Tourist Choice Processing: Evaluating Decision Rules and Methods of Their Measurement

A detailed understanding of decision rules is essential in order to better explain consumption behavior, yet the variety of decision rules used have been somewhat neglected in tourism research. This study adopts an innovative method, greedoid analysis, to estimate a noncompensatory type of decision rule known as lexicographic by aspect (LBA). It is quite different from the weighted additive (WADD) model commonly assumed in tourism studies. By utilizing an experimental research design, this study enables the evaluation of the two types of decision rules regarding their predictive and explanatory power. Additionally, we introduce a novel evaluation indicator (“cost”), which allows further investigation of the heterogeneity in the use of decision rules. The results suggest that although the out-of-sample accuracy is lower, the LBA model has a better explanatory performance on respondents’ preference order. Moreover, the different perspective provided by the LBA model is useful for obtaining managerial implications.


Introduction
As one of the cornerstones of tourism research, a great number of studies can be found investigating and theorizing tourism decision making, providing valuable insights about consumer processes. Recent reviews, however, reveal two fundamental problems regarding the body of knowledge established so far. Firstly, most of the theory developed in this area has been based on a variance perspective, which focuses only on the decisions made, at the expense of understanding the processes by which decisions are reached, and this has constrained theory building in relation to tourism consumer behavior (Smallman and Moore 2010). Secondly, among the studies exploring how tourists choose destinations (e.g., Papatheodorou 2001;Seddighi and Theocharous 2002), a single type of decision rule, the weighted additive model (WADD), is always implied. The result is that other types of possible decision rules have been largely overlooked (McCabe, Li, and Chen 2016).
The WADD model has its roots in the theory of ecological rationality, which assumes that decision makers are able and willing to make comprehensive trade-off evaluations, which allow the disadvantage of certain attributes to be compensated by the advantage of other attributes. The alternative with the highest summed-up utility will always be chosen (Araña and León 2009). However, the general applicability of the WADD model is questionable. For instance, because of cognitive limitations, consumers have been shown to use simplified rules, based on noncompensatory preferences (i.e., complex trade-off evaluation does not occur) in order to make judgments and decisions quickly and efficiently (Yee et al. 2007). Alternative models do exist; for example, the lexicographic model is a very prominent type of multiattribute decision rule, whose existence has been widely acknowledged in behavioral and consumer research (e.g. Yee et al. 2007;Dieckmann, Dippold, and Dietrich 2009).
In contrast to the comprehensive weighing process of attributes assumed by the WADD model, the lexicographic model proposes that decision makers evaluate alternatives based on the most important attribute. If there are ties between choices on this attribute, the decision maker moves to the second most important attribute and so on. Although the final choice may not be the alternative with the highest utility, the evaluation process requires much less time and 663651J TRXXX10.1177/0047287516663651Journal of Travel ResearchLi et al.  than that presupposed by the WADD model. When the attributes are binary variables or categorical variables (which is the case of our research), the lexicographic rule is known as the lexicographic by aspect (LBA) model. Apparently, the type of decision rule applied can make a substantial difference to what is chosen (Sen 1997) and different decision rules provide different perspectives to explain preference ordering, and this can also be applied to tourist decisions. Therefore, it is appropriate to explore possibilities of different decision rules to enrich the body of knowledge in tourism decision making.
Beyond the field of tourism, choice theory is a wellestablished aspect of buyer decision research. Yet empirical studies on decision rules remain sparse across disciplines and contexts, largely because the concept has been deemed rather opaque. The abstract nature of the problem requires advanced methods of analysis that are able to approximate the relevant mental processes, and these have only recently been developed. Additionally, the use of decision rules is likely to vary according to different people and different contexts (Crompton 1992;Crompton and Ankomah 1993). In order to investigate the heterogeneity in the use of different decision rules, a range of estimation methods together with evaluation indicators will need to be developed and deployed (McCabe, Li, and Chen 2016).
