't click 'accidentally' on anything" number one thing users say to every person who works in IT.
Sure. But I'm very privacy conscious and am very sure that I did not give google permission to harvest my queries. Not that I have any illusion that changing that setting does anything concrete but I'm kind of surprised to see that the setting did not stay in its 'do not log' position. There are accidental clicks on ads and then there are accidental clicks on privacy violating features like these and since it's down a few menu options clicking it by accident is just about impossible.
The point I believe the person above is making is that it isn't a few menus deep. They apparently (I've never seen it) use some dark ui patterns and pop up a little box "Do you want to turn search history on?" randomly. Unless someone has eidetic memory they can't really claim they haven't clicked something like that ever.
I don't have an android phone, don't use other products than 'search', 'maps' and 'docs', if there are 'dark pattern' 'do you want to turn your search history on' in those products that randomly pop up to trap unsuspecting users then I will discount those as not being valid. One thing I'm sure of: I never consciously re-enabled my search history, if google wishes to swindle people that's entirely their problem but I highly doubt that such practices are ethical, assuming they are legal.
What happens when you disable the search history?

A) Google no longer stores your search history.

B) Google no longer lets you see or download your search history.

This is exactly the question I'm asking myself. I have search history disabled for last (at least) 5 years, but I am not sure if google isn't storing it anyways.
I would probably bet for the second option. Google has a quite long history of keeping everything they can. The only option would be to deny the Google home page access to the Google account cookies and to add an addon to add random searches just in case.
For me it seems to be B: tried to download history as described in the linked blog post and it took me to a page asking if I want to enable search history. Clicked 'No thanks' and it just showed me the google start page, not even an error message or so.

edit forget the above. I got an email "Your Google search history archive is ready" with a link to a Drive document. Which contained an html file saying basically "No Searches". I cannot tell if that is really correct though: I don't actively use the account let alone I remember if I turned of search history before doing any searches while logged in..

I have had Search History disabled for years, but not forever. I use my Google account all over the place, including at work and on my Android phone. I downloaded the search archive and it contained the same "No Searches" HTML file and nothing else. It's impossible to know whether they actually store this data, but at least as far as their direct user-facing interfaces are concerned, Google does not track my search history.
It absolutely is option 'B'.

While have always had search history disabled, I regularly see "targeted" results that is obviously based on past searches.

These are likely related to cookies stored within your browser locally.

That's why I always search using Anon mode or obscure browser (such as IE) to get more or less unbiased results.

What cookies? While I purge those regularly, I can guarantee this is not cookies, as topics I did I lot of searching on ~1.5 years ago clearly influence search results today... after erased my firefox profile just under a year ago.

If we are talking other data that may be used for tracking, I do have a static IP.

Besides, cookies don't store complex search histories. That would be stored on google's servers... which was the point (that search history is saved). I'd love to know how searches about unit testing with automake could be tailored from new client cookies to include results that are suspiciously similar to the many searches I made >1 year ago about Minecraft.

edit: Oh, and regarding the amount of uniqueness being leaked by my browser, panopticlick currently reports my browser's fingerpoint only 14.14 bits.

Have you done a comparison on another IP/browser to verify this?
Google still has to store your search queries in order to associate them with your cookie. That means that even if you delete the cookie, they still have your old searches stored. They just can't associate the old searches with your browser anymore.
Those are not the only options. It could be

C) Google stores search history, but it is not associated with your Google ID.

...but it is associated with your IP address and Browser's USER_AGENT that google likely stores.
And also associated with your probably-unique 150 degree of freedom browser fingerprint.
All non-ASCII characters are missing from the JSON dump.
The curiosity in me wishes I didn't have search history disabled.
Don't worry - it's not THAT great. Mine went back to 2007, and taking a quick look it didn't really remind me of anything.

Maybe I should disable it...

somebody make a website or app that lets me Google as someone else.
This is why I (probably naively) often Google things in incognito mode.
Incognito from an IP that you have associated with one or more google accounts?
What really bugs me is that I switched this off in the past and now find that it is back on again!
Well I think this is interesting when I try to turn off sharing my searches with Google.

> Please note that even when this setting is paused, Google may still use searches you make within active sessions in order to improve the quality of your search results.

I google things using Bing. How can I get this to work?
And this is why I keep Google accounts quarantined in a separate browser (Safari), and never ever log in using Firefox.