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Hundreds of smartphone apps are monitoring users through their microphones
(www.the-independent.com)
On the other hand, it's amazingly easy for advertisers to figure out what topics / products you're talking about without the need for constantly recording via your microphone. In most instances, it doesn't even really make sense to constantly record audio via the mic to monitor folks, other means are much more cost efficient while being just as effective. That's not to say that some app isn't or hasn't done it, just that historically speaking, it hasn't been as ubiquitous as a lot of people seem to think or imply.
Sometimes with these things, you have to apply Occam's Razor.
I stayed with some family during the holidays a few years ago and they are conspiracy theory fanatics unfortunately. The type that swear their phones are listening to everything they say. They get ads for things they've only ever talked about in person. That sort of thing.
As proof, they pointed out how the prior night the topic of old timey candy from our childhoods came up and all of a sudden they were getting news stories and facebook ads about those liquid filled wax bottle candies. To them, the only plausible explanation is that our phones were listening to us.
Except, as I pointed out, I specifically looked those wax bottle candies up later that night because I was curious if they were still for sale. They live way out in the country and there's limited cellular data, so basically everybody there that night was using the same wifi connection. Which means, our internet activity is all linked because to the outside world, we're all on the same network/IP address. Even more curious, though, nobody got ads for any of the other candy that we talked about and which I didn't specifically look up. So, if our phones were actually recording us and serving up ads based on the things we talked about, then why didn't we get ads for Blackjack gum, wax lips, and Brach's? Only the very specific one I happened to search for.