However, excepting a single article (Decrop and Kozak 2009) that briefly discussed the possible kinds of decision rules, hardly any empirical research can be found which supports the inference of different decision rules in tourism destination choice, let alone which evaluate their performance and suitability. Above all, this study aims to contribute to the body of (tourism) decision-making research in the following ways: to apply an alternate perspective to the conventional WADD model to understand the process of destination choice; to introduce an innovative method (greedoid method) to approximate the high probability that the LBA decision rule is adopted by tourists; and to explore a new indicator for evaluating the different models (WADD vs. LBA).

How Does a Tourist Choose a Destination?
Among so many alternative destinations, how does a tourist decide on one in particular? The mental processes underlying decision making are known as decision rules, and in relation to destination choice can be complex, and as such have been the subject of research for decades (e.g., Woodside and Lysonski 1989;Um and Crompton 1990;Mansfield 1992;Seddighi and Theocharous 2002;Mas 2005, 2008;Grigolon, Kemperman, and Timmermans 2013). Tourists selecting a destination will necessarily resort to a certain rule (perhaps unconsciously), to make comparisons consistent, to work out their preference order among the alternatives and eventually to make a final choice. Although theoretically, tourists may evaluate destinations in a holistic sense (Decrop and Kozak 2009), often they do not derive utility by possessing or using travel destinations as a whole but by consuming destination-related attributes such as transport, accommodation, or attractions (Morley 1992;Tussyadiah, Kono, and Morisugi 2006). Although decision making is also influenced by contextual factors (e.g., travel companion), the attributes serve as evaluation instruments to attain different outcomes in the choice (Dellaert, Arentze, and Horeni 2014). To keep the research focused, this study refers to decision rules as the ways that destination-related attributes are considered and evaluated to reach a final choice among alternatives.
Multiattribute evaluation rules are usually classified as either being compensatory or noncompensatory (Harte and Koele 2001). If values on different attributes can be traded off against one another (i.e., perceived negative value of one attribute can be compensated by positive values of other attributes), the rule is said to be compensatory. Otherwise, the rules are non-compensatory (Abelson and Levi 1985). The WADD model is a typical compensatory decision rule that assumes decision makers would weigh each attribute he/ she considers and assign a part-worth utility value to each attribute aspect based on their judgment and then select a destination with the highest utility (Wright 1975).
For example, let us assume price level and temperatures are the two attributes considered by a tourist. There are two destinations: destination A with temperature at 20 degrees Celsius (7) and price level at 13,000 (3) and destination B with temperature at 30 degrees (2) and price level at 9,000 (4). The part-worth utilities assigned by this tourist for the attribute aspects are 7, 3, 2 and 4. Thus, destination A with a utility score of 10 (7+3) is preferred over destination B with a utility score of 6 (2+4). As the numbers of destinations and attributes increase, compensatory rules, especially the WADD model, demand complex cognitive processing on the part of the decision maker (Crompton and Ankomah 1993). The issue of information overload is becoming ever more pertinent in the current digital and globalized era (McCabe, Li, and Chen 2016). Thus, comprehensive information search and complex problem solving may be substituted by decision rules that require less intensive information processing (Hyde 2008).
Additionally, because of the intangibility of tourism products, destination choice may sometimes be based less on objective criteria and more on desired experience or impressions about places (Smallman and Moore 2010). These attributes are associated with emotions rather than cognitive processing, implying that the absence of a certain attribute may generate sufficient negative emotion for tourists to avoid using a compensatory strategy (Araña and León 2009). For instance, the idea of trading off an attribute such as the safety of a destination against other attributes can provoke significant negative emotions (Drolet and Luce 2004). These characteristics make the arena of destination choice a promising context to investigate the use of simpler noncompensatory rules. The literature distinguishes between three classic types of noncompensatory decision rules: conjunctive, disjunctive, and lexicographic (Abelson and Levi 1985;Bettman, Johnson, and Payne 1991).
