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THE RESEARCH SUPPLEMENT
(DEVELOPMENTS IN THEORY AND SOFTWARE)
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Supplement to the COOPERATION OR CONFLICT research letter
Vol 9 No 6 November 1995
Sent to users and champions every two months by Nigel Howard, 10
Bloomfield Road
Moseley Birmingham B13 9BY England. Phone/fax: 021-449-4480. E-mail
nigel@nhoward.demon.co.uk
This is a technical supplement to the COOPERATION OR CONFLICT research
letter for those
interested in pursuing the theory or developing applications. Technical
contributions
welcome.
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What, MORE
software?!
Jim Bryant (Sheffield Hallam University)
STUDIO is the name of a new software package joining CONAN, INTERACT and
DECISIONMAKER
as a tool for the analysis of interactions.
This article gives some justification for the addition of yet another
package to those
already available. In succeeding issues of this research letter a
'walk-through' of
the use of STUDIO will demonstrate its approach in more detail and let
readers see how
it might meet their needs.
Personal constructs
STUDIO takes as its starting point the individuality of personal
perceptions of
situations. Following the view put forward by George Kelly in his
well-known Theory of
Personal Constructs, people are seen as continually striving to make
sense of their
encountered worlds through idiosyncratic individual mental frameworks.
These frameworks
essentially consist of a network of theories about the world, and can be
used to
interpret or anticipate events. The core of a STUDIO application is
correspondingly a
set of mental maps that depict the thinking of those involved in a
situation.
Within a given context - eg, a particular dispute - an individual's
mental map will
show how means are seen as relating to ends and actions contribute to
goals. Taken
with that person's value system, the maps provide a crude means of
suggesting the
potency of alternative courses of action - ie, the degree to which each
separately or
in combination with others may lead to desired outcomes.
Work with STUDIO is organised around the drama-theoretic notion of the
frame. A frame
is owned by a set of characters who appear on stage carrying their own
mental baggage.
The development of frames is analysed conventionally enough in terms of
the potential
futures which their characters could bring about; that is, by scenario
analysis. This
is where the preferences that characters have between these futures enter
into
consideration; also, where changes in these preferences in the emotional
heat of a
dramatic crisis occur.
Strung together over time, episodes - movement from an initial to a final
scenario
within a frame - construct stories, and it is with the creation of
plausible or telling
stories that STUDIO is ultimately concerned.
Similar yet different
At its core STUDIO is broadly similar to the other products on the market
for
interaction analysis. It contains an analytical engine that corresponds
closely to
those in CONAN and INTERACT. In this sense it shares their differences
from
DECISIONMAKER (see Conan Supplement, Vol 6, No 5) by adopting an
'intuitive' approach
to complexity. Like CONAN and INTERACT it also provides extensive space
for annotation
of an analysis: it could even be viewed as a set of carefully structured
'situation
databases'.
The differences from earlier products are in two broad areas: scope and
interface.
STUDIO widens the modelling activity 'backwards' and 'forwards'. In a
backwards
direction, it goes behind the simple statement of a cast list in two
ways. First it
encourages consideration of the relationships between characters, and of
their
individual qualities. Second, as mentioned above, it requires explicit
statement of
their individual mental models, from which actions and goals naturally
emerge.
STUDIO takes the analysis 'forwards' by moving beyond strategic maps -
though it
prefers to substitute movement maps here - by enabling the user to
interactively change
preferences in such maps and see what emotions would accompany such
changes. It also
allows 'chaining together' of episodes to form alternative storylines.
The STUDIO interface is a standard Windows one. This alone represents a
shift from
earlier software, and should make the product more accessible to
newcomers.
Try it
How the product will be received is yet to be seen. Currently only a
pilot version is
available, though it is planned to release a test version during the
first half of
1996. If you would like to join the test panel, and so receive an early
version of the
software for trial, get in touch (e-mail: J.W.Bryant@shu.ac.uk). In due
course a
demonstration version of the software will also be available.
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MOMENTS OF TRUTH
Part 1 of The Mathematics of Drama Theory
(Note: In this electronic version of the research letter, subscripts are
shown in
square brackets, superscripts in curly brackets. So p[c]{i} stands for
letter p
subscripted by letter c and superscripted by letter i. Order the printed
research
letter to see it done properly!)
Drama theory has an essential mathematical foundation. Using mathematical
notation can,
however, give the wrong idea. People think it suggests (absurdly) that
only the
abstract structures captured in the mathematics matter!
An example: anyone who uses a mathematical model that's symmetric between
characters is
likely to be accused of assuming that characters have symmetric roles!
Absurd - not?
If I measure two people and find they have the same height, am I thereby
asserting
their identity? Of course not. Likewise, to use a symmetric model is not
to assume
symmetry. Yet the accusation is made.
For this reason we've tried to avoid mathematical notation in this
research letter.
