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>From: Steve Gardner <gardner@aurora.cc.monash.edu.au>
Message-Id: <199511101109.WAA11981@aurora.cc.monash.edu.au>
Subject: The Cereal Box CFJ (790)
To: nomic-discussion@teleport.com (Nomic Mailing List)
Date: Fri, 10 Nov 1995 22:09:09 +1100 (EST)
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Never mind, Vanyel, I've dug it up myself:

===============================================================
Judgement of CFJ 790

Steve receives 3 points for Judgement.

===============================================================

CFJ 790

Caller: Chuck

Statement: The Registrar's report of July 12 is incorrect in that
  it lists Swann as Notary, when in fact the Office is vacant. 

Barred: Kelly, elJefe, Vanyel

Requested Injunction: None

Judge: Steve
  Judgement: UNKNOWN
  Injunction: none

Effects reported by COTC (* indicates new to this report):
  Brian gains 3 Blots for defaulting
 *Steve receives 3 points for Judgement

==============================================================

==============================================================

History:

  Called by Chuck, July 17 1995, 14:12 CST
  Assigned to Brian, July 18 1995, 12:48 UTC
  Defaulted by Brian, July 25 1995, 12:48 UTC
  Assigned to Steve Tue, 25 Jul 95 12:41:55 CDT
  Judged UNKNOWN by Steve Mon, 31 Jul 1995 17:39:51 +1000 (EST)
  Judgement published {as of this message}

==============================================================

Arguments of Caller (Chuck):

On June 30, Registrar KoJen announced that the Office of Notary
was vacant, and asked for volunteers.  On July 7, KoJen wrote:

>Volunteers for the Vacant Office of Notary were Chuck and Swann. 
> 
>I will now randomly choose the Notary. 
> 
>I have a cereal box in my lunch bag. It is "Raisin Squares". I will now count 
>the number of separate ingredients listed in the ingredients list. If it is 
>even, Chuck is the new Notary. If it is odd, Swann is. 
> 
>The number is 13. 
> 
> 
>The new Notary is Swann. 
 
Rule 790 states, in part: 
 
      [...] the Electioneer shall randomly 
      choose one player from those who indicated a willingness to hold 
      the Office, and that Player shall become that Officer.
 
Thus, if there is no random selection, then the office is not filled.
(Random is defined in Rule 1079.) 
 
I maintain that KoJen's selection is non-random. 
 
Rule 1079 demands that the probabilities be equal for a random 
selection.  No one expects the probabilities of a random selection 
to be perfectly equal (despite the fact that some Players have claimed 
that I do); this is unreasonable for any method of random selection. 
How large a tolerance is then reasonable?   IMO, for a choice between 
two random alternatives, 51-49 is just on the border of being 
reasonable, and 52-48 is clearly too large a bias. 
 
Now, is it likely that the ingredients on KoJen's cereal boxes give 
an equal distribution between even and odd ingredients? 
 
Possible: yes.  Likely: no.  Let's assume, for a moment, that 
the cereal boxes in a grocery store are equally distributed between 
even and odd numbers of ingredients.  (Even this is probably
invalid, but lets assume it for a moment.)  Does that mean that 
KoJen's cereals are evenly distributed between even and odd?  No.
 
KoJen, in all likelihood, does not buy every type of cereal in the 
store with equal frequency.  I can't speak for KoJen, but it seems 
likely that he buys, oh, 10 or so kinds of cereals regularly (with 
any others making a negligibly small amount).  Are these split 5 odd, 
5 even?  It's possible.  But it's also likely that they're split 
6-4 or 7-3.  In order to be reasonably certain that the cereals 
were biased no worse than 51-49, KoJen would have to buy on the 
order of 10,000 cereals! 
 
Objection 1.  "But it's equally likely that they're split 4 odd, 6 even 
or 4 even, 6 odd, so overall the probability is 50-50."  This would 
be true if KoJen bought a different 10 cereals every month.  But 
for the most part, he probably buys the same cereals.  Thus, the 
split is fixed at one value or the other. 
 
