Saturday, December 15, 2007

Against Causal Decision Theory?

Too bad I missed last session of LOGOS RG on DT, where people discussed Andy Egan's 'Some Counterexamples to Causal Decision Theory'. Did anyone get why exactly CDT predicts that Paul should press the button?

20 comments:

Manolo Martínez said...

Carl did, and he told us:

Given that, according to causal DT you are not to conditionalise creedences on your actions, the expected value of pushing the button is:

Creedence(I am a psycho)*Value(I die) + Creedence(I am not a psycho)*Value(I live in a world without psychos)

The creedence in the first term of the addition (sort of: the initial creedence of my being a psycho, regardless of whether I actually push the button) is very low; say 0,3. I don't consider myself to be a psycho, but rather a fairly sensible guy.
The creedence of my not being a psycho is, then, 0,7. So, in the expected value formula, the high value gets multplied by the high creedence, and thus the result is very high. Mutatis mutandis for not pushing the button. Therefore, you have to push the button.

But, really, you shouldn't, etc. Counterexample to causal DT.

Dan López de Sa said...

So, in the expected value formula, the high value gets multplied by the high creedence, and thus the result is very high.

But it will all depend on how I value the different things, right? So if Paul disvalues his own death enough... I'm still dubious on how we get the counterexample. Were you all clear on that?

Dan López de Sa said...

To elaborate,

V(press)= .7v(no-psyco+press) + .3v(psyco+press)
V(no-press)= .7v(no-psyco+no-press) + .3v(psyco+no-press)

As the story is told, v(psyco+press) < v(no-psyco+no-press) < v(no-psyco+press). And I guess it’s reasonable that v(psyco+press) <<< v(psycho+no-press), right? How can we conclude that V(no-press) < V(press)?

Sorry if I'm missing something basic!

Manolo Martínez said...

The point is that you can adjust values, creedences, etc. so that evidential decision theory and causal decision theory propose different candidates for the best action. For instance

C(I'm a psycho) = 0,3
C(I'm a psycho | I press the button) = 0,9

V(I die) = -500
V(psycho-less world) = +500

With this values, edt advises not to press and cdt advises to press. And not pressing is, pre-theoretically, the rational option.
If you find the value of dying unrealistically high, imagine the following scenario:

Dan can press the "give me 500 euros" button. This button is peculiar in that, after pressing it, you are given 500 euros unless you are an alfa-type individual, in which case you will be requested to pay 500 euros yourself. Now, you are quite certain that only alfa-type persons ever press that button.

This Egan case does not need unrealistic assumptions about the value of dying or killing psychos.

Dan López de Sa said...

Sorry I'm being a bit slow. I take it that, in your usage, V(I die) = V(psycho+press) and V(psycho-less world) = V(no-psycho+press), right? If so, they only constrain the value of V(press), and thus we cannot yet settle the relation between this and V(no-press), am I wrong?

Carl3 said...

I suppose v(Press) = v(Press&psycho).p(psycho) + v(Press&-psycho).p(-psycho)

Using Manolo's numbers (which I think gave a little too much prior prob to (psycho)!), v(Press) = -500x(.3) + 500x(.7) = 200. v(-Press) = 0. So Paul should press the button.

The point, as Egan makes it, is that CDT requires you to use the prior probabilities p(psycho) & p(-psycho) in the calculation of expected value, and not the conditional probabilities p(psycho|press) & p(-psycho|press), which are quite different (say, 0.9 and 0.1). Plug in these conditional probabilities and you find that v(press) is very negative, so Paul shouldn't press. And the example is meant to be one where your intuition is that Paul really shouldn't press the button, and should be evidentially taking into account what being ready-to-press means concerning p(psycho)!

I think to some extent we got hung up on the "death" part of this example in our discussion - -500 doesn't really capture how strongly most of us prefer to avoid death! - so maybe you prefer to discuss the "murder lesion" example.

Carl

Dan López de Sa said...

Yes, given Manolo's numbers, V(press) = 200. But I still fail to see how these would by themselves settle anything for V(no-press), whereas you say V(no-press) = 0. Any help?

(I just lack proper intuitions in the "murder lesion" example, but according to Egan, the "psychopath button" should suffice, right?)

Carl3 said...

Ah, now I see what you mean. v(no-press) is zero just because nothing changes in the status quo. If you want you can assign it a slightly negative value if you want (to cover Paul's regret?), but basically 0 seems to be the right value.

Carl

Dan López de Sa said...

Mmm... Isn't there a stronger way of arguing against cdt?

Dan López de Sa said...

