Sign-in / Sign-up
Your question

Esoteric: Theory of a Perfect Adjudication Engine

Tags:
  • Engine
  • Video Games
Last response: in PC Gaming
Anonymous
January 18, 2005 6:29:17 PM

Archived from groups: rec.games.diplomacy (More info?)

***************************************
Theory of a Perfect Adjudication Engine
***************************************

This article in its current, updated format may be found at
http://www.geocities.com/Diplomacy2007/

Keep in mind that Diplomacy contains ambiguities in the writing of its
rules.
Also, the game of Diplomacy contains ambiguities because two reasonable
people
can interpret the set of rules differently due to the rules not being
written in
an air-tight fashion. Diplomacy also contains a type of ambiguity in
the sense
that there exists some situations where a set of legal move orders, if
carried
out, would result in fundamentally important rules of Diplomacy being
violated
(and this state is a paradox). Therefore, everything stated in this
document
can and must be only opinion.

Let it be theorized that there exists an adjudication engine (such as a
computer
program following a set of instructions or a human being following a
set of
instructions) which can in all cases correctly adjudicate any Diplomacy
board situation.

Of course, for us to reach this state, we would first need to have an
unambiguously written rule set (which doesn't exist), and we all need
to be
using the same published rule book (which also doesn't happen). But,
we will
assume, prior to postulating our theory, that the Dipomacy rules can be
unambiguously interpreted and that everyone uses exactly this same rule
set.

Here is a small, preliminary theory: For any given Diplomacy board
position
that does not in any way involve a paradox, there exists one and only
one
correct and true adjudication.

Here is the theory (which I ask to be taken as true until a real world
experience proves the theory wrong):

********************************************************************************
The Theory of the Existance of a Perfect Diplomacy Adjudication Engine
----------------------------------------------------------------------
IF
the Diplomacy rules can be interpreted unambiguously, and if
everyone is using these unambiguous rules,

AND

IF
no written orders will bring about a position which violates a
primary and fundamental rule of Diplomacy (that is, we will not be
asking the
adjudication engine to solve any positions that will result in a
paradox)

THEN

there exists one or more adjudication engines that can perfectly and
correctly
adjudicate any given Diplomacy board position.

(where "board position" is the position of the pieces at the beginning
of the
move as well as the orders which need to be adjudicated).
********************************************************************************




I suspect that most people might not object to accepting the above
theory as
true. The next theory I will propose may bring up some objections.

Let the algorithm or process I outlined in my article, "Inside the
Adjudicator's
Head," be given the name DipAlg.

********************************************************************************
The Theory that DipAlg is an Instance of a Perfect Diplomacy
Adjudication Engine
--------------------------------------------------------------------------------

Assuming that everyone can understand the DipAlg algorithm
unambiguously and
in exactly the same way, then the DipAlg algorithm is an instance of a
perfect
Diplomacy adjudication engine.
********************************************************************************

As a theory, I ask you to accept this theory as true until proven
otherwise.





I've asked you all to accept two theories as true until proven
otherwise.
But keep this in mind: if you find a case where you prove the theory
wrong,
then I will ask you to help me fix the algorithm so that the theory
still
stands!

Let's now see if we can leverage this acceptance to offer a proof in a
faster,
more efficient fashion than we may have otherwise been able to do.

As a reminder, here are the definitions of a "hot spot" which I have
brushed up
a little for this particular article (so this is the most accurate
representation of a hot spot to date, January 18, 2005):

A province on the Diplomacy map becomes a hot spot during the
adjudication
process when:

i. a unit has been ordered to move into a province that was unoccupied
at the
very beginning of the turn, or a unit has been ordered to move into a
province
that has, during the adjudication process, become vacant.

