[Epistemic status: I'm mostly trying to outline a class of strategy that you could use to do something rather similar to what people term "flirting", rather than say that everything that's ever called "flirting" fits this model. I'm lowering my standards so that this gets posted at all instead of sitting in my drafts folder, so I might've made some important mistakes somewhere.]

In this post, I'll use "X is common knowledge between you and me" to not only mean "you know X and I know X," but also "I know that you know X" and "I know that you know that I know X" and so on (this is pretty standard in mathematical logic contexts, although distinct from the colloquial meaning). The simplest way to get common knowledge of X is for one of us to just say X out loud.

These ideas are only partially my own: I've read bits and pieces of this theory in different places in the past few years. I haven't been able to find sources for most of it. I know some of it is scattered across Planecrash, and reading that story is what got me thinking about this again recently, but that's probably not their original source. As far as I can tell, I'm the only person to synthesize them all together in a post, but please let me know if I'm wrong.

What is flirting?

As stated above, this is less about trying to describe everything ever called flirting, rather trying to outline a strategy that can exist and then exploring the implications of that strategy.

Consider the situation where person A is romantically attracted to person B, but they're currently just friends. Flirting-like strategies likely apply more generally, but the romantic case is a good starting point. Let's say that person A's values are approximately:

  • If B can counterfactually reciprocate the romantic attraction, then A wants them to be in a romantic relationship where that attraction is reciprocated.
  • Otherwise, A wants to maintain the friendship with as little turbulence as possible.

(If you want to pause and ponder, pause right here, since I outline the strategy in the next paragraph.)

In certain social contexts, it's totally fine to just make the attraction common knowledge and move straight to the "A and B are in a romantic relationship" or the "nothing changes" outcomes. But in other cases, it can make a lot of sense for people to take things slower and convey the information in a more subtle way. Flirting is the deferment of common knowledge of attraction, and instead opting for sending little bits of Bayesian evidence about attraction. Instead of reaching common knowledge instantly, it takes some time get there, or never gets there at all. This has benefits over the "person A just makes it common knowledge immediately" approach:

  • It lessens the expected stress on person B, since they no longer have to make a decision on a short time scale about whether or not they reciprocate the attraction, if they don't already know. Being non-stressed is good for consent!
  • This deferment is fun for a lot of people, since it's a social game involving a romantic interest.
  • If, in response to person A flirting, person B starts "anti-flirting" (doing the same thing but instead giving evidence of lack of attraction), then the "we're still just friends" world hasn't been explicitly ruled out from the perspective of common knowledge, and this allows people to more smoothly return to that world if things don't work out.
  • Deferment distributes the emotional vulnerability for person A across time, rather than one big vulnerable moment where common knowledge is established with person B.

Generalization?

It really seems like this can be generalized beyond romantic contexts, but right now I am just trying to get these ideas out on the internet, rather than explore every possible corner of them. Some related-feeling things that might be interesting to explore this class of strategies with:

  • Asking someone to put their resources towards a project of yours, but you want to apply minimal pressure on them and you are okay with things taking a bit longer.
  • Working in an adversarial environment where you can't communicate freely but still need to find allies

There are definitely more avenues to theorize about this. I especially feel like I didn't capture how flirting interacts with the finer tensions in the social fabric, and I'm interested to hear other people's ways of articulating this.

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Flirting, if we continue to interpret it as a game between two agents, seems to have some interesting properties.

The "permission handshake" Scott Alexander points out (thanks, @noggin-scratcher) looks to be the core of the flirting game. 's goal is to gain permission to be romantically intimate with  while not letting  know that they're doing this, at least not immediately such that  can make up their mind regarding the matter. 's general strategy comes in two parts: gain this permission incrementally (i.e. spending time with , initiating physical contact as opposed to directly asking for a romantic relationship), and asking for permission using the handshake.

Because of this fundamental element of ambiguity, flirting is surprisingly challenging to understand using mathematical theories. The handshake, while easy for most humans to understand, in a sense flies in the face of classical logic because  genuinely wants to convey and not convey attraction. This can't be resolved by simply saying that  solely conveys attraction clearly. but in very small steps: an intelligent  would notice the pattern and could then realize too soon that  is romantically interested in them. It is not immediately obvious to me how one would regiment the handshake. Classical game theory makes the assumption that all agents' strategies are common knowledge. This is a comically bad assumption to make here: if  knew 's strategy, then they would immediately deduce that  is flirting, ruining the point of the exercise. I would imagine Young's theory of evolutionary game theory as presented in Individual Strategy and Social Structure, which is able to replicate much of game theory without this assumption, would help with that. Another wrinkle comes from the assumption that all agents are know they are playing a game. As already stated,  ideally should not immediately realize that  is playing the game with them. Continuing down the connection to evolutionary game theory, perhaps  has an initial strategy of "no strategy," but then develops one once they gain enough information to begin considering if the "flirting game" is being played.

