Vol 10 No 1 January 1996
THE RESEARCH SUPPLEMENT
(DEVELOPMENTS IN THEORY AND SOFTWARE)
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Supplement to the COOPERATION OR CONFLICT research letter
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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STUDIOS FRONT END:
Dramatis Personae
Jim Bryant (Sheffield Hallam University) in part 2 of this
series on STUDIO software
Getting into character is the first stage in action methods such as
sociodrama - or indeed in rehearsals in the theatre. The front end to
STUDIO - the new software for drama-theoretic analysis I introduced in
the last issue - helps you get into each character in a drama.
It lets you create a set of models to represent the thinking of those in
the cast. First, however, comes the creation of the cast list itself.
Ive found it helpful to spend some time on this first, critical step.
Mason and Mitroff in their SAST methodology (Challenging Strategic
Planning Assumptions, Wiley 1981) give a checklist for identifying
stakeholders as a prelude to scenario analysis. Use this to develop a
list of characters for a drama. It points you to those who are opinion-
shapers (eg, the media, politicians); who have issued imperatives (eg,
protesters); who are in positional roles to determine outcomes (eg,
legislative or governmental agencies); who relate to focal organisations
(eg, suppliers, customers); and so on.
Once youve exposed such parties, try organising and characterising
them. Organising means seeing how they relate to each other, in a
hierarchical or systemic sense. Characterising means anything from
plotting them in terms of power and activity to conducting a full
multiattribute analysis, producing their profiles along many dimensions.
Such character exploration is valuable and effective in workshop
settings. It helps to pool knowledge about those involved in a situation
as well as generating useful debates when placing characters on the more
controversial scales (eg potency).
How does this relate to STUDIO? STUDIO provides tools for describing
characters, relating them and associating each of them with a set of so-
called qualities that the user also develops interactively. Among
these are purposes and motivations; beliefs, resources, knowledge and
opinions; commitments, relationships and opportunities.
Mapping peoples values
Drama theorists have linked peoples underlying value systems, their
preferences and their emotions (see P Bennett and N Howard,
Rationality, emotion and preference change, forthcoming in Eur Jour of
Operational Res, 1996). But the options we assign to characters in a
drama are a product of their value systems just as much as the
objectives that explain their preferences. To ensure the necessary
coherence of actions and goals, STUDIO takes up the well-used and
successful idea of a cognitive map underpinning an individuals world-
view.
Impressive work has been done by Colin Eden and others (Messing about in
Problems, Pergamon 1983) using highly developed cognitive maps to
represent subjective views of problem situations. Beliefs are shown as
directed graphs with arrows linking constructs seen as causally linked.
General goals appear at the head of chains of argument and potential
actions at the tails.
This is just whats wanted for drama analysis. We need characters goals
to determine their preferences and their possible actions to give their
options. STUDIO could have imported cognitive maps produced using other
software (eg, Graphics COPE). Instead, it offers a cut-down version of
mapping which requires constructs - now termed intentions - to be
organised hierarchically.
This is a simplification. It seems to work. The STUDIO user, having
constructed a list of characters, develops for each an intention tree -
which is what the cognitive map reduces to. Though demanding, this
generates valuable discussion in a workshop, often exposing areas of
ignorance to be filled. In the end, potential actions and goals are
highlighted in the intention trees, paving the way for analysis of
interactions.
A further facility enables a user to produce a shortish list of
potential actions from the potentially long one generated by the tree.
Some simple tools make possible what is in effect a multi-attribute
utility analysis, letting a user consider to what degree each action
contributes to goals and how much each goal is valued by the character.
Alpha-test panellists should be receiving a preliminary version of
STUDIO soon after Easter. A larger test group will evaluate the beta
version during the Autumn, prior to launch in Spring 1997. If youd like
to take part in any of these activities, contact me (fax: (+44) 114 253
3161. e-mail:J.W.Bryant@shu.ac.uk).
__________________________________________________________
THE COOPERATION GRADIENT: HOW TO CREATE TRUST
Part 2 of The Mathematics of Drama Theory
(Note: In this electronic version of the article, subscripts are shown
by square brackets [] and superscripts by curly ones {}.)
__________________________________________________________
Drama theory is based on game theory but differs from it fundamentally.
Game theory seeks to solve a game seen as fixed. Drama theory posits
that the unbearable paradoxes found in all solutions to a fixed game
cause emotion in those trapped within it - emotion that may be strong
enough to cause them to reframe their situation in a way that
eliminates the paradoxes.
The emphasis of drama theory is thus on how the frame (its term for a
game) and certain objects defined in it are transformed by emotion so
as to make possible a solution that is paradox-free. And so, in analogy
with the mathematical study of physical transformations, drama theory
seeks to define the gradient (tendency to change) of a so-called moment
of truth - which is an object consisting of a frame together with the
positions taken and fallback strategies threatened by its characters.
Gradient sets
Part 1 of this series (see last issue) formally defined a frame and a
moment of truth (mot) within it. Well continue with the same notation,
so refer to Part 1 - available on request or via the drama theory
mailing list - if you dont understand what follows.