ii. two units have been ordered into each other's province (for
instance,
French fleet in Mid-Atlantic to West Mediterranean, and Italian Fleet
in West
Mediterranean to Mid-Atlantic; also for instance, French Fleet in
Spain(nc) to
Portugal, and Italian Fleet in Portugal to Spain(sc); also the next
example is
a for instance which does not count as a hot spot because it is a
simple
rotation: French Army in Spain to Protugal, and French Fleet in
Mid-Atlantic
convoys French Army in Spain to Portugal, and Italian Army in Portugal
to Spain),

iii. a unit X has been ordered into a province which at the very
beginning of
the turn already contained a military unit Y such that unit Y did not
receive a
move order or else upon adjudicating unit Y's move order it was found
that for
one reason or another unit Y's move order could not be fulfilled (for
instance,
it was pushed back or "bounced" back to its original province and
is now
holding).

iv. two or more units have been ordered into a province P, such that
before
these unit's move orders are adjudicated and executed, neither unit is
currently
in province P. Example 1: Italian Army in Roma to Tuscany; French
Army in
Piemonte to Tuscany. Example 2: Italian Army in Roma to Tuscany;
French army
in Piemonte to Tuscany; Turkish Army in Tuscany holds. Example 3:
Russian
Army in Tunisia to Tuscany; Russian Fleet in Tyrhennian Sea convoys
Russian
Army in Tunisia to Tuscany; French Army in Spain to Tuscany; French
Fleet in
Gulf of Lyon convoys French Army in Spain to Tuscany; Italian Army in
Piemonte
to Tuscany; Turkish Army in Tuscany holds; Turkish Army in Venezia
supports
Turkish Army in Tuscany. Not an Example A: Italian Army in Piemonte
to
Tuscany. Not an Example B: French Army in Piemonte to Tuscany;
Italian Army
in Tuscany to Piemonte. Not an Example C: French Army in Piemonte to
Tuscany;
Italian Army in Tuscany holds. Not an Example D: French Army in
Piemonte to
Tuscany; Italian Army in Tuscany to Venezia.

v. if two or more units are involved in a closed loop rotation of
provinces,
each province that was initially occupied by these units prior to them
executing
their orders becomes a hot spot. For example, the British army moves
from
Norway to Sweden via a convoy conducted in the Skagerrak, and a Russian
army
moves from Sweden to Norway by foot; there are two hot spots: Norway
and
Sweden. Another example: French Army in Brest to London; French
fleet in
English Channel convoys French Army in Brest to London; British Army
in London
to Belgium; British Fleet in North Sea convoys Army in London to
Belgium;
German Army in Belgium to Picardy; French Army in Picardy to Brest;
in this
example of a closed looped rotation, there are four hot spots: Brest,
London,
Belgium, and Picardy.


Note that a hot spot can't be processed during the adjudication process
until
it is deemed to already be in existence at the start of the
adjudication process
or because it "lights up" due to previous steps in the adjudication
process.
Thus, one necessarily cannot begin the adjudication process on any
province
chosen arbitrarily or randomly.



I've asked you all to accept two theories as true until proven
otherwise. I've
also tightened up the definition of a hot spot (which may, as time
unfolds,
need further tightening as the community uproots the above theories).

Let's now see if we can leverage this acceptance to offer a proof in a
faster,
more efficient fashion than we may have otherwise been able to do.

Let's consider DATC test case 6.G.10 as it exists now, January 18,
2005.

It gives this scenario (and I turned the German convoying fleet into an
English convoying fleet so that I need not use the term "via convoy" in
the
written orders and so that no other issues are considered but those
that
this example will focus on):
Scenario:
England:
Army in Norway to Sweden
Fleet in Denmark supports Army in Norway to Sweden.
Fleet in Finland supports Army in Norway to Sweden.
Fleet in Skagerrak convoys Army in Norway to Sweden.
Russia:
Army in Sweden to Norway.
Fleet in Barents Sea supports Army in Sweden to Norway.
France:
Fleet in Norwegian Sea to Norway.
Fleet in North Sea supports Fleet in Norwegian Sea to Norway.