Objection 2.  "But we don't know which way the split goes, so 
it's still 50-50."  The fact that we don't know the probability of
KoJen picking an odd or even cereal does not magically make that 
probability 50-50.  Take, for example, the cereals in my apartment
at the time I wrote this.  3 of them have an odd number of ingredients, 
and 1 has an even number of ingredients.  Thus there is a 75-25 bias 
towards odd.  Now what would the case be if I had not gone and 
counted the ingredients on my cereals beforehand?  The probability 
would still be 75 odd, 25 even.  The fact that I didn't know what 
the probability was does not change the probability.  Likewise, 
it is likely that KoJen's selection is biased.  The fact that 
we do not know the bias does not change the fact that it *is* biased. 
 
Objection 3.  "The assignment of Swann to odd and Chuck to even was 
random."  No, this was an arbitrary assignment by KoJen.  He did 
not use any method of chance, but assigned them arbitrarily.   Is 
this random?  It may not be possible to predict in advance of KoJen's 
decision which will end up with which, but I maintain that the selection 
is not random.  It is impossible for the human brain, in and of itself, 
to make a truly random selection.   Digits that you pick out of thin 
air are not random.  If humans could pick randomly, we would not 
need to bother with any other random devices at all--how many
people would be willing to accept that? 

Objection 4.  "But since KoJen didn't know whether odd or even was 
more likely, he couldn't bias the outcome by assigning one player 
or the other to odd or even."  Correction: he couldn't *intentionally* 
bias the outcome.  No one is claiming he did.  But was his picking 
either (Swann odd, Chuck even) or (Swann even, Chuck odd) out of 
thin air truly random?  It was not, as we cannot make truly random 
decisions without some external random device. 
 
Objection 5.  "But weren't KoJen's assignments close to random?" 
I'm not saying there was a huge, 90-10 bias in KoJen's assignments. 
But it seems to me not unreasonable that there might be a 60-40 
bias. 
 
Objection 6.  "Don't the combined near-randomness of KoJen's 
assignments and the cereal boxes make the selection random?" 
They make it better, but still not close enough.  If KoJen's 
assignments were biased 60-40 (not an unreasonable assumption, 
IMO) and KoJen's cereal boxes were biased 60-40 (not an
unreasonable assumption, IMO), then the final selection is 
biased 52-48 (detailed explanation of this can be provided upon
request), an unacceptable deviation from 50-50. 
 
Thus, it is reasonably likely that KoJen's selection was nonrandom, 
and thus, the office of Notary has remained vacant. 
 
Objection 7: "You haven't proved that KoJen's selection was nonrandom; 
the burden of proof is on you."  I will grant that I cannot prove 
that KoJen's selection was nonrandom, but neither has anyone proven 
that the selection was random.  The assertion that the burden of 
proof lies on me is simply untrue.  In a CFJ, neither side 
has the burden of proof--the caller is not required to prove 
anything!  Rather, the burden is on the Judge to search out any 
relevant information not included in the CFJ and arrive at the 
correct conclusion emself, regardless of what the caller has 
or has not "proven."  If e is unable to gather information which 
is relevant to the truth of the CFJ, e must Judge UNKNOWN. 
(See Rule 591.)

============================================================

Arguments of Judge (Steve):

I am reluctant to deliver this Judgement, since I regard it as
desirable that there should be a clear cut answer to the question of
whether Swann is the Notary. However, careful consideration of
the facts and arguments presented have led me inexorably to the
conclusion that I am unable to obtain the information necessary
to determine the truth or falsity of the Statement. Hence I must,
by Rule 591, Judge UNKNOWN.

There seem to me to be two issues to consider: (i) was KoJen's
'coin' fair? That is, did KoJen's method of *selection* distribute
probability equally between its two possible outcomes? (ii) was
KoJen's *assignment* fair? That is, was his method of assigning
Chuck to even and Swann to odd a fair one? Now, if the answer to
*either* of these questions were 'yes', then that would suffice,
in my opinion, to prove the fairness of KoJen's method as a whole.
In that case, the Statement would be FALSE. To see this, consider
the following two extreme and opposite cases:

1. KoJen uses a completely biased method of selection, whose bias is
known to him prior to making the selection, eg, "if today's date is
even-numbered then Chuck is the Notary, otherwise Swann is the
Notary", when KoJen already knows what today's date is. However,
KoJen uses a completely fair method (such as flipping a fair coin) to
make the assignment of Chuck to even-numbered days and Swann to
odd-numbered days. 

