[cap-talk] Authority vs. Information Flow

David Wagner daw at cs.berkeley.edu
Thu Feb 14 03:41:44 EST 2008

```Toby Murray writes:
>Example 2: In which Authority exists, but perhaps not Info Flow
>---------------------------------------------------------------
>
>Now imagine the same scenario, except that now there is a third party,
>Dave. Dave also has a button like Alice, that turns on the light in
>Bob's room when it is pressed. Both Alice and Dave now have control over
>the light.
>
>We presume further, that Bob's behaviour is fully specified and does not
>permit the possibility that Bob will refuse to push his button if Alice
>hasn't already pushed hers. We make a symmetric assumption for Alice.
>Whoever pushes their button first, then, causes the light to turn on.
>
>Both Alice and Dave now have authority to cause Bob to be able to see
>the light turn on. But can either of them pass information to Bob?

(I assume you mean that _Dave_'s behavior is fully specified, and
that Alice and Dave will both race to push the button and surely at
least one of them will succeed in pushing the button.  I assume that's
a typo above.)

I'll assume that Bob cannot using timing channels (or anything
case) to distinguish the case where both Alice and Dave try to push
the button from the case where only Dave tries to push the button.

In that case, where Dave's behavior is fully specified, I'm not convinced
that Alice has authority to turn the light on.  MarkM's thesis defines
authority as causation through overt channels.  If I understand the
standard scientific notion of causation, we imagine two experiments:

Experiment 1: Everything is as you specified above.

Experiment 2: Same as Experiment 1, except that Alice's behavior
is modified so that she does not try to push the button.

Notice that the definition of Experiment 1 and 2 are identical except
for Alice's behavior.

Now, Bob cannot distinguish between Experiment 1 vs Experiment 2.
Therefore Alice's push of the button does not cause Bob to see the
light, because Bob sees the light whether Alice pushes it or not.
Consequently it seems to me that Alice does not have authority to
cause Bob to see the light.

This notion of causation is one where Dave's behavior is presumed
to be known and fixed, and the only question is how Alice chooses
to behave.  I'm inclined to think that is probably the right notion.
What do you think?  (Of course, there could be some other configuration
or some other definition of Dave under which Alice _did_ have authority
to cause Bob to see a light, but that'd be a different question.)

I realize I didn't answer your question of whether this counts as
information flow (and my answer to that would also be "No"), but by
denying the premise, hopefully I have resolved the paradox.  Do you