We make the assumption that the Army in Norway will attempt to travel
by
Convoy to Sweden instead of ever considering walking to Sweden for all
scenarios given in this article. Convoy order ambiguities are not the
topic at
this time, that is why this assumption need be stated.

Now, consider this DATC text from this section:
QUOTE
The more interesting question is whether the French fleet in the
Norwegian Sea
is bounced by the Russian army from Sweden. This depends on the
interpretation
of issue 4.A.7. If the rulebook is taken literally (choice a of issue
4.A.7),
then a dislodged unit cannot bounce a unit in the area where the
attacker came
from. This would mean that the move of the fleet in the Norwegian Sea
succeeds.
However, if choice b (of issue 4.A.7) is taken (which I prefer), then a
bounce
is still possible, when there is no head to head battle. So, the fleet
in the
Norwegian Sea will fail to move.
UNQUOTE

Let me attempt to reword what is being discussed concerning selecting
option a
of issue 4.A.7 in the above scenario. Basically, it is saying that the
Russian
fleet in Sweden is dislodged from Sweden during the adjudication
process prior
to there ever having been a stand-off in Norway between this Russian
fleet and
the French fleet in the Norwegian Sea.

We wish to focus in on this scenario and determine if it is legitimate.

Therefore, we simplify, because the core of this alternate
interpretation needs
only three units:
Scenario:
Britain:
Army in Norway to Sweden
Fleet in Skagerrak convoys Army in Norway to Sweden.
Russia:
Army in Sweden to Norway.

By the rules, which I don't think anybody has any ambiguity about, this
is a
rotation where one military unit is convoyed.

Because we have two armies attempting to move into each other's
province such
that a closed loop is formed, by rule HotSpot.iv, there are two hot
spots to
consider: Norway and Sweden. We can arbitrarily begin with either.

01--What happens in Norway?

That depends on whether or not the British attempt to leave Norway
fails.

02--What happens in Sweden?

That depends on whether or not the Russian attempt to leave Sweden
fails.

03--Are there any OTHER units bringing any type of weight or effect on
Sweden?
AND, Are there any OTHER units bringing any tpe of weight or effect on
Norway?

"No," is the answer for both cases.

Therefore, the two armies swap and we have answered all the questions
in our
to-do list.

Correct adjudication: British army moves from Norway to Sweden; the
Russian
army moves from Sweden to Norway.

Now we add a little more spice to this scenario, and support Britain's
convoy
into Sweden:
Scenario:
England:
Army in Norway to Sweden
Fleet in Denmark supports Army in Norway to Sweden.
Fleet in Skagerrak convoys Army in Norway to Sweden.
Russia:
Army in Sweden to Norway.

I would argue at this stage to a human listener, and say: we have just
seen an
example where a rotation occurred, and I suggest that by England simply
adding
a support to its convoyed army's destination does not change the fact
the the
Russians and the British are still rotating.

But what can our perfect adjudication engine tell us? Or will it get
confused!

The adjudication recognizes two hot spots as before: Norway and
Sweden. They
are given equal weight, and any one may be arbitrated first.

Let's arbitrarily start with Norway (as it exercises the algorithm
more).

01--What happens in Norway?

Well, we don't know because we are not yet certain if the British will
leave
Norway.

02--What happens in Sweden?

Ah, that's easy. For even if we assume that the Russians eventually
end up
in Sweden (due to a hypothetical "bounce" which might occur in other
positions),
Britain will take Sweden with a strength of 2 to 1. So, we can
definitely say
that the British army successfully convoys from Norway to Sweden and
remove
question 02 from the to-do list.

Now we answer question 01--What happens in Norway?

At this stage we know that the British have left Norway, therefore the
Russian army can walk into Norway.

The final adjudicated result: the British army in Norway moves to
Sweden;
the Russian army in Sweden moves to Norway.

It is important to note that the Russian army was never, ever dislodged
from
Sweden, for it never engaged the British army.