2. KoJen uses a completely biased method to make the *assignment*,
but a completely fair method to make the selection.

I think it's clear that in both these cases, the method as a whole
is a fair one. Consider now the actual methods of assignment and 
selection employed by KoJen. His method of selection is by now
infamous - he looked at a cereal box he happened to have with him
to see if the number of ingredients listed on it was odd or even.
Less attention has been paid to his method of assignment, but it
appears that KoJen simply picked his assignment of Chuck to even
and Swann to odd out of his head. The question is: are either of 
these methods demonstrably fair, in the sense given above (which
is the sense of Rule 1079)? If either of them are demonstrably fair,
the Statement is FALSE.

But neither of the methods is demonstrably fair. Considering first
KoJen's method of selection, we should need to know much more about
which breakfast cereals KoJen buys, and about how the numbers of
ingredients listed on them are distributed among the even and odd
integers. (And why stop at breakfast cereals? Might not KoJen equally
have employed some other foodstuff that happened to be at hand? Even,
god forbid, a can of Nile Spice Black Bean Soup?) In the absence of
this information, we cannot know whether KoJen's 'coin' was fair.

Of course, all this would not matter if it could be demonstrated that
KoJen's *assignment* was fair. That's the point of the argument I
gave above. But was KoJen's assignment fair? Once again we seem to be
confronted with insurmountable epistemological obstacles. It is
apparently a part of widely accepted scientific wisdom that human
beings are not particularly reliable generators of random numbers,
(although I cannot cite specific scientific studies which confirm
this).  But what this implies for a given human being's ability to
choose randomly and fairly between two alternatives on a given
occasion is entirely unclear. It seems to me that we should need to
know a great deal not only about the neurophysiological mechanisms
which underpin the making of such choices generally, but also about
how they were operating in this specific instance. And once again,
this is information which it seems we cannot have. So we cannot know
that KoJen's assignment was fair, either.

So, given that we cannot definitively answer 'yes' to either of the
two questions above, the Statement cannot be FALSE. But it seems
to follow relatively straightforwardly that the Statement also cannot
be TRUE. For all we know, KoJen's method as a whole *might* have been
fair. It also might not have been. We should need to know a great deal
more than we do now - more, indeed, than we're ever likely to know - 
to determine whether or not it was. Since this crucial information
is unobtainable, I must Judge that the Statement is UNKNOWN.

============================================================

Evidence provided by Caller (Chuck):

1. Rule 591 
2. Rule 790 
3. Rule 1079 
4. KoJen's announcement of vacancy of the Office of Notary, Jun. 30 (some 
   header information deleted) 
5. KoJen's "selection" of the Notary, Jul. 7 (some header information 
   deleted) 
6. Registrar's Report of Jul. 12 (excerpts) 
 
The complete text of documents excerpted in 4, 5, and 6 are available 
upon request. 
 
======1. Rule 591 
 
Rule 591/2 (Mutable, MI=1) 
Legal Judgements 
 
      A legal Judgement is either TRUE, FALSE, UNDECIDABLE, or
      UNKNOWN.  The Judgement of UNDECIDABLE is reserved for those 
      statements which are logically neither TRUE nor FALSE.  The 
      Judgement of UNKNOWN is for those statements for which the 
      Judge is unable to obtain information necessary to determine 
      whether the statement is TRUE, FALSE, or UNDECIDABLE. 
 
      The Judge must make a reasonable effort to obtain all 
      information necessary to determine whether the statement 
      is TRUE, FALSE, or UNDECIDABLE. 
 
      The Judgement must be accompanied by reasons and arguments, 
      which include, but are not necessarily limited to, citations of 
      deciding Rules, past Judgements, and game custom. A Judgement 
      delivered without reasons and/or arguments is completely 
      invalid. 
 