In any case, notice that in a Newcomb scenario, and just assuming (quite uncontroversially) that the player values more more money than less, we got a clear dominance-based argument establishing that one should two-box, against EDT.

We do not seem to have here anything of the sort against CDT, do we?

Dan López de Sa said...

To elaborate: it would be nice if we had a case such that (i) only assumed relative preferences among the different outputs; (ii) CDT predicted that one should A; whereas (iii) intuitively one should not-A (or (iii*) we had a strong argument (based on dominance or the like) why one should not-A).

This would indeed consitute a challenge to CDT similar to the one Newcomb poses to EDT. Do you agree?

Manolo Martínez said...

Why isn't the case I gave you above one with the characteristics you desire?:

i) It only assumes that you prefer 500 euros to 0 and to -500 euros

ii) CDT predicts that you should press the button

iii) You should not, intuitively.

I forgot one detail about the case above: you strongly believe you are not an alfa-type (most of them have characteristic traits that you don't have).

This is just the psychopath button case, but with well-behaved values.

Carl3 said...

Dan seems to be under the impression that the original Newcomb problem is a counterexample to EDT . . . but to me, it's more of a counterexample to CDT *and* the dominance principle!

The "smoking lesion" case you find in Egan is a case where I find myself agreeing with the CDT prescription (smoke up, johnny), but I would try to argue that EDT properly applied in this case can give the correct result too.

So to sum up, I neither find the original NP a strong counterexample to EDT, nor the psycho button (or Manolo's Alpha-personality version) particularly weak . . .

Carl

Dan López de Sa said...

How would it go? Let V1 be the value of paying 500€, V2 be the value of getting 0€ and V3 be the value of getting 500€. Assume my credence of my not being alpha is .9. Then:

V(press) = .1xV1 + .9xV3
V(not-press) = V2

But we cannot infer from here that V(not-press) < V(press) just on the assumption that V1 < V2 < V3 (i.e. (i) above), can we? So how (ii) would then be justified?

Carl3 said...

I don't get what's puzzling you; just suppose that our player's euros-utiles function is linear in the range from -1000 to +1000. Then we CAN infer that v(not-pres) < v(press). But now poor Paul learns that almost all people who press are alpha-types . . .

Manolo Martínez said...

Well, you need to assume three concrete values that make the equations true, but there are a bunch of values for V1, V2 and V3 that would do the trick. E.g., -500, 0 and 500.
These very ones are not particularly unrealistic values: given that we are talking of small amounts of money, we can assume linear utility. But, if you are not convinced about them, you just need to choose any other of the infinite triples that work.

Carl, I would like to understand better your reluctance to go causal. Is this because of previous metaphysical commitments of yours, is it because of methodological reasons (being epistemically ciscunspect, etc.)? Or you think that it's easier to protect edt against Newcomb than cdt against Egan?

Manolo Martínez said...

Sorry, the first paragraph of my comment was an answer to Dan, not to the later reply by Carl.

Dan López de Sa said...

Well, you need to assume three concrete values that make the equations true, but there are a bunch of values for V1, V2 and V3 that would do the trick. E.g., -500, 0 and 500.

Exactly, so we have to go beyond (i), as opposed to what is the case wrt the Newcomb. I'm not sure how important this disanalogy will turn out to be, but it is a disanalogy, or so it seems to me. Similarly for the fact that in the Newcomb the intuition about which action is rational is supported by a strong argument such as the dominance-based.

Manolo Martínez said...

I see. Yep, that is a disanalogy.

Carl3 said...

@Dan, who wrote: ". . .in the Newcomb the intuition about which action is rational is supported by a strong argument such as the dominance-based." But for some 1-boxers, the intuition that 1-boxing is more rational is also very strong. And notice that if you are not the player in NP but a spectator, and you are asked for your credence in the next contestant winning 1M or more, given that he will choose to 2-box, you will (if you are rational) apply PP and say "0.1". (that being the error probability for the predictor). Mutatis mutandis you will have credence 0.9 in his winning, given that he chooses to 1-box. Why is it rational for *you* to update your credences with this information, but not for the player? Or is it that you think that the player should indeed update, and in the moment of reaching for the two boxes become convinced to degree 0.9 that he will lose . . . another unfortunate victim of the dominance principle?

@Manolo, it's a combination of 3 things: a fairly strong conviction that EDT gets it right in NP (but not "smoking lesion"), a metaphysical conviction that causality is not fundamental, and a glimmer of a few ideas of how EDT might be protected against its counterexamples. Maybe it is possible to protect CDT against Egan's examples too, but I haven't thought along those lines yet . . .

C.