Monday, September 29, 2008

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.

2 comments:

James Andrix said...

This is cataclysmically wrong.

Note that you break off your owner biting dog example. If you carry it through, your notion of probability is obviously silly.

First, let's look at a realistic, rational way to deal with the problem: a risk analysis.

There is a 5% chance a given puppy will bite. A dog bite will incur certain costs and hardships. Shelia feels this is outweighed by a lifetime of a loving dog. So she gets a puppy.

She does not play Russian roulette with a 20 chambered revolver. Not even for $10,000. Why not? The odds are the same, the certainty is the same. It's an easy ten grand.
She doesn't because the benefit does not outweigh the risk. For a billion, she might seriously consider it.

The 'probability' is not '100% or '0%' as you say. Even if we took puppies and revolvers to be fully deterministic, the bit signifying what actually happens is not the probability. Probability is something shelia assigns based on what she knows.

Going forward from where you left off, she does not act as if the oracle told her the dog would not bite. Instead she takes steps to lower the probability, because this lowers her expected cost.

You switch gears to the wallet example, and at the same time you transition the risk-mitigation to something that happens before the binary decision decision to take the wallet with you or not. Then you handwave it away as if it were just something that happened. Both of these risk mitigations (caring for the puppy and chaining the wallet) are counterexamples to your claim that people act as if they had 100% certainty.

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.

Then she would have no preference for a puppy mill that sold 0.001% biting dogs over on that sold 8% biting dogs?
If she got one dog from each she would treat them the same?
Why 9%?

Law of excluded middle. There is no third option. Sheila acts exactly as if she had 100% certainty, no matter her actual certainty.
Perhaps when you confine yourself to binary decisions! Yes, every binary decision someone makes with uncertainty corresponds to a decision they could make if they were certain (even if wrong). Brilliant!
Now do you have something meaningful to say?

This dependence on binary decisions and binary outcomes is why you had to move the risk mitigations off to somewhere else. Your model doesn't make sense when you're looking at the things people do that aren't get/not-get or take/not-take based on bite/not-bite and stolen/not-stolen.

That's incredible. You seriously expect me to define 'expectation' for you?
But what, exactly, I mean by 'reasonably expect' I cannot, apparently, reasonably expect anyone to figure out.
This is expectation. This is the binary nature of expectation.

Frankly, I think you owe me an apology.

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.


Well now hold on, if it doesn't work in general cases, how on earth is this a special case in which it does work? Are you certain that the current ownership of Israel came about through a chain of ownership without hypocrisy?

And if that test doesn't work in a situation, then what does?

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.

But you don't lay down how property rights _can_ be extended. Except by the state or other arbitrary force, and that still amounts to might makes right. (and offers no guide to determining what is owned by whom.)

That is, if a societal technology allows me to own more things than I can personally secure, the morality of theft is completely unaffected.

I'm increasingly thinking the morality of theft is sketchy in your model anyway. Even at the level of self ownership.

Alrenous said...

This is cataclysmically wrong.

You think I can make cataclysms! How cute.

I could answer your objections, I'm certainly capable, but I'm also capable of not wasting my time, so I won't.

It's pretty clear that you've already decided, and there's nothing I can say or do.