A moment of truth was defined as a triple (F, p, f), where F is a frame
(defined last time), p = (p{c} | c in C) is a family of futures defined
in F, (the future p{c} being character cs position) and f = (f[c] | c
in C) is a particular outcome in S composed of the fallback strategy
f[c] of each character c.
Now the gradient of an mot has to be defined separately for each group
G of characters that share the same position p{G} = p{c} ( c in G). Its
defined as consisting of a number of sets, the non-emptiness of any of
which creates for those in G a certain emotional pressure for change.
Unfortunately, the names for these gradient sets given last time
contradicted previous usage (eg in N Howards Drama Theory and its
Relation to Game Theory, Group Decision and Negotiation, 3, 1994 and
Negotiation as Drama, International Negotiation, 1, 1996). So ignore
those names! Name the sets, for a given group G, the cooperation
gradient, deterrence gradient, positioning gradient, fallback gradient
and inducement gradient.
First, well define and discuss the cooperation gradient.
How to cooperate
This idea is easily grasped by those familiar with the well-known
prisoners dilemma (pd) - last discussed by Peter Bennett in our 6, 5,
1992. The real significance of the pd paradox is that the position
prisoners would want to take - Both Cooperate - is irrational! Both are
tempted to defect from it. Hence they can neither trust the others
position nor make their own credible.
This is so because a certain set is non-empty - the set of potentially
preferred moves from the position.
Accordingly, the definition of the cooperation gradient is built up as
follows.
Define outcome s as potentially preferred to outcome t by a group G
subset-of C when
- Qs <> Qt
- and u[c](s) >= u[c](t) for all c in G.
Write s >[G] t to represent this relation. (Note: thus we regard s as
potentially preferred to t even when all in G are indifferent
between the two - provided they arent equivalent, ie, Qs <> Qt.)
Next, use the notation
- s[G] = (s[c] | c in G)
for a strategy of group G, and s[-G] = (s[c] | c not-in G) for the
complementary group strategy, so that for any s and G subset-of C we
have s = (s[G], s[ G]). Then define the set Ms of potentially preferred
moves from s as
- Ms = {t[G] | (t[G], s[-G]) >[G] s}.
In prisoners dilemma, for example, the set M(Both Cooperate) has two
members - the Defect strategies for each prisoner. The set M(Both
Defect) has one - the group strategy (Cooperate, Cooperate) of the two
choosing together.
The cooperation gradient for a group G with common position p[G] at an
mot (F, p, f) is now defined as
- Mp[G] = {s[H] | (s[H], p{G}[-H]) >[H] p{G}}.
Pressures for change
So the question is: what emotional pressures for change does the non-
emptiness of Mp{G} generate in members of G?
To answer this mathematically, ask, for any element s[H] in Mp{G}: what
changes in (F, p, f) might cause s[H] to cease to obey the condition
(s[H], p{G}[-H]) >[H] p{G}?
Example: What changes in pd might cause 1 Defects to cease being a
preferred move from Both Cooperate?
One answer is a preference transformation u -> u such that, for some c
in H and delta[1], delta[2] > 0:
- u[c](p{G}) = u[c](p{G}) + delta[1],
- u[c](s[H], p{G}[-H]) = u[c](s[H], p{G}[-H]) - delta[2]
If delta[1] + delta[2] is large enough, s[H] then ceases to obey the
condition. In pd, such a transformation might mean that Both Cooperate
becomes preferred by prisoner 1 to 1 Alone Defects.
Another possibility is a consequence transformation Q -> Q such that
either
- Q(s[H], p{G}[-H]) = p{G}
or, for some c in H and delta > 0:
- u[c](Q(s[H], p{G}[-H])) = u[c](s[H], p{G}[-H]) - delta.
The first transformation makes s[H] cease to be a feasible strategy
choice, starting from p{G}. The second makes it lead to a consequence
that - if delta is large enough - c will find worse than p{G}. In either
case, s[H] ceases to be an element of the cooperation gradient.
In pd, for example, 1 Defects ceases to be in the gradient at Both
Cooperate if the prisoners become convinced either that its impossible
for 1 to Defect or that for it to do so will inevitably lead to Both
Defect.
The transformations so far discussed change the frame. Characters
values and beliefs are involved. The energy needed for them to reframe
their world in this way is provided by positive emotion toward others -
spurred on by the urge to gain their trust.
But more than emotion is called for. Lasting, convincing change requires
that emotion lead characters to reevaluate objective evidence and
retrace rational thought processes in a way that consolidates the
change.
Finally, a transformation that merely changes a characters tactics -
its choice of a position - is a position transformation p -> p such
that
for some c in G, p{c} <> p{G}.
This takes the pressure off character c. In pd, for example, one
prisoner might give up trying to cooperate and take Both Defect as its
position. The emotion that goes with this transformation is fear,
despair or depression.
___________________________________________________________
--
Nigel Howard Immersive Soap Co/Nigel Howard Systems
Phone/Fax: (44)(0)121-449-4480
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