## 2008-01-13

### Predictor, Shmedictor

Scott Aaronson attempts to tackle the so-called Newcomb's Paradox, and discovers a new angle into it. To recapitulate quickly, the paradox poses a putative entity, the Predictor, which confronts everybody with to boxes: the first either has \$1,000,000 in it or nothing, the second always contains \$1,000. The catch is that the Predictor knows with perfect, inerrant foresight what your actions will be: if you choose to open only the first box, It will put the million inside it; if you choose to open both boxes, It will leave it empty. This way, you have no rational choice based on probabilistic expectations, as both alternatives of an either-or analysis contradicts the other possibility.

Aaronson's tackle on this is that the Predictor need not be omniscient, just a detailed-enough simulation of yourself that "runs" you forward enough to predict your choice and set up the boxes accordingly. Cosma Shalizi's view is that the paradox stems from trying to reason about the Predictor from the point of view of our own finiteness. I call bullshit: my view on this is that the Paradox is not, but just the result of a categorical mistake. I read the list of attempts at cracking it and cannot help but think "where's Wittgenstein when we need him?"

What I find bogus about the Paradox is the insistence to take at face value its setup in a probabilistic framework. To me it is obvious that the Predictor isn't such, but just a deterministic function from choice to payoff. Put it in these terms, it is wrong to use expectations to tackle the problem; for me, the right avenue of attack is to treat it as a maximization problem.

In other words, even if the problem poser insists on accounting for the phenomenological reality of the Predictor as defined by the problem, I can still sidestep the issue of Its nature and behave as if It does not exist as postulated. That is, it is irrelevant if the Predictor predicts my moves, as Aaronson chooses to explain, as It acts consistently independently of the chooser. Its actions are only dependent on the chooser's choice, hence, It is still a deterministic function from choice to payoff. The choice has a finite domain isomorphic to the booleans (open the second box or not):

choicepayoff
false\$1,000,000
true\$1,000

with maximum value at false.

Don't open that second box, silly!

#### 1 comment:

Anonymous said...

"The choice has a finite domain isomorphic to the booleans"

a.k.a. "there are two different choices" if we're speaking english here :)