In early work relating to choice reduction and filtering, a lexicographic rule was proposed whereby decision-makers were assumed to identify attributes of outcomes which are of
primary importance. Individuals are then assumed to apply ranking rules to attributes which may be expressed in categorical form as; “good”, “neutral” or bad”. Accordingly, such lexicographic rules are applied to determine the option which best fits the most desirable attributes (von Neumann and Morgenstern, 1944). Only in the event of indifference between competing choices is the decision-maker assumed to consider the second most desirable attribute, and so on, until a unique solution is found.
This procedure was expressed more formally by Tversky (1969, 1972) using
semiordering to impose thresholds on partial rankings. Therefore, assuming a function f on a choice set X, we can derive an ordered sequence of dimensions based upon an individual’s preferences with regard to attributes, f = (f1, …. , fn). It is then assumed that there is a
threshold, , which is required to distinguish between dimensions. The preference, fi(x) > fi(y)
therefore holds only in the case; fi(x) > fi(y) + Since the dimensions are ranked in terms of
order of importance, the decision-maker considers them in sequence; when a dimension i is found for which x > y + , the condition rule is satisfied given the threshold and x is
This process incorporates conjunctive and disjunctive rules proposed by Coombs (1951) and Dawes (1964). Under the conjunctive rule, prospects which exceed all thresholds are considered desirable while under the disjunctive rule, a prospect exceeding any of the thresholds is potentially acceptable. Jedidi and Kohli (2005) provided generalisations of conjunctive and disjunctive rules by assuming that decision rules can be based upon a minimum number of possible decision-criteria being met. Therefore, assuming that options must satisfy at least h out of n possible criteria, h = 1 would describe a disjunctive rule while h = n defines a conjunctive rule. As h moves higher, more and more criteria must be fulfilled in order to be considered acceptable. Jedidi and Kohli defined this as a “subset-conjunctive rule”, accommodating situations where there is incomplete information with regard to alternatives. A probabilistic component was also added to the model, denoting a decision- maker’s perception of the likelihood of finding a particular level of an attribute acceptable. Such probabilities can then be taken to reflect the importance attached to a particular attribute.
Empirical evidence suggests that consumers do indeed engage in considerable choice reduction based upon choice attributes. For example, studies have shown that consumers typically reduce consideration of packaged goods to a subset of 3 to 4 attributes out of a possible 30 to 40 (Hauser & Wernerfelt, 1990; Urban & Hauser, 1993). Various generic attributes have also been found to affect subset choice. Therefore, variability in the perceived brand quality across choice sets has been found to influence consumer subsets, with increasing variability in quality reducing the overall number of brands considered (Belonax Jr & Javalgi, 1989). However, abundant choice of broadly similar goods can lead to weaker preferences, requiring greater cognitive effort (Chernev, 2003), although focusing upon unique, or distinguishing attributes of items on the part of sellers has been found to increase the
Kivetz & Simonson, 2000). This implies that consumers do indeed seek differentiating
characteristics, on which they place more weight, when comparing broadly similar competing items.
The lexicographic models described above suggest a framework for achieving choice reduction by matching alternatives to defined criteria. It is assumed, therefore, that not all of the available information relating to competing choices is relevant to the decision taken. The models thus have both decision and stopping rules; once sufficient conditions are met, there is no need to proceed further. The process described therefore assumes a degree of economy with regard to cognitive resource.
Heuristic decision rules similarly describe processes whereby choices are made on the basis of partial information and cues. As task complexity increases, either based upon the number of alternatives or their salient characteristics, decision-makers seek to reduce that complexity by simplifying the dimensions of the task. As with other decision-rule models, not all aspects of alternatives are assumed to be considered in a systematic manner. Instead, decision-makers are deemed to be “fast and frugal”, undertaking an evaluation by applying a type of mental process whereby judgments about current events, objects or options are made based upon past knowledge or by reference to other known cues, events, objects or options which are considered to be sufficiently similar. Tversky and Kahneman (1974) considered heuristics to be “mental shortcuts” which often triggered biases and “errors” (violations of axiomatic behaviour). They argued that each of the three main heuristics which they identified: representativeness, availability and adjustment and anchoring, often led to predictable biases in decision-making. These heuristics can be summarised as follows;
Representativeness describes a process whereby decision-makers evaluate A on the basis of the characteristics of B which is deemed to be similar and about which something is known. Therefore, the probability of event A is inferred to be similar to that of B. Alternatively, individuals may classify A as similar to B based upon shared characteristics or may extend the characteristics of a small sample to assume they apply across a much larger sample.