I'd like to linger on that last realization that  isn't fully aware that they are participating in a game, as that's connected to a core part of flirting: it is simultaneously cooperative and adversarial. Assuming that they are a boundedly rational agent,  does not know if  has figured out that  is flirting with them, and does not want them to know before  is comfortable making their attraction common knowledge, as stated above. Once  has collected enough information such that they're a conscious player of the game, they do not want 's attraction to  to become common knowledge, if at all, until they've decided how to respond, and they do not know if  knows they know assuming  too is boundedly rational. So, flirting is adversarial from the point of . At the same time,  and  assumedly have a common goal: to preserve their relationship and possibly elevate it if mutually desired. Thusly, flirting is a cooperative game where both players are incentivized to work together without directly communicating.

In realizing the above, it is clear that flirting for each player is asymmetric in its adversarial aspect:  is primarily focused on intelligently conveying information, while  deduces and ultimately ends the game. Furthermore, this behavior comes about because  is, ideally for , not a conscious participant of the game the whole time: the game slowly transitions from being a one— to two-player game as  gets more info. 

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I think a good next step is defining an ontology of flirting and then understanding it from an information-theoretic perspective. Gaining more intuition for how to logically regiment interactions should enable one to get over the conceptual roadblocks discussed above and give us tools to understand how  might interpret "hints" given by . Fox's "Flirting Report" gives a good starting point in this regard. Below are some rules of thumb for a prior distribution of whether someone is flirting or not:
- (cisgender) men are inclined to interpret most positive (cisgender) women behavior conveying attraction (pg. 5)
- men flirt slightly more than women (pg. 8)
- young people flirt a lot (pg. 8)
- single people flirt more with friends or strangers by quite a large margin (pg. 8)
- flirting with someone's partner is generally taboo (pg. 9)
- flirting is most considered socially acceptable where initiating conversation with strangers is common place, alcohol is available, and where A and B share some common interest (pg. 11)

An important part of this ontology will be distinguishing playful teasing and flirting. A large part of the ambiguity present in the flirting comes about due to, absent of context, flirting and teasing being identical. Of course,  is trying to shield  from said context. If and how  can distinguish between the two will be an important part of understanding flirting in this context.

I really appreciate you taking the time and writing a whole post in response to my post, essentially. I think I fundamentally disagree with the notion that any past of this game is adversarial, however. There are competing tensions, one pulling to communicate more overtly about their feelings, and one pulling to be discreet and communicate less overtly. I don't see this as adversarial because I don't model the event " finds out that is into them" to be terminally bad, just instrumentally bad; It is bad because it can cause the bad things, which is what a large part of my post is dedicated to.

I find it much more useful to model this as a cooperative game, but one in which is cooperating with two different counterfactual s, the one who reciprocates the attraction and the one who does not. is trying to maximize both people's values by flirting in the way I define in this post, there's just uncertainty over which world they live in. If they knew which world they lived in, then the strategy for maximizing both and 's values looks a lot less conflicted and complicated; either they do something friendship-shaped or something romance-shaped, probably.

I could swear there was a similar Scott Alexander post, about flirting deliberately skirting the edge of plausible deniability to avoid prematurely creating common knowledge. With an analogy to spies trying to identify a fellow operative without overtly tipping their hand in case they were mistaken and speaking to a non-spy.

Can't find it now: might have since been deleted, or might have only ever existed on LiveJournal or Tumblr or something.

https://slatestarcodex.com/2017/06/26/conversation-deliberately-skirts-the-border-of-incomprehensibility/ is similar but not explicitly about flirting.

You're probably thinking of the russian spies analogy, under section 2 in this (archived) livejournal post.

Ah that's interesting, thanks for finding that. I've never read that before, so that wasn't directly where I was drawing any of my ideas from, but maybe the content from the post made it somewhere else that I did read. I feel like that post is mostly missing the point about flirting, but I agree that it's descriptively outlining the same thing as I am.

That definitely looks like the one. Appears I'd forgotten some of the context/details though.