Representing Negotiation Space - Regional Science Matters - page 273

Sect. 14.2 . To be complete, it should be mentioned that conflict and negotiation are
complementary, the latter being one form of conflict resolution (Paelinck 2000 ).

14.3.1 Hypergraph Conflict Analysis

Hypergraph Conflict Analysis (HCA) was introduced by Paelinck and Vossen
( 1983a ). Since then a certain number of further contributions have appeared, in
particular three studies on hypergraph conflict resolution (or reduction: de Koster
and Paelinck 1985 ; van Gastel and Paelinck 1992 ; Paelinck 2000 ).
Suppose there to be a number of agents, or groups of agents (A i ), confronted with
a set of possible options (O j ), whatever the latter may be; in spatial analysis one
might encounter infrastructural projects, regional development issues, and many
other strategic choice problems. The agents could agree or disagree with some of
the options, and this state of affairs can be set out in a table or matrix (

C ), Table 14.1

reproducing a 3 3 binary (only full agreement or disagreement is assumed

here) case.
The hypergraph nature of Table 14.2 results from the fact that for each agent the
agreeable options are a subset of the overall set of possible options.
Several measures can be proposed to show the “degree of conflict”. One, which
will be noted

, divides the minimum number of zeros taken over the columns of C
by the number of agents, n i (for Table 14.1 this is 2/3). Another measure, noted

ʴ

˄

,is
the transversal number, defined as the cardinal of the minimal set of options on
which all agents taken together agree; for Table 14.1 this number is 3. A relative
transversal number, 1 by the cardinal of the set of potential

options minus one, so in the case of Table 14.1 , ˄

˄ * , would divide ˄

* ¼ 1 . It should be intuitively clear

that ʴ and ˄ (or ˄ * ) are interrelated.

0) there would be no conflict, as
all agents agree on at least one option. Hypergraph conflict resolution aims at
computing an optimal way of “turning over” agents, so as to drive

If ʴ ¼ 0, or alternatively, ˄ ¼ 1, (or ˄ * ¼

ʴ down to zero

or up to 1.

Fuzzy generalisation of the above ideas is possible, but this topic will not be
addressed here.

˄

14.3.2 Topographical Representation

Starting point will be the initial situation, for which we assume a multidimensional
framework (see Paelinck ( 2000 ), Sect. 14.3.4 ); in each dimension k ,

ʴ k ¼ n i 1 ,or

n k , where n k is the corresponding number of options; one defines,
as said in Sect. 14.2 :

˄ k ¼

alternatively,

˄ k ¼ ˄ k 1 ð Þ= n k 1 ð Þ ð 14 : 24 Þ

and so obviously 0 ˄ k 1.