The conjunctive rule is also called the satisficing strategy (Rossi and Allenby 2003). It assumes that decision makers define minimum cut-off points for several important attributes. If an alternative falls below any of the cut-off points, it is rejected. In a tourism context, a destination would be selected only if minimum cut-off points on all important attributes are exceeded. The disjunctive rule also requires a set of cut-off points on the attributes. In contrast to the conjunctive rule, an alternative may be accepted when it has at least one value greater than the corresponding cut-off. The disjunctive rule is often used to screen a wide range of alternatives to generate a smaller, more manageable consideration set in which each alternative surpasses a threshold on at least one criterion. These two types of rules do not require any ranking or weighting of attributes by the decision maker.
However, in many decision making contexts, the evaluation attributes considered by decision makers are not equally important. When attributes are rank ordered in importance, they are said to be in lexicographic order (Laroche and Kim 2003). The lexicographic model proposes that individuals compare attributes among alternatives in a stepwise fashion (Crompton and Ankomah 1993). When the attributes presented are binary or categorical variables such as the mode of transport (the aspect can be "bus," "plane," "car," etc.) used to reach the destination, the process is known as the lexicographic by aspect. According to the LBA model, a decision maker starts with the most important attribute, and only the alternatives possessing the desired attribute aspect are selected for further consideration. When there are ties, the comparison process is continued based on the second most important attribute aspect. This is repeated until all alternative destinations have been sorted, and the top-ranked destination is the final choice. The hierarchical order of these aspects that decision makers use to make the selection is termed the aspect order. In a recent theoretical study on tourism decision making, it was argued that when faced with the complex travel decision problems, this kind of structured hierarchical approach of mental representation is usually adopted by tourists (Dellaert, Arentze, and Horeni 2014).
According to Sen (1997), different decision rules reflect different selection preferences, which often lead to different choices. The WADD rule is usually adopted to identify the most attractive combinations of attribute aspects, which emphasizes the compensatory relationships among different attributes, while the LBA model focuses on the hierarchical order of the attribute aspects in terms of their importance, which reflects potential nonnegotiable preference patterns of decision makers. Therefore, the investigation of the decision rules applied is fundamental for us to get a better insight into tourists' preferences.
In addition, it is evident that decision rules differ in terms of how much effort they require (Bettman et al. 1991). Tourists using a lexicographic decision rule make less effort in sorting information than those using a WADD rule. In certain contexts (e.g., time poverty, emotionally involved), tourists may tend to adopt simplifying decision rules (Araña, León, and Hanemann 2008). In this research, the data were obtained from Chinese long-haul (outside Asia) outbound tourists since most are first-time tourists . They have limited knowledge of long-haul alternative destinations to make a comprehensive compensatory evaluation, which implies a promising context in which the noncompensatory decision rule may be adopted. Besides, unlike the short-haul market, this group of long-haul tourists has not been studied comprehensively in previous research. The issues considered by this market may be different from their short-haul counterparts such as their concerns regarding visa application processes (Lai, Li, and Harrill 2013). Thus, the findings of this study contribute to our understanding of an important emerging market in addition to choice processing.

How to Estimate Tourists' Destination Choice?
In decision-making studies, various methods can be found for multiattribute choice investigation. One type of method consists of qualitative techniques only focusing on tracing the train of thought leading to a final decision, such as the information display board, verbal protocol analysis (Harte and Koele 2001), and causal network elicitation technique (Dellaert, Arentze, and Horeni 2014). By observing (e.g., information display board) or asking the subject to think aloud (e.g., verbal protocol analysis) while performing the evaluation task (Araña and León 2009), researchers are able to speculate the type of decision rules applied or to construct the mental representation of respondents. These qualitative methods are quite valuable for exploring the possible decision rules applied and for making general inferences. However, these techniques suffer from the disadvantages of being time consuming, containing inconsistencies of judgment (Harte and Koele 2001) and social desirability bias (Dellaert, Arentze, and Horeni 2014). Thus, further quantitative estimation is required for more objective and accurate inference of the existence or model fit of certain decision rule(s).
