On Sat, Nov 10, 2012 at 06:44:36PM -0800, meekerdb wrote:
> On 11/10/2012 5:37 PM, Russell Standish wrote:
> >Only for some extended, loose definition of "rational". The
> >non-deterministic choices themselves are not rationally determined.
> 
> Of course not by your definition of rational for in that case they
> would be deterministic and potentially predictable and hence
> worthless in the game.
> 
> But the definitions I find in Dictionary of Philosophy by Angeles:
> 
> 1. Containing or possessing reason or characterized by reason.
> 2. Capable of functioning rationally.
> 3. Capable of being understood.
> 4. In comformity with reason. Intelligble.
> 5. Adhering to qualities of thought such as consistency, coherence,
> simplicity, abstractness, completeness, order, logical structure.
> 
> or online:
> 
> *1. * Having or exercising the ability to reason.
> *2. * Of sound mind; sane.
> *3. * Consistent with or based on reason; logical: rational
> behavior. See Synonyms at logical
> <http://www.thefreedictionary.com/logical>.
> 
> /a/ *:* having reason or understanding
> /b/ *:* relating to, based on, or agreeable to reason *:

I'm sure you would agree that none of those definitions are technical
in nature - they are more like what you'd find in a regular English
dictionary - so are of little help.

> *Or the Stanford Encyclopedia of Philosophy:
> 
> http://plato.stanford.edu/entries/epistemology-bayesian/
> 
> 'Bayesian epistemology' became an epistemological movement in the
> 20^th century, though its two main features can be traced back to
> the eponymous Reverend Thomas Bayes (c. 1701-61). Those two features
> are: (1) the introduction of a /formal apparatus/ for inductive
> logic; (2) the introduction of a /pragmatic self-defeat test/ (as
> illustrated by Dutch Book Arguments) for /epistemic/ /*rationality*/
> as a way of extending the justification of the laws of deductive
> logic to include a justification for the laws of inductive logic

I agree, a rational agent should never choose an action that can be
exploited by a Dutch book. I would say this supports my claim that the
rational agent doesn't have a free choice in the matter.

> 
> 
> There are 915 entries turned up by searching the SEP for "rational"
> I looked a about a dozen and found nothing that would require
> rational to be deterministic.
> 
> >
> >I have never come across the term rational agent applying to a
> >stochastic one in the literature. By contrast, I see definitions such
> >as the one I quoted from Wikipedia's article indicating that rational
> >agents are strictly deterministic.
> 
> In looking at my dictionaries of philosophy I find nothing saying
> that rational implies deterministic.  And it's common knowledge that
> stochastic decisions can be optimal in games - so I don't see how
> you can call them anything but rational.  The same Wikipedia article
> you cited goes on to say,"A *rational* decision is one that is not
> just reasoned, but is also optimal for achieving a goal or solving a
> problem."
> 

Correct. A stochastic decision is obviously not reasoned, so the
decision itself cannot be rational.

The question is whether an agent using a stochastic strategy can be
said to be behaving rationally. I do see your point that the choice of
strategy is rational, but then in that case the strategy choice is
deterministic. What is hard to get a grips on is how the term is used
in the literature, particularly vis-a-vis iterated games, where
stochatsic strategies can have better payoff.

The following thread is interesting, as it would appear the situation
is rather more murky than the black-and-white positions we've been
arguing. 

http://www.urch.com/forums/phd-economics/126310-economic-definition-rationality-irrationality.html

But for instance the example of me buying an apple instead of
an orange one day, then buying an orange instead of an apple the next
is usually explained in terms of time dependent utility, rather than
me as behaving irrationally!

> The Cambridge Philosophical Dictionary cited in the Wikepedia entry
> on "Rationality" doesn't actually have an entry defining
> "rationality" (although the word "rational" appears about a 100
> times).  It has one on "rationalism" which is contrasted with
> empiricism.  The definition of "rationality" on page 772 is part of
> a discussion of "rationalism, moral".
> 

Not much help then. Thanks for looking it up!


-- 

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Prof Russell Standish                  Phone 0425 253119 (mobile)
Principal, High Performance Coders
Visiting Professor of Mathematics      hpco...@hpcoders.com.au
University of New South Wales          http://www.hpcoders.com.au
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