A big succes
In our enthusiasm about the detection of mathematical models for decision making we had applied such a mathematical model on the arguments which Margret of Austria and Carles V exchanged about the peace treaty they prepared. By coding the statements on probabilities and utilities on continuous scales we were able to apply the mathematical model and it led to the decisions made (See here). However after studying 231 arguments of the Dutch government we did not believe anymore in this approach. The information used in the arguments of the politicians was always very simple. It would require a lot of assumptions to derive from these remarks the numerical values for the probabilities and utilities of the outcomes. In several examples we have presented so far, we saw that the politicians even did not specify the utilities and probabilities explicitly but implied them by the connotation of words used. Occasionally they compared outcomes but only by rank ordering them. The same happened with the probabilities. Stimulated by the work of Herbert Simon we also concluded that politicians in their discussions cannot use the formal approach since they don’t have the necessary information about the utilities and probabilities for this approach.
However, this raised the question: “How could they draw their conclusions?"
This question was even more challenging because the decision makers did not specify a rule to draw their conclusions. These conclusions were also clear to us but it was not immediately clear why. Given this situation we had to determine whether our approach was completely wrong or there had to exist simple rules which were obvious for everybody.
This question was even more challenging because the decision makers did not specify a rule to draw their conclusions. These conclusions were also clear to us but it was not immediately clear why. Given this situation we had to determine whether our approach was completely wrong or there had to exist simple rules which were obvious for everybody.
Classification of the arguments
To study this issue, we first classified the arguments made by the decision makers with respect to the amount of information they gave about the probabilities and the utilities of outcomes. If the decsion makers indicated that the probability or utility was larger for one outcome than for another than we called this ranking of the information. Often ranking did not happen for the probabilities as well for the utilities.
In total we studied 136 decision situations in which 231 arguments of individual politicians were studied. These 231 arguments were summarized with respect to the information provided by the decision makers in the table below.
_____________________________________________________________________________________
The characteristics of the information used in 231 Dutch foreign policy arguments
No ranking of Rank ordered Total
probabilities probabilities
No ranking of
utilities 109 70 179
Rank ordered
utilities 49 3 52
Total 158 73 231
_____________________________________________________________________________________
The descriptions of the decision problems were classified on the basis of the amount of detail in the descriptions of the utilities and probabilities. The table shows that most politicians indicated only the possible consequences, without the rank ordering of utilities and probabilities (109).
Besides that, frequently they used either probabilities with rank ordering (70) or utililities with rank ordering (49), but rarely were both rank ordered (3). Because most foreign policy decision problems are “Multi Attribute Utility problems with uncertainty”, this table indicates that politicians considerably simplified the decision problems. This is done by omitting many aspects and ignoring differences in utilities or probabilities between different consequences, or even in both characteristics of the outcomes.
To study this issue, we first classified the arguments made by the decision makers with respect to the amount of information they gave about the probabilities and the utilities of outcomes. If the decsion makers indicated that the probability or utility was larger for one outcome than for another than we called this ranking of the information. Often ranking did not happen for the probabilities as well for the utilities.
In total we studied 136 decision situations in which 231 arguments of individual politicians were studied. These 231 arguments were summarized with respect to the information provided by the decision makers in the table below.
_____________________________________________________________________________________
The characteristics of the information used in 231 Dutch foreign policy arguments
No ranking of Rank ordered Total
probabilities probabilities
No ranking of
utilities 109 70 179
Rank ordered
utilities 49 3 52
Total 158 73 231
_____________________________________________________________________________________
The descriptions of the decision problems were classified on the basis of the amount of detail in the descriptions of the utilities and probabilities. The table shows that most politicians indicated only the possible consequences, without the rank ordering of utilities and probabilities (109).
Besides that, frequently they used either probabilities with rank ordering (70) or utililities with rank ordering (49), but rarely were both rank ordered (3). Because most foreign policy decision problems are “Multi Attribute Utility problems with uncertainty”, this table indicates that politicians considerably simplified the decision problems. This is done by omitting many aspects and ignoring differences in utilities or probabilities between different consequences, or even in both characteristics of the outcomes.
Decision rules
Given that only limited information about the utilities and probabilities is provided in the problem descriptions, the question is raised: How can the choices be derived from these descriptions of the decision problems? These rules should be obvious because the politicians rarely specify them. In seeking rules that were specific to the different situations specified in the table, we assumed that the rules should use the information given in the description. For example, if utilities are indicated with rank ordering then the rule should use this information. The same applies if probabilities are rank ordered as well as if both are specified with rank ordering. This basic assumption led to the development of seven “decision rules”.
If no rank ordering is specified at all the rule should be capable of suggesting a choice without such information. In this class we specified two rules inspired by the work of Simon (1957), the so called Simons rules. Simon suggested that people do not evaluate all possible actions before making a choice but that they select the first strategy that provides a satisfactory result. We could not use the sequential aspect of this rule but concentrated on the satisficing aspect. In doing so we specified two rules. We called it the Simon rule and the Reversed Simon rule. They are formulated as follows (Gallhofer and Saris 1979).
The Simon rule says:
If the outcomes of one strategy are all positive while for the other strategies at least one of the outcomes is negative then the strategy with only positive outcomes should be chosen
The Reversed Simon rule states:
If for one strategy at least one positive outcome is possible while for all other strategies only negative outcomes are obtained, the strategy which can lead to a positive result should be chosen.