Other types of methods include the AHP analysis (Analytic Hierarchy Process) (e.g., Hsu, Tsai, and Wu 2009), conjoint analysis (e.g., Ciná 2012), and discrete choice experiments (DCEs) based on quantitative data utilizing various logit regressions (e.g., Papatheodorou 2001;Seddighi and Theocharous 2002;Grigolon, Kemperman, and Timmermans 2013). These methods serve to provide insights on the actual decision-making process by incorporating simulations of reality. AHP analysis explains the decision making as a hierarchical comparison process in which the decision criteria (attributes) can be divided into several layers of subcriteria. Conjoint analysis assumes that decision making is a selection process of attributes' combinations and can be used to determine what combination of attributes has most influence on respondent choice (Dieckmann, Dippold, and Dietrich 2009). DCEs are rooted in random utility theory, which can be very similar to choicebased conjoint analysis, but are usually based on various logit regressions and emphasize the influence of contextual factors on the probability of an alternative being chosen (Louviere, Flynn, and Carson 2010). Despite the fact that the methods are different in form, they all investigate the part-worth utility of attributes or attribute aspects, which implies that estimations are based on a compensatory (weighed additive) decision-making process. Furthermore, these methods focusing on a single type of decision rule do not allow for further investigation on consumer heterogeneity. The existence of other types of decision rules is largely neglected in empirical tourism studies (Li 2014). One reason for oversight may be due to the lack of advanced estimation methods and evaluation tools.
Recently however, a new tool, called the greedoid method, has been developed to deduce non-compensatory (lexicographic) decision processes from preference data in consumer research (Yee et al. 2007;Kohli and Jedidi 2007). Although the greedoid method is not able to estimate partworth utilities of the attributes, it is specifically designed for lexicographic decision models in which the computer deduces the aspect order through a matching procedure rather than identifying utility values of attribute aspects through regressions. It provides a possible tool to quantify lexicographic decision rules empirically (Kohli and Jedidi 2007). Therefore, this study adapted the greedoid analysis method to infer lexicographic decision rules that might be used in tourism destination choice by Chinese long-haul outbound tourists. In order to answer the key question of how powerful the LBA model can be for explaining or predicting tourists' preference, the WAAD model estimated by conjoint analysis with ordinary least squares (OLS) regression 1 was used as a conservative benchmark for comparison.

Greedoid Analysis
Greedoid analysis is based on a so-called greedy algorithm. The greedy algorithm aims to solve a combinatorial optimization problem step by step (Edmonds 1971;Korte and Lovász 1984). It can be used to mimic noncompensatory decision rules, particularly lexicographic preferences. Generally speaking, greedoid analysis serves two functions. Firstly, in analyzing respondents' preference data regarding a range of alternatives (different combinations of attribute aspects), greedoid analysis deduces the "aspect order" (i.e., the ranking) that was used to make a selection. Second, since not everyone follows a perfect LBA rule, the greedoid analysis provides a "cost" indicator for each respondent that reveals the extent to which the LBA rule was applied (Yee et al. 2007). In this research, we adopted the greedoid algorithm introduced by Yee et al. (2007), which had previously been applied on ranking data. Here, a simple example of tourism destination decision making is presented to illustrate how greedoid analysis works.
Assume there are three important attributes (each one of them has two aspects) considered by tourists in their destination choice: price (13,000 and 18,000), distance (long-haul and short-haul), and types of destination (natural landscape and culture). There are eight combinations of the different attribute aspects. In the empirical setup, each respondent is presented with a corresponding set of eight "stimuli cards" and asked to rank them in order of preference.
A typical preference ranking of the 8 possible combinations presented by stimuli cards may be 1>2>3>4>5>6>7>8: By observing the preference ranking, it is possible to tell that this respondent uses a perfect LBA decision rule, since all long-haul destinations are put forward before any other destinations and then where there are ties, the destinations with lower price level are ranked above the destinations with higher ones; and then if there are still ties, the ones with natural landscape are ranked before cultural destinations. Thus, the "aspect order" deduced for this respondent is long-haul > price 13,000 > natural landscape.
