While the system configuration is controllable by the users – or the system designer – a further independent variable not at the discretion of the system designer or user is the negotiation problem as an input to the system. In sensitivity analysis – concerning the sensitivity of the output of the simulation to its inputs – we use the integrativeness of the negotiation problem as an aggregate measure for the input to the system – i.e. the negotiation problem resulting from the preferences of the users over the negotiation object as discussed in Section 3.1.1 – an investigate how outcome measures not only depend on the components of the system configuration but also on this uncontrollable input factor.
5.2. Measurement 109
A commonly used classification of negotiation problems is to distinguish between distributive and integrative negotiations, which was first introduced by Walton and McKersie (1965) and is often used as structuring criterion for courses or books about negotiation (e.g. Lewicki et al., 1994; Raiffa et al., 2002; Kersten, 2007). Though used exchangeably in this text the term ’bargaining’ often is used to refer to distributive and ’negotiation’ to integrative settings (Lewicki et al., 1994). Many models of bargaining and negotiation focus exclusively on one of these two, either on distributive bargaining or on integrative negotiation – while Walton and McKersie (1965) see them as only two of four subprocesses, besides attitudinal structuring as efforts to influence the quality and nature of the relationship between the negotiating parties and intra-organizational
bargaining as the conflict resolution within negotiating teams of one party, of their theory of
negotiation (Lewicki et al., 1992). Others limit distributive bargaining to the exchange of more or less specific proposals for the terms of agreement on particular issues (Gulliver, 1979), while integrative negotiation is seen as the broader approach of defining and redefining the terms of the interdependence of parties (Walton and McKersie, 1965). Integrative negotiation then covers more than just offer exchange for specific issues, but also the search for new alternatives, issues, and options for mutual benefit, and is a more cooperative and creative task (Lewicki et al., 1992; Kersten et al., 2000).
The subsequently proposed measure of ’integrativeness of the negotiation problem’ is inspired by the work of Tripp and Sondak (1992), who propose and discuss measures for assessing the integra- tiveness of an agreement found by parties in bilateral negotiations.3 Assessing the integrativeness
of one solution (the agreement) means comparing this focal solution to other possible solutions of the negotiation problem, however, assessing the integrativeness of the whole negotiation problem is more problematic as it involves the discussion of the whole set of possible solutions of the negotiation problem. Basis for our measure of integrativeness of the negotiation problem is a discussion of integrative and distributive negotiations. The distinction between integrative and distributive negotiations, though as mentioned, often used in negotiation literature and having a long tradition reaching back to the seminal contributions of Walton and McKersie (1965), is not clear at all, but definitions of integrative and distributive negotiations are ambiguous (Kersten et al., 2000). We define distributive negotiations as negotiations where the parties (at best – i.e. without leaving potential value at the bargaining table) can divide a fixed pie, such that any gain of one party is made at the expense of the other party. Therefore the best outcomes of distributive negotiations lie on the line connecting the maximum outcome of the two parties. On the other hand in integrative negotiations there exist solutions in the negotiation problem that allow for gains of both parties beyond splitting a fixed pie. Therefore the outcomes of integrative negotiations can exceed the linear combination of the maximal payoffs of the parties – see Figure 5.1.
3The measure of integrativeness of the agreement proposed by Tripp and Sondak (1992) bases on the comparison
of the agreement with the number of other solutions in the negotiation problem that either dominate it or are
dominated by it. Integrativeness of an agreement then is defined as ’1-(the number of possible agreements
Pareto superior to the reference agreement/the sum of the number of possible agreements Pareto superior to the agreement and the number of possible agreements Pareto inferior to the agreement)’ (Tripp and Sondak, 1992, p.291).
0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 (a) distributive 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 (b) integrative
Figure 5.1: Distributive and integrative negotiation problems
A measure of integrativeness therefore needs to determine the amount of such integrative so- lutions possible due to the structure of the negotiation problem at hand. Having a set X = {x1, . . . , xn} of n solutions xi, and preferences of the negotiators represented by utility functions
uj(·) and u−j(·) we define the set of distributive solutions D as those lying at or below the
line connecting the best outcome for the two parties. The set of distributive solutions therefore consists of those solutions where the parties at best split a fixed pie among them (5.1).
0 20 40 60 80 100 0 20 40 60 80 100
D
I
Figure 5.2: Integrativeness of the negotiation problem
D = {x ∈ X|u−j(x) ≤ −
maxxiu−j(xi)
maxxiuj(xi)
uj(x) + maxxiu−j(xi)} (5.1)
5.2. Measurement 111
connecting the extreme outcomes – are assigned to the set I of integrative solutions (5.2). The sets D and I are also presented graphically in Figure 5.2.
I = {xi|u2(xi) > −
maxxiu−j(xi)
maxxiuj(xi)
uj(x) + maxxiu−j(xi)} (5.2)
Integrativeness of the negotiation problem then can be calculated by (5.3).
Integrativeness = |I|
n (5.3)
This measure has the appealing feature that it ranges from 0 – if all solutions of the negotiation problem are distributive – to 1 – in case all solutions of the negotiation problem are integrative – and allows to compare different negotiation problems as it standardizes for the number of possible solutions. The measure depends on the structure of the negotiation problem and therefore covers the effect of all the factors influencing it – weight differences, partial utility curves, etc.4
For the negotiation problems of this study, where the best possible outcomes for the parties achieve a maximum utility of 100, this measure of integrativeness implies that all solutions that afford a sum of utilities of both negotiators of at most 100 are conceived as distributive solutions. Descriptive statistics of the integrativeness of the 2,065 negotiation problems of the experiments used for this study are provided in tabular form in Table 5.3, as well as in form of a histogram and a box-plot in Figure 5.3.
Integrativeness of the negotiation problem
Frequency 0.0 0.2 0.4 0.6 0.8 1.0 0 50 100 150 200 (a) Histogram 0.0 0.2 0.4 0.6 0.8 1.0 Integrativeness (b) Box-plot
Figure 5.3: Illustrations on the integrativeness of the negotiation problems
4Integrativeness as determined above can be conceived as the proportion of integrative solutions of all possible
solutions of the negotiation problem, or the probability of selecting a integrative solution if one solution out of all possible solutions of the negotiation problem is chosen randomly.
min 0.00 1st Q. 0.48 median 0.66 3rd Q. 0.77 max 1.00 ⊘ 0.61 ± 0.22
Table 5.3: Integrativeness of the negotiation problems