Therefore, the text in the DATC which reads:
"The following interpretations are possible: a. A dislodged unit has
never
any effect on the area where the attacked departed from. ..."

cannot possibly be applicable to the example in any way, because our
perfect
adjudicator has not told us that the Russian army was dislodged from
Sweden (in
fact, it told us that the Russian army moved to Norway).

Let's add even more excitement to our example and this example is more
in line
with the original example:
Scenario:
England:
Army in Norway to Sweden
Fleet in Denmark supports Army in Norway to Sweden.
Fleet in Skagerrak convoys Army in Norway to Sweden.
Russia:
Army in Sweden to Norway.
France:
Fleet in Norwegian Sea to Norway.

By rule HotSpot.iv, there are two hot spots: Norway and Sweden.

Let's arbitrarily begin our adjudication process looking at Norway.

01--What happens in Norway?

Ah, that's easy. If the British end up in Norway because they were
unable to
move (such as due to a bounce), or if the British end up being able to
leave
Norway, the result with respect to France and Russian is identical:
they do
not move into Norway because they are attackers of equal strength and
they
bounce off one another.

We've answered part of the question concerning Norway, but not with
respect
yet to the British troops.

02--What happens in Sweden.

At this stage in the adjudication process we know that the Russians
have been
bounced and are now holding in Sweden. Furthermore, we know that the
British
are attacking Sweden with a force of 2 against 1. Therefore, the
Russians
NOW are dislodged from Sweden during the adjudication process; the
British move
into Sweden. We can now remove question 02 from the to-do list.

The answer to question 01 can now be answered and question 01 removed
from the
to-do list: because the British successfully made it from Norway to
Sweden,
Norway is now unoccupied.

The final adjudication: Russia is dislodged from Sweden; the British
army in
Norway moves to Sweden; no other military units move.

Again, our perfect adjudicator has told us two things: during the
adjudication
process Russia bounced off Norway, and that later in the adjudication
process
when Russia went into a hold, it was dislodged from Sweden.

Therefore, the assertion in the DATC, "A dislodged unit has never
effect on the
area where the attacker departed from. This is the literal
interpretation of
the rulebook," this assertion cannot ever be a true statement in this
particular
scenario.

So, the DATC may remove all this discussion about choices under section
4.A.7. Given our assumption of a perfect adjudicator, option "a" under
section 4.A.7 need not even be mentioned, because it is an
impossibility.

That ends this article. Is it circular reasoning? Yes, in that it
assumed
the existence of a perfect adjudicator, that such an adjudicator
exists, and
that there can only be one correct adjudication for any given Diplomacy
scenario. But, are these assumptions so impossible? If they are not
so
impossible, then it is not circular reasoning.

Thanks

More about : esoteric theory perfect adjudication engine

Anonymous
January 19, 2005 8:14:01 AM

Archived from groups: rec.games.diplomacy (More info?)

Hi,

Another aspect of the perfect adjudication engine is, if
possible, to break it up into three passes; this is an interesting
topic of study which perhaps others may assist in (as well
as assisting in strenghtening the theoretically perfect
adjudication engine as outlined above).

The boundary between a written order, a conversion to a legal
order, and exactly which convoy an army takes, if any, is all
generally fuzzy, and may not be partitionable easily into one
compartment within our perfect adjudication engine.

We would, I think, definitely want these compartimentalized,
if possible, because of even more ambiguity and different
interpretations about how to convert a legal order to an
actual order and how to define exactly which convoy, if any,
an army took. Furthermore, it is my understanding that there
are at least rule variants, if not rule ambiguities about how
to handle a unit once it is determined to have been dislodged.

So, this would be an interesting area of study: can we
compartimentalize
the "perfect adjudication engine" such that we have three passes
1. The conversion of written orders into a legal orders, as well as
the
determination of which convoy, if any, an army will take.
2. Then, and only then, adjudicating the position.
3. Finally, if there are any dislodgements, then adjudicating this
step
would be a final, separate step.
Again, my writings to date only deal with item (2) above.

Thanks