On Wed, 9 Sep 2009, Pavitra wrote:
> The question then is: does the mathematical meaning (R754(3)) of
> "random" imply that the random choice is made platonically and
> invisibly, or does it leave that to "other Agoran legal documents"
> (R754(4)), arguably including former Rules and probably including past
> judicial precedents, to determine?
>
> If the former, the rule is broken. If the latter, we may be okay.
>
> Is anyone here a mathematician of randomness?
I'm a part-statistician anyway, but the question is philosophical.
The rule in question doesn't talk about "choice" at all, but says that
"random cards are destroyed" as an external event, rather than an event
made after a random choice (e.g. "the auditor selects N cards at random,
which are destroyed").
Given this, we have two choices:
1. Infer that despite the language, our legal precedents on randomness
lead us to assume that someone does make the choice, in which case
a court would have to figure out who it was (likely the auditor or the
recordkeepor) or decide that since there's no one authorized to make
the choice, doing the destruction is IMPOSSIBLE. This favors the
spirit and some precedents but very much ignores the language. In this
case, past precedents hold that the timing of a random choice is when
the random choice is made public, even if it's after the choice event.
(This assumes that there's very little time between the person making
the choice and publishing it; if e acts on the choice before publishing
it's not random to that person, something that was debated during CFJ
1435).
2. Decide that we're dealing with a measurement issue rather than
a process issue ("an event happened, but we haven't sampled/measured
the system to see what event occurred").
If we decide this, we can look at statistical theory:
1. Before an event, we can speak of its probability.
2. After the event, the platonic probability of what actually happened
is 1 and the probability of all other events is 0.
3. But from a statistical/measurement standpoint, we have no new
information about the process, so we can still speak of the
probabilities as in (1). But can we make further inferences?
- If you believe in a frequentist viewpoint, there's no new data to
falsify a hypothesis of any particular outcome, so the result
remains UNDETERMINED.
- If you take a Bayesian standpoint (with the process probabilities
as your priors) you come to the conclusion that 1/Nth of each
possible types of N cards were destroyed. Since this is
IMPOSSIBLE (a higher-powered rule prevents destroying fractions
of cards) the destruction simply didn't function.
- If you take a legal/decision standpoint (where legally a decision
must be made based on uncertain data - see particularly natural
resource management for situations like this - a court CAN
determine a likely outcome and make it the legal reality; for
example by the court making a fair choice itself or delegating to
the recordkeepor.
Choose your statistical worldview!
-G.