However, sometimes respondents do not follow a perfect LBA rule and no such aspect order can be deduced to replicate a respondent's preference ranking exactly. In these cases, the greedoid programming would find the best-fit aspect order to replicate the closest preference ranking at the minimum "cost." The "cost" is the number of violated ranking pairs produced by comparing the preference ranking of the respondent and the preference ranking produced by the deduced aspect order. A higher number of violated ranking pairs means the less likelihood that the LBA strategy can be inferred.
Take the example above, if the preference ranking of the respondent is 1>2>3>4>5>8>7>6, the best-fit aspect order deduced would be long-haul > price 13,000 > natural landscape and the replicated preference order based on the best-fit aspect order is 1>2>3>4>5>6>7>8. The number of violated ranking pairs by comparing the two ranking orders would be 3 (Errors: 8>7, 8>6, 7>6). So the output of the greedoid analysis for this respondent would be "Aspect order: long-haul > price 13,000 > natural landscape; Cost: 3." The original algorithm used in Yee et al. (2007) calculates the number of violated ranking pairs irrespective of whether the error happens at the beginning or at the end of the ranking sequence. However, based on observation during the data collection for this study, for the selection of tourist destinations, it was noted that people tended to restrict their attention to a subset of the destinations presented; that is, some of the destinations they simply did not consider to be places they would visit, and they consequently spent less time evaluating them. This suggests that the ranking order at the beginning may be more reflective of respondents' real preferences than the ranking order at the end.
If the errors at the beginning are counted as equal to those at the end, there is a risk that the detection of the optimal aspect order may be driven by the responses (rankings) that are actually least reflective of a respondent's preferences. This concern raises a critical question about how to calculate the "cost" in greedoid analysis. We opted to use a weighting scheme to calculate the "costs." Since there was no reference in the literature specifying criteria or strategies for weighting, we chose to apply a linearly decreasing scheme. 2 Thus, for a ranking of N options, the weights for calculating the violated pairs from the first to the second last position (rank) are from (N − 1) to 1. Following the previous example, there are two errors that happened at the third last position (8>7, 8>6 with weight 2) and one at the second last position (7>6 with weight 1). So the "cost" (i.e., weighted number of errors) is 5 (2*2+1*1). The modified algorithm (see Table 2) would find an aspect order that costs the minimum weighted number of violated ranking pairs.
One point of clarification: the greedoid analysis can deal with full-rank (i.e., respondents have to rank all the stimuli cards provided), partial-rank (i.e., respondents can randomly select a few cards among the stimuli cards provided and rank them) and consider-then-rank tasks (i.e., respondents can select the cards they would consider first and then only rank these cards). For conjoint analysis, respondents need to fully rank all the stimuli provided. If a respondent only ranked some of the stimuli, since he or she assumes the remaining stimuli are the same, his or her preference data cannot be analyzed, which is a waste of useful information. Since greedoid analysis does not need the stimuli to be fully ranked, it requires a smaller respondent workload than traditional conjoint analysis, which could lead to higher response rates.

Questionnaire Design
A stated preference experimental survey was designed for estimation of the LBA model and the WAAD model. Commonly considered evaluation attributes by Chinese longhaul outbound tourists were identified from previous studies through desk research (e.g., Yu and Weiler 2001;Kim, Guo, and Agrusa 2005;Arlt 2006;Sparks and Pan 2009), and these were compared and confirmed through six in-depth interviews with staff 3 in major tour operators. These interviewees were selected because of their knowledge of the Chinese outbound tourism market. They were familiar with various longhaul destination packages, which ensured that the attribute aspects (i.e., level of price) used in the experimental design adequately represented actual destination products.
