# Uncertainty Wednesday: Are Our Phones Listening To Us?

This post is by Continuations by Albert Wenger from Continuations by Albert Wenger

From time to time, I see people online posting how they simply talked about something only to be presented an ad about that very thing soon thereafter. This quickly leads into speculation that some software on the phone was using the microphone to listen in on conversations and used that information for ad targeting. There has been extensive discussion online of the technical feasibility and the likely legal consequences. The rough consensus appears to be that it is theoretically possible, has not actually been observed using tools that listen in on traffic and would be a huge legal risk for whoever does it.

In today’s Uncertainty Wednesday I want to take a different approach though. And that’s asking if we should necessarily be surprised by such seemingly eerie ad targeting. Consider a similar coincidence: you meet a stranger, say on an airplane flight (writing this in the air) and you after some conversation that you both really like a rather obscure arthouse movie. “What a coincidence” you both say. But is it?

Here we are in one of the weirder aspects of probability that has to do with the frame of reference. Something can be simultaneously highly unlikely and certain. Come again? This seems like a perfect contradiction. Well, consider the type of lottery that one person wins every time there is a drawing. If millions of people participate in a drawing, then your chances of winning are super low (1 in, well, millions). But the chances of someone winning are 100%. For a lottery the distinction between the frame of reference of you, the individual (a sample of size 1), and the lottery as a whole (the population) is self evident.

But your conversation with the stranger on the airplane is similarly just one of tens of millions of people are having with a stranger today. And among that larger number there are bound to be people who discover that they share some obscure interest with the person they are talking. So once you zoom out to the level of all people it is not clear that anything has been learned. Just like there is no information in someone winning the lottery of the kind I described above. We already knew before the drawing that this would be true.

Now let’s come back to internet advertising. Billions of ads are served to hundreds of millions of people every day. Even if there were no targeting of any kind, we should, at the population level expect to see quite a few dead on hits, such as hearing aids being advertised to someone who never before searched for hearing aids but recently mentioned them in conversation. Put differently, the base rate of coincidences in the population is meaningfully above zero. But you only observe what is happening to you. And so for you it feels like an incredible coincidence. Too incredible in fact, which is why you search for some kind of explanation.

Just to be clear: please don’t take this as my saying that “phones listening” is definitively a tin foil hat paranoia. It may well be real. All I am saying is that there are statistical reasons for why people may feel like they have been targeted even though they have not.

PS Apologies for the lack of links, but I wrote this on a flight with super slow internet connection