Monday, October 16, 2017

Information asymmetry and the "me too" meme

Since last night, my FB feed (but, strangely, given where it originated, not my twitter feed) has been filled with my friends posting "me too". The reason? (In case there is anyone who doesn't know):

If all the women who have been sexually harassed or assaulted wrote "Me too." as a status, we might give people a sense of the magnitude of the problem.

(Some people have changed it to "all the people", recognizing that not only women are sexually harassed and assaulted; some people have compared such a change to the shift from #BlackLivesMatter to #AllLivesMatter. Which version you prefer matters not for the purposes of this post.) Friend after friend after friend of mine has posted it, to the point where there was a moment where all the feed visible on my phone was a litany of these posts, and many of these people have explicitly broken their "no meme participation" rules in order to do so.

So I've been thinking about this all day, because there is something about the final phrase about the explanation of the meme that bothers me, this idea that people by posting "me too" can indicate "the magnitude of the problem". I don't think that this is possible, or, at least, it depends on how you define magnitude, and this depends on the essential informational asymmetry about these types of memes.

With respect to memes of the "participate in this meme if you have had X happen" type, there are two types of people: Those who participate and those who do not. With respect to those who do participate, one can derive the consequence "if they participated in the meme, they had X happen to them" -- note that this is the converse of what the meme is actually saying! And that's where the problem arises. Participation in the meme can only get a greatest lower bound for an absolute number; that is, the sense of magnitude participation can convey any information about is the magnitude of "size". But this says nothing about proportion. This is because while every person who participates in the meme does so for the same reason, but not everyone who doesn't participates for the same reason. Some people are insular enough to never see it, and thus do not participate (this is probably a very low number of people, at least in some circles). Some people see it, but do not participate, for whatever reason -- perhaps they have a strict anti-meme participation rule. But some people will see it and not participate because doing so would falsify the "if they participated in the meme, they had X happen to them" consequence.

I've had reason to comment on a few of my friend's "me too" posts -- usually when someone else has said something to the effect "what's the point of this meme, we all know this has happened to EVERY woman". Well, no. I have never been sexually assaulted. I struggle to remember any incident which rises to the level of harassment. (Note that this latter fact is not entirely indicative; I've written before about my obliviousness about a lot of these things. However -- and this is best the topic of another post so I will not go into it in more detail here -- I also struggle with the possibility that one can be harassed without feeling that they are being harassed.) So the reason I have not posted "me too" is because I fall into that third category. Who knows how many other women are in my category? That isn't an idle rhetorical question: We don't know, and we can't, not with the way the meme is currently structured. This essential asymmetry between the participators and the non-participators mean that the magnitude that is being evidenced by the participators can only ever be one of strict cardinality, and not of proportion.

Maybe this isn't anything to be bothered by. Even (merely) demonstrating the magnitude of the cardinality is (perhaps) a worthy thing to do. But it does bother me, because it feels so imprecise. It feels like people are taking the data to say more than it really does -- that is, this is a bother to my scientific sensibilities more than anything else. But a bother is a bother and sometimes the best way to deal with the itch is to scratch it, hence this post.

But the bother isn't entirely a scientific one. It also bothers me on a more personal level. When I voiced my reasons for not participating in the meme, someone -- someone I don't know, a friend of a friend, and, more importantly, a woman -- questioned me on this. Someone whom I don't know did not believe me when reported my own experience (or lack thereof!) of sexual assault and harassment. As I commented in reply:

I'm rather curious that one issue that has given rise to this meme is women speaking out about harassment and assault and not being believed -- and yet, when I report on MY experience, people's response is to question. Trust me. Believe me. I have nothing to gain from lying in this context.

So, yeah, while I'm quite confident that speaking out about being assaulted or harassed and not being believed is way, way worse than speaking out about not being assaulted or harassed and not being believed, I do think that a misinterpretation of the "magnitude" being illustrated as one of proportion instead of cardinality contributed to my having to justify my own experiences to another person, whom I don't even know, but whose default position was to suspect my self-testimony.

EDIT: Thanks to the varied and thoughtful conversations of my friends on FB in response to linking to this post, I think I may have just discovered what bothers me. It certainly isn't the meme (other than the fact that so many of my friends have cause to participate in it -- that CERTAINLY bothers me), or people participating in the meme (ditto prev. parenthetical), but rather that one participates in the meme to show the magnitude of the problem.

THAT is what I think is the problem, because it doesn't do that, because of the information asymmetry.