If only the probabilities are specified with rank ordering we thought that the rules should take these rank ordering into account (Gallhofer and Saris 1979). There were two rules specified: a positive and negative risk avoiding rule.
The positive Risk Avoiding rule suggests:
If the probability of a positive result is larger for one strategy than for any other strategy the former strategy has to be chosen.
The negative Risk Avoiding rule states:
If the probability of a negative result is smaller for one strategy than for any other strategy the former strategy has to be chosen.
If only the utilities were specified with rank ordering the rules should be based on these rank ordering. In this case there were 5 decision rules specified but only three of these rules have been observed in our research. The first is the Dominance rule (Keeney and Raiffa,1976), the second is the Lexicographic rule and the third is the Addition of Utilities rules (Fishburn,1974).
The Dominance rule suggests:
If one strategy is better on at least one aspect (outcome) and equally good with respect to all other aspects (outcomes) compared with the other strategies then the former strategy has to be chosen.
The Lexicographic rule says:
If one strategy is better on the most important aspect of the decision problem than the other strategies, the former one has to be chosen
The Addition of Utilities rule states:
If the total utility of the outcomes of one strategy is better that the total utility of the outcomes for the other strategies the former strategy has to be chosen.
It will be clear that the application of the last two rules requires that the decision maker not only specifies the decision problem but also provides further information about the importance of the different aspects or the total utility of all outcomes together for all strategies.
For the situation with rank ordering for utilities and probabilities we suggested an ordinal version of the SEU decision rule. However this rule can only be applied under a very special condition. For details of these rules we refer to Gallhofer and Saris (1996).
Given that only limited information about the utilities and probabilities is provided in the problem descriptions, the question is raised: How can the choices be derived from these descriptions of the decision problems? These rules should be obvious because the politicians rarely specify them. In seeking rules that were specific to the different situations specified in the table, we assumed that the rules should use the information given in the description. For example, if utilities are indicated with rank ordering then the rule should use this information. The same applies if probabilities are rank ordered as well as if both are specified with rank ordering. This basic assumption led to the development of seven “decision rules”.
If no rank ordering is specified at all the rule should be capable of suggesting a choice without such information. In this class we specified two rules inspired by the work of Simon (1957), the so called Simons rules. Simon suggested that people do not evaluate all possible actions before making a choice but that they select the first strategy that provides a satisfactory result. We could not use the sequential aspect of this rule but concentrated on the satisficing aspect. In doing so we specified two rules. We called it the Simon rule and the Reversed Simon rule. They are formulated as follows (Gallhofer and Saris 1979).
The Simon rule says:
If the outcomes of one strategy are all positive while for the other strategies at least one of the outcomes is negative then the strategy with only positive outcomes should be chosen
The Reversed Simon rule states:
If for one strategy at least one positive outcome is possible while for all other strategies only negative outcomes are obtained, the strategy which can lead to a positive result should be chosen.
If only the probabilities are specified with rank ordering we thought that the rules should take these rank ordering into account (Gallhofer and Saris 1979). There were two rules specified: a positive and negative risk avoiding rule.
The positive Risk Avoiding rule suggests:
If the probability of a positive result is larger for one strategy than for any other strategy the former strategy has to be chosen.
The negative Risk Avoiding rule states:
If the probability of a negative result is smaller for one strategy than for any other strategy the former strategy has to be chosen.
If only the utilities were specified with rank ordering the rules should be based on these rank ordering. In this case there were 5 decision rules specified but only three of these rules have been observed in our research. The first is the Dominance rule (Keeney and Raiffa,1976), the second is the Lexicographic rule and the third is the Addition of Utilities rules (Fishburn,1974).
The Dominance rule suggests:
If one strategy is better on at least one aspect (outcome) and equally good with respect to all other aspects (outcomes) compared with the other strategies then the former strategy has to be chosen.
The Lexicographic rule says:
If one strategy is better on the most important aspect of the decision problem than the other strategies, the former one has to be chosen
The Addition of Utilities rule states:
If the total utility of the outcomes of one strategy is better that the total utility of the outcomes for the other strategies the former strategy has to be chosen.
It will be clear that the application of the last two rules requires that the decision maker not only specifies the decision problem but also provides further information about the importance of the different aspects or the total utility of all outcomes together for all strategies.
For the situation with rank ordering for utilities and probabilities we suggested an ordinal version of the SEU decision rule. However this rule can only be applied under a very special condition. For details of these rules we refer to Gallhofer and Saris (1996).
A remarkable result
Having done this, a crucial phase in our research followed: We had to check for 231 arguments whether the rule suggested by the table above, given the level of information, produced the decision that the politician had made. To our great relief the result of this research was that in 219 of the 231 arguments the rule that we expected to predict the choice was indeed producing the choice mentioned by the decision maker. This was a remarkable result. We were extremely happy with this finding and stimulated us to continue this research because this finding was not the definite proof that people indeed knew these rules and applied them.
Having done this, a crucial phase in our research followed: We had to check for 231 arguments whether the rule suggested by the table above, given the level of information, produced the decision that the politician had made. To our great relief the result of this research was that in 219 of the 231 arguments the rule that we expected to predict the choice was indeed producing the choice mentioned by the decision maker. This was a remarkable result. We were extremely happy with this finding and stimulated us to continue this research because this finding was not the definite proof that people indeed knew these rules and applied them.