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The puzzle of the Hi-Lo Game

Professor Nick Chater explains the paradox of the seemingly-simple Hi-Lo game and what it tells us about a uniquely human ability: 'we-thinking'.
So here’s something puzzling. Imagine a simple game in which you and somebody else have to do one of two things– shout high or low, simultaneously. If you both shout high, you get a big prize. If you both shout low, you get a small prize. And if you shout something different from the other, neither of you get anything. Now, that’s a really easy game to play. It’s completely obvious– and it’s indeed true when you try it– that immediately, we all think, well, we’ll shout high. Why would we do anything else? And we do, and we both get a big prize– easy.
But actually, it’s very puzzling– in fact, paradoxical– because if you imagine, from an individualistic perspective, from me thinking what should I do, it’s very hard to understand why I would choose one option rather than the other. And the reason is that my natural thought is I guess I’d better do the same as you, in which case, I should think, well, what are you going to do? But then again, no I think about the other, I realise that you’re thinking that you should do the same as me. But I don’t know what I’m going to do. I haven’t decided yet. So we’re in a loop.
I’m trying to guess what’s in your mind and you’re trying to guess what’s in my mind. And that just goes round and round in circles forever. Now, in practise, of course, we don’t have this problem at all. It’s completely obvious that we will choose high. And we do, and get our big prize. Now, this is the fundamental problem of how people coordinate. People coordinate of behaviour when they play music together, when they pass each other in the corridor, when they communicate, where I can send you a single, and you have to understand that signal in just the way I intended it to be understood.
Coordination is everywhere, but it’s very puzzling from an individualistic point of view, from seeing the world as consisting of individuals who are trying to mind read other people. Because if I’m trying to mind read you and I know you’re trying to mind read me, where does the regress stop? Nowhere. Instead, though, there’s a different way to think. And the different way to think I think is actually very natural and possibly even uniquely human. And that is to think about us, not to think about me thinking about you thinking about me thinking about you, but to think, what should we do? And just to make it a bit more concrete, just imagine we could talk about it.
Suppose we just have a quick aside to each other and say, well, what should we do in this game? It’s completely obvious to both of us that we should say, well, we both do the same thing and clearly high is better than low, so let’s both say high, easy. We don’t have to actually have the conversation, because we know what we should do. So we do it anyway. So the magic trick about human coordination is that we don’t coordinate with other people by being individuals trying to each other’s minds. Or if we do, that’s only part of the story.
To really explain how we coordinate, we have to break out of the power of the paradoxical infinite regress of me following you following me following you following me. Instead, we have to think, what would we agree if we could talk about it? We don’t actually have to talk about it when it’s obvious. We just jump to the conclusion and do it. So you might think this is a bit esoteric and wouldn’t really arise much in real life. But it does arise all the time. So suppose for example that we notice that we need to move a table to another room.
Now, one of us has got to grab one end of the table and one of us has got to grab the other. So which is which? Now, we could have a long conversation about it, but normally, we don’t have to. It’s effortless for us to think, well, I’ll take this end, you take that end. We do that effortlessly because we know these things like, well, I’m slightly nearer to this end and you’re slightly nearer to that end. So obviously, if we could think about it, we would agree that we’d choose me to go this end, you to go that end, because that’s less effort than the opposite, because we know that we just do it.
So we don’t just coordinate actions. We also coordinate interpretations. So that arises in language, where when I send you a signal, I want you to understand that signal in the way I meant it to be understood. And you know that want to understand the signal in the way I intended. And that again, can lead into this nasty infinite regress. So somehow, we have to coordinate on the sensible interpretation that we would agree on. But that sounds rather abstract. Let’s take something even more concrete. Let’s talk about agreeing, coordinating, on an interpretation of a particular social interaction. And it’s more complex than that. Suppose, for example, I give you something and you give it back.
Now, if you think I’m trying to swap something with you, then you may say, oh, thank you for that banana, but I don’t I actually want it. I would like to hold onto my apple, thank you. So I push the banana back. But if it’s a gift, now I feel outraged. I tried to give you something, and you’re pushing my banana back and saying, no, I don’t want it. And that seems somehow insulting. So correctly understanding the intentions behind simple things like exchanging objects or not exchanging them is actually very crucial to cohesive social behaviour. And of course, the most basic economic transaction of all is exchanging goods.
So even understanding the very process of exchange in which I give you something and you give me something and understanding that’s different from a gift requires understanding coordination. So it could be that the reason humans can use language and coordinate their behaviour in complex ways and engage in economic transactions, and indeed, gifts, and build complex societies may depend on the crucial ability to think about what we should do. And it might be that we thinking, the act of imagining what we would do, perhaps, if we could discuss, although we don’t actually have to discuss, is a uniquely human ability. So it could be, perhaps, that the ability to coordinate is what it is to be human.

In this first video of the week I begin to expand the discussion from the ways we each make decisions on our own, to the factors that come into play when we have to jointly come to a decision with someone else.

We start by exploring the puzzle of the Hi-Lo game.

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