The Binary Nature of Probability Judgements; Application to Property

Also raising dogs.


It's come to my attention that my understanding of how people deal with probability and Ignorance is radically different than anyone else's. I use the concept 'reasonably expect' in my definition of property. In fact, I use this idea all over the place. But what, exactly, I mean by 'reasonably expect' I cannot, apparently, reasonably expect anyone to figure out.

To start, let me analyze dogs, owners, biting, and pet stores. I'm simplifying the example, so hopefully I will explicitly give all the information my analysis uses. It turns out the extra information is irrelevant anyway.

A woman walks into a pet store. It's a small shop, with a polished hardwood board floor, a large front window, and two rows of various cages and aquaria around the walls. She must step forward from the doorway to see the counter on her right past a cage stack. She wants a dog, of which this store has 20. (They're on the left wall with the older dogs on the bottom row.)

She knows that 5% of dogs bite their owner, which, statistically speaking, means one of those dogs will bite her. She does not know anything else: it could be any of the dogs. Nevertheless, she walks up to the counter, buys a puppy, and takes it home.

For this woman, I'll call her Sheila, the biting is a deal breaker; if she knew for certain her dog would bite her, she would never have bought it or would immediately return it.

Now, what is the probability her dog will bite her?

It's 100%. Or 0%. If Sheila talked to an oracle, the oracle would immediately know that she should either keep or return the dog. However, with the actually available information, Sheila is 95% certain her dog will not bite her. She takes it home and raises it.

She is acting, in other words, exactly as if she had talked to the oracle, and was told the probability is 0%. She would continue acting this way all the way up to 9%, in which case she would not buy a dog.

Law of excluded middle. There is no third option. Sheila acts exactly as if she had 100% certainty, no matter her actual certainty.


Now I'll return somewhat to the real world. The way Sheila raises her dog affects the probability she will be bitten. I'm going to analyze pickpocketing instead, however.

If I am sufficiently certain my wallet will get stolen, I'm not going to take it with me. Let's say for the sake of argument this number is 5%. But, I can improve my security, perhaps by chaining the wallet to my belt. Assume that I do, and I take my wallet to the shady area. Am I still acting as if I had 100% certainty?

Yes. I have not entered the excluded middle, but rather I've found that I have power over the probabilities. In my estimation, adding the chain lowered the probability from 8% to less than 1%; I have passed the threshold with delineates taking my wallet versus not.

This is expectation. This is the binary nature of expectation.


I use the construction 'if you reasonably expect to control it, you own it.'

By 'reasonable' I simply mean that - again, we're in the real world - I didn't try to consult an oracle. Rather, I read the news and found that the area was shady; 8% of people were getting their wallets stolen there. Similarly, I believe that a chain would prevent this. It doesn't matter that, in fact, my chain is faulty and if I'm one of those 8% the pickpocket will easily circumvent it, because I had no reason to believe so. (Again, either I will be targeted or not. For me, it's either 100% or 0%...although technically the future doesn't exist.) However, I cannot be insane; I can't put Jello on my wallet and reasonably expect to always still have it at the end of the day.

This is also to forestall saying "Well, the Palestinians expect to control Jerusalem, doesn't that mean they own it?" Sure, they do, but not reasonably. In this case, we can just test it; are the actions of Israel directly controlled by Palestine?

However, for the purposes of ownership in general, we cannot, or ownership would simply be synonymous with control, and theft would be meaningless. Instead, the link above attempts to prove that once property rights are extended beyond self-ownership, they retain the intrinsic moral status of self-ownership. That is, if a societal technology allows me to own more things than I can personally secure, the morality of theft is completely unaffected.


Incidentally, Sheila was right. She raised the dog with affection and respect, but firmly asserted her own rights. She did not, in other words, abuse it. Her puppy grew into a strong, healthy dog who knew exactly who the pack leader was, and never felt the need to attack to communicate with Sheila.

Re-reading that, it sounds awfully...pat. Like I've memorized a public service announcement. Yet, for once, it's true. Affection. Respect - the dog has feelings too, along with desires and rights. Assertion - setting limits for your own health, so that you can continue to interact healthily with the dog. If you want to do it right, of course, you have to look up all the details, but these things will drop the chance that your dog will bite you to infinitesimal levels. Also, you do get a much happier dog.