Strategic Choice
Fraser and Hipel (1984) proposed a method for identifying stable solutions to multi-party, multi-issue disputes, including ones involving coalitions, unknown options, and incorrect or misleading information.
The method is applicable in disputes in which each party can rank all possible solutions in preference order.Consider the forty-year dispute over whether and how to save the California condor. Many groups were involved, but because our purpose is to explain the method we can label as ZOO the groups led by the Los Angeles and San Diego Zoos that advocated intervention. We label as FOE the opponents led by Friends of the Earth.
ZOO believed in making every possible effort to ensure survival of the condor, so advocated captive breeding or double clutching5 in that preference order. FOE believed in letting nature take its course even if it meant extinction for the condors, so preferred doing nothing, habitat protection, or feeding uncontaminated cattle to condors in that order. Using binary notation, “1” represents proposing a strategy, while “0” represents opposing it. The columns of Figure 2.2 shows every possibility (0000 is the do nothing strategy preferred by FOE).
An analyst can write out every possible outcome no matter how many parties and strategies are involved. Alternate 0 and 1 in the first row. Alternate pairs of zeros and ones on the next. Continue doubling the number of adjacent zeros in each subsequent row and duplicate them as ones until a row in which all the zeros appear on the left and all the ones on the right is reached. Every possible combination is included in such an array, regardless of the number of strategies.
Next, inspect for and eliminate absurd combinations. Birds cannot both be entirely in the wild and entirely in captivity, so 0101 is absurd.
Similarly, 1001, 1101, 1011, 0111 and 1111 make no sense. Rearrange the remaining strategies in preference order for each disputant. Where two or more disputants have identical preference orders, perhaps because they have formed a coalition, eliminate the duplicate arrays. FOE prefers minimum interference in nature, so from left to right, its preferences are those of Figure 2.3. ZOO prefers species preservation by the most cost-effective possible method (explaining why 0001 is preferred to 0011). Its preferences, from left to right are those of Figure 2.4.Convert each binomial column to base ten, resulting in the unique codes for each strategy in the final row of Figures 2.3 and 2.4, providing a convenient way to “name” each possible outcome. The result is designated a “preference vector.” To make the conversion, multiply each binomial times the power-of-two value to which the location corresponds, using the top number as the low-order digit. For example, 1110 (the eighth column of numbers in Figure 2.3 and the third one in Figure 2.4) converts as follows:
These arrays provide a complete description of the conflict between the two parties, with the preferences of each clearly ranked. All mathematical models clarify at the expense of simplification. In this system, the emotion and intensity associated with each possibility are lost.
The remaining steps are more tedious than difficult, although as the number of parties and issues multiply, efficiency requires computer analysis. Begin by identifying “unilateral improvements,” designating them with the symbol UI. These improve one party’s position without inducing other parties to change their strategy. They occur whenever the opponent’s preferences do not change from left to right. For example, ZOO can move from its second-choice 0011 solution to 0001, ZOO’s first choice solution, because FOE prefers 00 in both instances.
While this is the only unilateral improvement for ZOO, FOE has several such improvements, as indicated in Figure 2.5.The next step is to determine stabilities, there being four possible types. The analysis is a matter of inspection and logic rather than calculation. The first type, rational stability, occurs whenever a disputant has no unilateral improvement to make from an outcome. Figure 2.5 indicates each one by the symbol r.
Second, check for sequentially sanctioned stabilities (s). These occur when a disputant has an improvement that allows the opponent to respond unilaterally and leaves the disputant worse off. Identify them by checking each disputant’s unilateral improvements one by one. There are none in the current situation, but if ZOO had one from 2 to 1, FOE would then have its own from 1 to 0, which ZOO regards as a worse outcome to the dispute. Therefore, ZOO would be “sequentially sanctioned” against a unilateral move to strategy 1.
Third, identify instabilities. These occur if a disputant can make a unilateral improvement the opponent cannot respond to with a credible action that results in a less preferred outcome for that disputant. In effect, any strategy not already identified by an r or an s is unstable and can be marked with a u. Figure 2.5 indicates them for both parties.
Fourth, inspect the arrays to identify cases in which a change in strategy would be unstable for all disputants and would leave one or both worse off. Neither disputant would willingly accept such a choice, so these cases are termed “simultaneously sanctioned stabilities.” Use the base-ten notation to identify them. Add the base ten values of two unilateral improvements for each player and subtract the strategy being analyzed. Sequential sanctioning exists only if the base ten value that results appears on the array to the left of the base ten value resulting from the calculation for all disputants. They are exceptionally rare (in this case there are none) but if found can be indicated by a slash (/) through the symbol u.
An outcome rated r or s for all disputants constitutes a possible resolution to the conflict and is labeled E for equilibrium. In practice, even very complex conflicts have three or fewer equilibriums. Each is likely to be meaningful. In this case, they identify the three historical solutions. No action (0000) was taken for 33 years. Double clutching (0010) followed but was not successful. Finally, all surviving condors were captured (0001). By February 1992, captive breeding was working well enough to begin releasing birds into the wild.
The condor dispute illustrates how to analyze and identify potentially stable solutions to complex conflicts. How best to use the information rests entirely on the methods used to manage the conflict (Chapter 17).