This, however, may give the impression that there is no maths, or that
its role is
unimportant. We are therefore, with due warning, setting out some of the
basic maths
that's been developed. Research, of course, continues.
The frame
A frame (the drama-theoretic equivalent of a game) may be defined as a
pair
(Q, u).
Here
- Q:S -> S is a *consequence function* to and from a set S of outcomes.
- The set S is the product
S = product(S[c] | c in C)
of a family (S[c] | c in C) of strategy sets indexed by a set C called
the cast.
Members of C are called characters. The idea is that each character c in
C chooses a
strategy s[c] from S[c]. The result is an outcome s = (s[c]| c in C) in
S.
- u = (u[c]| c in C) is a family of utility functions u[c]:S -> R (the
set of
real numbers). u[c](s) is the 'utility' or 'payoff' c derives from the
prospect of s.
(Usually u[c] is regarded as having ordinal significance only - ie, any
function that
ordered outcomes in the same way as u[c] could be used in its place. The
use of
cardinal utilities has not been explored - a research opportunity here!)
Qs - the consequence of s - is the outcome characters would actually
implement if they
tried to implement s. If Qs = s, s is called *feasible*; otherwise,
*infeasible*.
A feasible outcome is also called a *future*; it represents the future
that's
projected if the strategies listed in it are carried out. Q models
interdependencies
between characters' strategy choices in determining the future - eg, (to
take a common
example) if you decide to fight a decision I decide not to make, the
consequence may be
that I don't make it and you don't fight it - there being nothing to
fight!
Q obeys the rule: Q(Qs) = Qs for all s (every outcome has a feasiUse of uninitialized value in concatenation (.) or string at E:\listplex\SYSTEM\SCRIPTS\filearea.cgi line 451, line 359.
ble
consequence). Q
and u together obey the rule u[c](s) = u[c](Qs) for all c, s (the utility
of any
outcome is that of its consequence).
A moment of truth
A dramatic episode takes place within an informationally closed
environment. This may
be conceptualised as a set E of frames - the set of all frames the
characters might
possibly use as models of their situation, given the information they
have between
them.
Here 'possibly' means not only 'as they exchange information' but 'when
they are forced
to be creative at an emotional climax'. As neither the characters
themselves nor an
analyst can say beforehand what such creativity might engender, the set E
is in
principle unspecifiable. We can use it in a general mathematical
description of
dramatic resolution; we can't, realistically, specify it in any
particular
application.
The dramatic episode proceeds through a build-up phase to a climax.
During the
build-up, characters model the situation in terms of a number of frames
from E. These
represent their developing views of the situation and of other's
viewpoints. When the
climax is reached, they will normally have converged on a single frame;
without such
convergence, a full confrontation between opposing viewpoints is
impossible.
The common frame they then share is *common knowledge* - meaning that
each believes
that it represents the situation, believes that each other believes this,
believes that
each other believes that each other believes it... etc.
They share more than a common frame, however. Also common knowledge
between the
characters at this point are the positions and implied fallback
strategies of each of
them. They thus arrive, when the episode reaches a climax, at a moment of
truth,
defined as a triple
(F, p, f),
where
- F is a frame;
- p = (p{c}| c in C) is a family of futures defined in F, the future
p{c} in
Q[S] being character c's position - ie, the future it claims to want and
seeks to
persuade others to accept;
- f = (f[c]| c in C) is a particular outcome in S composed of the
fallback
strategy f[c] of each character c - meaning the strategy f[c] in S[c]
that c implicitly
threatens to carry out if its position p{c} is not convincingly accepted
by the others.
France, for example, is currently at a moment of truth. The government's
position is
(No Concessions, No Strike) and its fallback strategy is No Concessions.
The unions'
position is (Concessions, No Strike) and its fallback strategy is Strike.
The current
situation is f = (No Concessions, Strike).
What is a gradient?
The 'gradient' of a moment of truth (or mot) is its tendency to cause
characters to
feel emotion, act irrationally and reframe their situation. This arises
from the
non-emptiness of certain sets.
These sets make up the mathematical definition of the gradient. Each
represents one
aspect or dimension of the total gradient. There is, moreover, a
different gradient for
each 'group' of characters - where a group is a non-empty set of
characters all of whom
share the same position.
If and only if all gradient sets are empty for all groups, the gradient
of the mot as a
whole is zero and there is full and complete dramatic resolution.
We'll define these gradient sets in our next issue. For now, let's name
them.
The gradient sets for a group G with a common position p{G} are the
*inducement*
gradient, the *position* gradient, the *promise* gradient, the *threat*
gradient and
the *resistance* gradient. Each weakens in a different way the arguments
G can make for
p{G}. Thus each element of the inducement gradient lessens an inducement
for others to
join G, each element of the promise gradient lessens the credibility of
G's promise to
implement p{G} - and so on. More next issue.
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