      Such reasons and arguments form no part of the Judgement itself. 
      However, the Clerk of the Courts must distribute the reasons and 
      arguments along with the Judgement. 
 
      Any evidence which is used to justify the Judgement, other than 
      appeals to Game Custom or to common sense, must be presented by 
      the Judge.  If the Judge introduces evidence beyond that 
      submitted in the Call for Judgement, e must include this 
      evidence in eir Judgement.  All such added evidence must be 
      distributed as part of the reasons and arguments by the Clerk of 
      the Courts. 
 
History: 
.. 
Amended(1) by Proposal 1320, Nov. 21 1994 
Amended(2) by Proposal 1487, Mar. 15 1995 
 
======2. Rule 790 
 
Rule 790/0 (Mutable, MI=1) 
Filling Vacant Offices 
 
      If, for any reason, an Office is vacant, that fact shall be 
      announced by the Electioneer.  The Electioneer shall be the 
      Registrar; or in eir absence, the Speaker.  All Players willing 
      to hold the Office shall notify the Electioneer of that fact 
      within three days of eir announcement of the vacancy.  At the 
      end of the three day period, the Electioneer shall randomly 
      choose one player from those who indicated a willingness to hold 
      the Office, and that Player shall become that Officer.  This 
      rule applies to Offices in general, and thus defers to Rules for 
      specific Offices. 
      (*Was: 689*) 
 
======3. Rule 1079 
 
Rule 1079/0 (Mutable, MI=1) 
Definition of "Random" 
 
      All occurrences of the word "random" or forms of it shall be 
      taken to mean "any one of the choices with equally distributed 
      possibility for each choice". 
 
======4. KoJen's announcement of vacancy of the Office of Notary, Jun. 
         30 (some header information deleted) 
 
Date: Fri, 30 Jun 95 08:15:18 -0400 
>From: cogen@ll.mit.edu (David Cogen) 
To: nomic-official@teleport.com 
Subject: OFF: vacancy of Notary 
 
Notary Office is Vacant. (yawn.) 
 
Anyone want it? Notify Registrar within 3 days. 
 
-- KoJen 
 
======5. KoJen's "selection" of the Notary, Jul. 7 (some header 
         information deleted) 
 
Date: Fri,  7 Jul 95 15:17:15 -0400 
>From: cogen@ll.mit.edu (David Cogen) 
To: nomic-official@teleport.com 
Subject: OFF: Office of Notary 
 
Volunteers for the Vacant Office of Notary were Chuck and Swann. 
 
I will now randomly choose the Notary. 
 
I have a cereal box in my lunch bag. It is "Raisin Squares". I will now count 
the number of separate ingredients listed in the ingredients list. If it is 
even, Chuck is the new Notary. If it is odd, Swann is. 
 
The number is 13. 
 
The new Notary is Swann. 
 
-- KoJen 
 
======6. Registrar's Report of Jul. 12 (excerpts) 
 
===== Agora Nomic Registrar's Reports ================================= 
 
      DATE OF LAST REPORT : 95.07.07 
      DATE OF THIS REPORT : 95.07.12 
 
===== 3.0 Officers (Blue Pages) ======================================= 
 
{Listing of Officers, the Speaker; etc. Please see the full listing 
(section  6) for email addresses.} 
 
SPEAKER                 : Kelly 
 
OFFICERS: 
    Ambassador          : Kelly 
    Archivist           : Vanyel 
    Assessor            : Steve 
    Assistant           : Vanyel 
    Banker              : Andre 
    Clerk Of The Courts : Andre 
    Distributor         : Vanyel 
    Herald              : Swann 
    Justiciar           : Steve 
    Notary              : Swann 
    Promotor            : KoJen 
    Registrar           : Ian 
    Rulekeepor          : Chuck 
    Scorekeepor         : Kelly 
    Tabulator           : Ian 
 
 
=================================================================

End of CFJ 790

=================================================================


Steve Gardner                     |  "Justice? You get justice in the next
Dept. of Philosophy, Monash Uni.  |   world, in this world you get the law."
gardner@aurora.cc.monash.edu.au   |          --  William Gaddis --