Old Content: On the Maths of Internet Flirtation

The following was originally published on Fetlife. I made small corrections following points raised in the comments there; this post includes those corrections.


 

(This was written as a response to the excellent subryna, possessor of the sexiest of all buckets, and grew large enough that I wanted to publish it as a separate piece.)

Subryna: “I just don’t understand how anyone could think [sending a message consisting of nothing but ‘how r u?’ is] a persuasive argument.”

I don’t think they think it’s persuasive. It’s not intended to be persuasive. Let’s get all game theoretic up in this thing and explain it properly, because maths is the key to all knowledge.

If you don’t like maths, skip to the bolded bits which are the conclusions. Also: learn maths. It’s fun!

A given online flirting strategy has a cost to the flirter C, a cost to the recipient R, and a chance of success S. Any flirter wishes to maximise S, usually by going for more than one person at once, but only has limited resources L with which to pay the cost C. (In this case, L is the time during their day that they can spend sending messages, the amount of emotional energy they have for them, and their creative writing talent.)

Therefore, we can see that the number of people you contact is given by L/C; let this number be called N.

The total probabilistic success rate is thus N x S. Therefore, to rearrange:

Total success = (L x S) / C

Since L is a constant for any given flirter, let’s set it to 1 to make the maths flow easier.

Total success = S / C

Now, how do we express S in terms of C? Clearly, the two are connected; a better approach takes more energy but also gives better rewards. The “better approach” may consist of taking time to check whether the person you’re messaging would be likely to respond favourably; it might also consist of carefully personalising messages to them. It might even consist of taking time to become a better writer and a funnier and more charismatic human being.

However, is it a linear relationship? No, for two reasons:

a) It’s an established fact that among humans, a little bit extra quality results in vastly increased rewards, since humans who’re beyond a basic starvation level tend to seek quality rather than quantity. Frederick Lanchester studied this and came up with the idea that it’s a square relationship (that is, that twice the energy pays off four times as much.)

b) However, for humans who are at or below a starvation level of resources, any effort at all is rewarded. After all, if you’re freezing to death you don’t care if your clothes are rags or Armani, you just want enough of them.

Therefore, we’re likely to see a relationship between S and C which takes the form:

S = C^2 + k

Where k is the starvation factor, so that even if C is zero, there is still some reward because of the people who are literally desperate.

Plugging this back into the earlier formula, we find:

Total success = (C^2 + k) / C
Total success = C + (k/C)

Please note that when C is zero (that is, your message takes no time at all to write and send, and you could hypothetically send one to the whole of fetlife in no time) your success rate rises to infinity.

Since nobody can write a message in zero time, what this means is that the shorter your message is, the more success you get, so long as k is nonzero. In other words, if you believe that there is at least one woman out there so desperate that they will respond favourably to a “hi there”, then the optimal strategy is to make your entire flirting strategy as low-cost as possible.

This gives us two possible outcomes: the “gentleman”, and the “mouthbreathing asshat”, where C is large and small respectively.

For the gentleman case (C >> k):

Total success ~= C

For the mouthbreathing asshat case (k >> C):

Total success ~= k/C

If your eyes have already glazed over from the maths, here it is in words:

“If you have high standards, you get more out of it the more you put into it. If you have low standards, you get more out of it the less you put into it.”

There’s the answer to your question: for people who have very low standards, the optimal strategy is to write messages that are as close to zero-cost as possible. This is also why they don’t read your profile: reading it would take time that they could spend spamming you.


However, do you remember R from earlier, the cost to recipient? That exists. R is likely to be influenced by C (after all, longer messages take longer to read, and very persuasive ones may lead to you checking out the writer’s fetlife page) but also includes a lot of stuff that’s the same whether it’s the best or worst message out there. You open fetlife, click on the message, read it, then click out. That’s a few seconds of your life, regardless of whom the writer is.

Thus, R can be phrased in the form:

R = Cq + r

Where r is the time and energy it would take to read the worst message ever, and q is the ratio between the energy it takes to write a message and to read it (including time taken fetlife-stalking the person.)

Therefore, the total amount of time and energy a single message costs humanity is given by:

Energy = C + R
Energy = C + Cq + r
Energy = C (q+ r/C + 1)

We can multiply this by the total number of messages sent N to arrive at the total energy that all that person’s messages have cost humanity that day:

Total energy = N C (q + r/C + 1)
Total energy = (L / C) C (q + r/C + 1)
Total energy = L (q + r/C + 1)

This gives us two possible outcomes (as above): the “gentleman”, and the “mouthbreathing asshat”, where C is large and small respectively.

For the gentleman case (C >> r):

Total energy ~= L (q + 1)

For the mouthbreathing asshat case (r >> C):

Total energy ~= L (r/C)

Here we see that for constant L, the first case is q-dominated and the second is r-dominated.

Or, to phrase it in words for those who can’t do maths:

“The total cost to humanity inflicted by a thoughtful, intelligent and articulate person’s message is determined by the amount of time people spend reading, rereading and considering the message. The total cost to humanity inflicted by a brainless spammer’s message is determined by the time it takes for people to open the message, say “ugh, no thanks” and close it.”

Or, in other words:

“If you’re a spammer, you’re a sociopath who doesn’t care about others (which is weird, because you’re trying to get them to sleep with you.)”

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