My ex-girlfriend has asked me, on several occasions, including in writing, and in court, to stop surveilling her apartment, reading her private messages, following her to activities, and obtaining information about her through people who do not know we have broken up. I have read all of these requests carefully, in some cases before she sent them.
My position is that this confuses a preference over information-gathering procedures with the underlying decision problem. Kayla's internal state is a latent variable; my choice of action is being made under partial observability; and deliberately discarding available evidence because one of the subjects of the evidence objects to its collection would amount to imposing an arbitrary constraint on Bayesian updating.
The Decision Problem
Kayla and I separated fourteen months ago. I face a recurring choice between three actions: reach out, wait, or move on. The right action depends on her state, which I cannot observe directly. She might still have feelings for me, she might be ambivalent, or she might be done.
Decision theory has a precise tool for this situation. The expected value of information is the difference between how well you can decide after observing the world and how well you can decide before:
EVI = E_s[ max_a U(a, s) ] − max_a E_s[ U(a, s) ]
Using my current priors (0.25 still has feelings, 0.35 ambivalent, 0.40 done) and payoffs I have estimated with some care, the best I can do without information is to wait, for an expected utility of 2.1. With perfect information about her state, I would reach out when she still has feelings, wait when she's ambivalent, and move on when she's done, for an expected utility of 6.8. The value of knowing is therefore 4.7 utils per decision cycle. I face a new decision cycle roughly every day.
Anyone who tells me to stop monitoring is asking me to give up 4.7 utils a day on the grounds that gathering the information makes them uncomfortable. I have not heard a principled reason to accept that trade.
Data Collection
Direct observation. Her apartment is on the ground floor and faces a strip of hydrangeas across the courtyard. Kneeling behind them, I have a clear view into her living room from about 7 PM until she draws the blinds, usually around 10:40. I bring a thermos, a gardening pad for my knees, and a notebook. I have logged 212 evenings. A neighbor called the police in March. I told the officer I was birdwatching, which was partly true: I had logged two cardinals that evening, and I showed him the entries.
Her accounts. We lived together for two years, and she never changed her passwords. I read her email and her messages each night and go through her calendar on Sundays. I consider this less invasive than asking her friends, since it spares them the awkwardness. Her messages are extremely informative.
Her mother. Linda and I have played Words With Friends every day for eleven months. She is warm and talkative, and the in-game chat has become my best channel. I learned about Kayla's Lisbon trip nine days before Kayla posted about it. Linda doesn't know we broke up. The subject has never come up, and I have never lied to her.
Pottery. In October I enrolled in Kayla's Wednesday wheel-throwing class under my middle name, Graham. The next week she switched to Thursdays, and so did I. Her switching was itself informative: it tells me she noticed me, and noticing is not indifference. My mugs have improved considerably.
The dog. Kayla's dog, Biscuit, came from a breeder in Lancaster County. In December I adopted Biscuit's littermate, Rufus. When Biscuit appears in a post limping or with a new haircut, Rufus lets me separate breed-typical events from events specific to her household. This is the most rigorous thing I have ever done.
Her Distress
Kayla has said she feels unsafe. I take that seriously as a report of her internal state. But feeling unsafe is not a probability of harm, and I have never harmed her. Her fear is evidence about her model of me. When a model is miscalibrated, the remedy is more information, which is exactly what she has been refusing to exchange.
This is also where Aumann's agreement theorem applies. Two rational agents with common priors cannot agree to disagree. Kayla and I disagree about whether the relationship is over. Either our priors differ or one of us is not updating properly. I have offered to exchange information and she has declined, so gathering it myself is the only option she has left me.
The Protective Order
In June a judge granted Kayla a protective order requiring me to stay 500 feet from her, her home and her workplace. Several commenters have told me to update on this, and I have.
A protective order is expensive to obtain. It takes paperwork, a hearing and time off work. In signaling theory, costly signals carry far more information than cheap talk, and this is the costliest signal Kayla has ever sent me. Someone who was indifferent to me would not spend a day in court. I have raised my estimate that she still has feelings from 0.25 to 0.33.
I am complying fully. I have bought a laser rangefinder to make sure of it. My sources are reduced, but Linda knows nothing about the order and has, if anything, become more talkative. The value of information has never been higher.
Value of information is only value if you can act on what you learn. Since June, "reach out" isn't an available action, and "move on" is absorbing. Information about a state you can't act on is worth exactly zero in the formula you wrote down. With the order in place your EVI per cycle is roughly nothing, and you're paying a lot for it.
The order constrains one action. Information still informs the choice between waiting and moving on.
Then the only decision left is when to move on, and none of what you're collecting bears on that. Her calendar doesn't tell you when you're done.
Aumann needs common priors and common knowledge of each other's posteriors. You have her posterior. She has stated it repeatedly, in writing and once in court. If the theorem applies here, it says you're the one who should be updating.
The costly-signal paragraph has the sign backwards. A costly signal tells you the sender's type because only some types are willing to pay the cost. The type of person who will spend a day in court to keep you 500 feet away is the type who wants you 500 feet away. That should move 0.25 down.
Indifference is also a type, and indifferent people don't pay the cost. The signal rules out indifference, which is the state I've been most worried about.
It rules out indifference in favor of "done and afraid," which isn't one of your three states. Your model doesn't have a state for the most likely explanation.
This is Linda. Kayla told me you broke up. I kept playing because you're the only person who will accept a 19-point word.
Lawyer, not yours. Most protective orders bar indirect contact as well as direct, and depending on the wording that can include communicating about her through family members. I'd stop talking about her with her mother today, not after you've finished this thread.
The littermate design is the one methodological choice here I'd actually defend. Shared breeder and genetics is a reasonable control for breed-typical events. The problem is that it controls for the dog, and the dog was never the variable.
If you need a rangefinder to comply, you're planning to spend your evenings right at the boundary. Judges tend to read that as intent, whatever the rangefinder says.
kayla if you're reading this, change your passwords
I'd go back further than everyone else here. Where did 0.25 come from fourteen months after a breakup she initiated? I don't see a reference class anywhere in the post.
For whatever it's worth, the Thursday class is a lot quieter now.