Availability assumes that decision-makers make evaluations based upon
immediate examples, recent events, experiences or observations. The matching element of this heuristic can therefore be seen to reinforce representativeness. Adjustment and anchoring describes a process whereby decision-makers assess
probabilities intuitively, taking an anchor which acts as a reference point and then adjusting until a “reasonable” representation is found.
Many other heuristics have been identified defining frugal mental processes (see Gigerenzer & Gaissmaier, 2011; Blumenthal-Barby, 2016). Some, such as tallying and take-the-best can be seen to correspond closely with sequential decision models as described earlier. Tallying, for example, is a process whereby class objects are compared one to another; one option may therefore be found to dominate another based upon a cumulation of comparative measures. For example, if asked to judge whether the UK or Germany would achieve a stronger rate of economic growth over the next twelve-months, we may consider a number of primary indicators to help us make that judgment (for example; recent GDP growth, labour
productivity, unemployment, inflation and interest rates, debt levels and relative exchange rates). The decision-maker applying the tallying heuristic would then evaluate the two countries based upon each metric with the one scoring higher cumulatively then being
would derive weights via regression coefficients for each of these variables resulting in an equation providing a numerical forecast for growth in each country, the heuristic approach assumes that the various factors are equally weighted in the tallying process (although there would appear to be no reason why the decision-maker could not mentally apply some sort of weighting procedure). This replicates the conjunctive and subset-conjunctive rules outlined above. The take-the-best heuristic more closely aligns with the disjunctive rule whereby a decision is made based upon a primary characteristic or metric. Therefore, in the case of economic growth comparisons, a decision-maker might rank the factors in terms of
importance. Once a difference is found between two options, the preference is made without any further consideration.
Heuristics and choice reduction models typically involve trade-offs between cognitive effort and decision-accuracy; they are not utility maximising strategies as prescribed by the axioms of rational behaviour as those models assume full comparison of available options. Instead, choice reduction is more closely aligned with satisficing behaviour and bounded rationality. Satisficing behaviour exists when decision-makers seek acceptable outcomes considering all costs including those of information gathering, search and cognitive effort; bounded rationality exists when rational agents are constrained in their ability to formulate and solve complex problems (Simon, 1956).
In general terms, satisficing can be described as a type of decision-optimising process whereby individuals seek to maximise an objective function subject to constraints. The objective function can be defined in terms of utility which is maximised subject to constraints in the forms of cognitive and other costs. If we assume a decision-maker faces a number of choices represented by a consumption set ℝ+n, preferences with regard to the consumption set
can then be expressed by a utility function defined on the choice set. Assuming a general constraint the optimising objective function can be expressed as;
Maxxϵ ℝ+n = u(∑ 𝑥𝑖) subject to; ∑ 𝑥𝑖 ≤ Equation 22
where ∑ 𝑥𝑖 ≤ represents the overall “resource” constraint condition of the decision- maker; constraints may be cognitive or due to a limit on the amount of effort the decision- maker is prepared to undertake and can be thought of in the same way as an income constraint in a normal consumption setting.
Maximising this function is consistent with bounded rationality. Satisficing behaviour does not require the objective function to be maximised but presumes that the decision-maker achieves at least an acceptable payoff from their choices. We can express this by assuming that individuals aspire to achieve a minimum payoff sufficiently close to the constrained optimum. Therefore, if the difference between the optimum payoff and aspiration level is denoted as = Umax – A, where A is the minimum required level of utility, satisficing can be defined as the choice set s which satisfies;
U(s) ≥ Umax -
Satisficing heuristics and bounded rationality are examples of non-axiomatic decision-rules which diverge from the as if framework of the various iterations of expected utility theory. They describe an adaptive process whereby decision-makers pursue a method of information acquisition designed to match the complexity of a task. While inherently suboptimal and potentially prone to bias and error, heuristics have been found to perform well in relation to choices with binary attributes (Katsikopoulos, 2013) and have, in some cases, outperformed
formal regression models (Czerlinski, Gigerenzer, & Goldstein, 1999). By taking an
algorithmic approach to decision-making, such rule-based models go some way to looking at process rather than simply output.