Wednesday, October 11, 2017

"I'm thinking of an animal...": Public Announcements and Gricean Implicatures

Yesterday walking home from school, G. and I mutually stumbled upon a new game. Neither of us had ever played it before (or even heard of it before), and yet it was one of those games where it was completely obvious what the right rules were. The game is "I'm thinking of an animal", and it goes something like this:

  1. Person 1: "I'm thinking of an animal that swims."
  2. Person 2: "A fish."
  3. Person 1: "I'm thinking of an animal that swims and flies."
  4. Person 2: "A flying fish."
  5. Person 1: "I'm thinking of an animal that swims and flies and bends its head underwater to eat."
  6. Person 2: "A swan?"
  7. Person 1: "I'm thinking of an animal that swims, flies, bends its head underwater to eat, and has many colors."
  8. Person 2: "A duck!"
  9. Person 1: "Yaaay!!!"

Or another version:

  1. Person 1: "I'm thinking of an animal that lives in the desert."
  2. Person 2: "A camel!"
  3. Person 1: "Oh, I thought that one would be harder."

Or this fun instance:

  1. Person 1: "I'm thinking of an animal that loves to fly."
  2. Person 2: "A bird."
  3. Person 1: "I'm thinking of an animal that loves to fly and has clear wings."
  4. Person 2: "A fly?"
  5. Person 1: "I'm thinking of an animal that loves to fly, has clear wings, and isn't true."
  6. Person 2: "Oh, a fairy!"
  7. Person 1: "Yaaaayyyy!!!"

(It's a great game).

Of course, #occupationalhazard, I started thinking about what sort of strategies are being used to play such a game, and what sort of properties make certain moves good or bad, and how one would go about modeling this. Clearly, Player 1 is making public announcements that successively carve pieces out of Player 2's epistemic space until Player 2 is left with either the right option (in which case Player 2 wins) or no option (in which case Player 2 loses). But winning and losing isn't merely a matter of guessing the right answer or not; if Player 2 gets the answer right after the first clue, then it's a victory but not a very satisfying one; Player 1 should've been more strategic.

This strategic aspect of Player 1's choice of clues to give is intimately tied up with Grice's conversational maxims, specifically the maxim of quantity:

The maxim of quantity: Be as informative as one possibly can, giving as much information as is needed, and no more.

If Player 1 played according to this maxim, she'd offer as a first clue something like "I'm thinking of an animal that moos" or "I'm think of an animal that is called 'cow' in English" -- and these entirely defeat the purpose of the game. The first clue does need to narrow down the possibility space somewhat ("I'm thinking of an animal" is of no use, nor even is "I'm thinking of an animal that is alive" -- though the complement of that, "I'm thinking of an animal that is extinct", is a good first clue!), but after that, the best way to play the game is for Player 1 with each successive clue to:

  • Make an announcement that clearly excludes the previous wrong guess of Player 2
  • Exclude as little else as possible.

Bonus points if you can give clues that misdirect, e.g. "lives in England" followed by "has two legs" and a few others before following up with "talks", at which point I finally realised the answer wasn't any kind of bird, but rather humans! Or when I did "goes very slow", "likes water", "has a shell", hoping to trick her into saying snail when I was aiming for tortoise.

Another dimension that makes the game interesting is the presence of common knowledge amongst the group of players that is unlikely to be shared by people outside that group. For instance "you cuddle with this animal at night" and "I have a pair of socks with them on" are unlikely to elicit "lemur" from many other pairs of players, whereas it was a dead give away for us.

So, what then is the best strategy? The first public announcement Player 1 makes needs to be understood to be carving away a large portion of the candidates, while still leaving a large enough set behind, and successive announcements should be made flouting the maxim of quantity as much as possible, that is, one should try to say as little as possible with every given announcement, all the while being sensitive to the group knowledge of the players.

It's a fun game (and easily extendible to "I'm thinking of an X" for pretty much any X), and because Player 1 (who knows the answer) controls the rate of reduction of the model, it is less open ended than similar games like "20 Questions", where it is Player 2 (who doesn't know the answer but asks the questions) who controls the rate of reduction. You should play it!

Edit: Just after I published this, Rineke Verbrugge over on FB mentioned an excellent paper touching on many of the aspects illustrated in "I'm thinking of an animal...": Rineke Verbrugge & Lisette Mol, "Learning to Apply Theory of Mind", Journal of Logic, Language and Information 17 (2008): 489-511.