==============================  CFJ 1826  ==============================

    The AFO's VVLOP changed as a result of comex's message with
    Message-ID
    <6bf32280711281839g6adde4a4wdf21f00d231c776b@mail.gmail.com>

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Caller:                                 Murphy

Judge:                                  root
Judgement:                              FALSE

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History:

Called by Murphy:                       06 Dec 2007 19:15:52 GMT
Assigned to root:                       09 Dec 2007 23:23:20 GMT
Judged FALSE by root:                   20 Dec 2007 05:53:31 GMT

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Caller's Arguments:

In CFJ 1813, Goethe argued that VVLOP is defined as a "parameter",
implicitly treated as a number, but could also be interpreted as a set
of numbers (added up whenever the value of VVLOP is queried).  In this
hypothetical context, "decrease by -1" is interpreted as "remove -1 from
the set".  However, this only works if the set contains a -1 to be
removed.  This is sufficiently unworkable to shoot down the implicit
application of this interpretation.  Even if this interpretation were
explicitly stated, the AFO's VVLOP set did not contain enough -1's to
remove 104 of them.

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Judge root's Arguments:

When I initially read Judge Goethe's arguments in CFJ 1813, they
seemed very reasonable.  Upon closer inspection, the interpretation of
VVLOP as a summed multiset is reasonable but not necessary.  It is
equally reasonable to interpret VVLOP as simply a rational number;
both interpretations are consistent with the rules.  With that in
mind, I would adhere to Goethe's precedent if it aligned with the best
interests of the game, but I find that it does not.

The initiator of these cases argues that to remove a number of -1
values from the set, there must be at least that number of -1 values
in the set to begin with.  Considering this argument, the set must be
finite, or it would be impossible to sum.  Furthermore, Goethe's
interpretation provides no way to replenish the -1 values in the set,
so they must eventually deplete, at which point this interpretation
breaks.  Since there is no indication as to the initial number of -1
values in the set, there is no way to know when this condition is
reached, leading to a nondeterministic split in game state each time
the clause is exercised.  This is clearly in opposition to the best
interests of the game.

Additionally, the rules do not only define ways to increase and
decrease VVLOP by integral values; Rule 2126(d) defines a means for
multiplying VVLOP by fractional multiples of 0.1 and 0.

The multiplication could be performed in three ways, none of which are
satisfactory:  first, a number of copies of the set equal to the
multiplicand could be joined together, but this only works when the
multiplicand is an integer.  Additionally, upon multiplication by 0,
the set would be empty and thus would no longer contain any negative
values to be removed under R2126(c).

Second, every element of the set could be multiplied individually, but
this is also incompatible with the interpretation of removing negative
values.  In particular, upon multiplication by zero, all the elements
in the set would be zero and thus non-negative.  Upon multiplication
by a fraction, it is unknown at what point the set ceases to have
integral values, which again results in nondeterminism, and not just
when applying the scam.

Third, to multiply by a fraction or zero, we could remove copies of
each type of element in proportion.  In addition to having the same
multiplication by 0 issue as the first method, this would result in
slight nondeterministic errors when the elements of the set do not
happen to exist in the correct proportions.

Finally, Rule 2156 defines circumstances under which VVLOP is
specifically set to an integer value.  Each week, EVLOP is explicitly
"rounded to an integer", making it clearly an integer, and VVLOP is
then "set to the same rounded value", not to an equivalent set-based
value.  To support the set interpretation, VVLOP must at some point be
changed back into a set, and it is not clear how this must occur.

As stated above, I find that all of these points conflict with the
best interests of the game, and so I think it important to deviate
from the set interpretation.  In contrast, a rational number
interpretation results in no such problems.  Based upon that, and upon
Judge Goethe's prior reasoning if VVLOP is assumed to be a number, I
judge CFJs 1826 and 1827 FALSE.

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