Through this process, five attributes with 11 aspects were confirmed for the experimental survey design. The 5 attributes (in italics) and their aspects were: 1. Package price per person: around ren min bi [RMB] 9,000, around RMB 13,000-17,000, above RMB 18,000. 2. Risk involved in obtaining a visa: less risk/more risk of being refused 3. Whether the destination country is well known to the Chinese public: famous country/nonfamous country 4. Suitability for branded shopping opportunities: good for brand shopping/not suitable for brand shopping 5. Time schedule: tightly organized journey with tours of more scenic spots/relaxing journey with more free time The 48 (3*2 4 ) possible combinations based on the five attributes' aspects were reduced to an eight-profile nearly orthogonal design. This plan generated by SPSS ensures the highest level of coverage of different combinations of aspects with the minimum number of stimuli necessary for the estimation of conjoint analysis. Besides the eight profiles, another two hold-out profiles randomly generated by SPSS were included in the design (see Table 3). The hold-out profiles were not used for the estimation of different decision rule models but to test how well the models derived from the analysis predict new data. The use of hold-out profiles enables comparison on predictive accuracy between compensatory and noncompensatory choice models. The questionnaire consisted of two parts. The first part was a tailor-made experimental design in which respondents were asked to sort and rank the 10 stimuli profiles, where 1 was the most attractive destination tour and 10 the least. No attempt was made to present respondents with actual destinations, and the cards were labeled simply "Destination itinerary 1" through to "Destination itinerary 10." The 10 stimuli cards are presented in Figure 1. The second part of the survey was composed of three demographic questions including gender, age, and occupation to distinguish different groups of tourists.

Data Collection
A survey was conducted by using a convenience sampling approach from March to June 2012. In total, 201 participants completed the survey. Of those, 78 were recruited at an international tour operator 4 while they were enquiring about information about outbound trips or when they were identified as imminently due to take an outbound trip. Because of a low response rate (25%), it took an average 8 hours each working day to recruit 8 respondents who met the requirements and were willing to assist with the survey.
In order to control the bias that may be generated due to the selection of a particular tour operator, the other 123 respondents were recruited through a snowball sampling method. The initial respondents of the snowball sampling were generated from leads provided by the interview informants, who then recommended relatives or friends. The criterion for the selection of respondents was that they planned to take a long-haul outbound trip within one year. Since the experimental task is relatively complex, the survey was conducted face-to-face and the sorting process of each respondent was observed in order to obtain more reliable and complete data. The sorting task took on average 15-20 minutes for each to complete.
Although the convenience sampling method may not produce representative results for the whole population, there were two reasons for its use in this research; the exploratory nature of the study and the difficulties encountered in locating actual or potential long-haul outbound tourists. Although convenience sampling may be weak regarding statistical inferences relating to the population outside the sample, it has proved very useful for identifying issues, exploring promising hypotheses and collecting other sorts of non-inferential data (Fricker and Schonlau 2002). As the main purpose of the study was to explore the use of non-compensatory choice models rather than the generation of generalizable statistical conclusions, this approach was deemed appropriate.

Data Analysis
The data analysis included two steps: preference estimation based on LBA choice model and model fit evaluation between the LBA decision rule and the WADD decision rule. Because greedoid analysis is a preference estimation method based on a noncompensatory decision rule, it reveals the hierarchical aspects order for each respondent. Unlike the indicator of overall utility, which is central to conjoint analysis, it is not possible to average aspect orders to obtain a description of preferences in the whole sample. Instead, based on aspect orders of each individual, we constructed a hierarchical clustering tree for the whole sample. The procedure was used to summarize the proportions of the respondent sample selecting a given aspect as their primary choice criterion. Subsequently, it summarized the proportions selecting a given aspect as their second choice criterion within the group of respondents who chose the same primary choice criterion. The procedure continued until all the aspect orders were summarized. In terms of model fit evaluation, two indicators were used to evaluate the two choice models: the accuracy of prediction a. The 10 profiles designed are randomly numbered by SPSS and the stimuli number is the card number of the destination itinerary used for the sorting task (see Figure 1).
on the hold-out data and the number of costs. Since cards 9 and 10 were hold-out profiles, the rankings of the two cards were used as the hold-out data. The hold-out accuracy has been widely used to compare the out-of-sample predictive power of choice models in marketing and consumer studies (Kohli and Jedidi 2007;Yee et al. 2007;Dieckmann, Dippold, and Dietrich 2009). However, for the respondents whose destination preference could be predicted accurately by both models, this basis of comparison is intrinsically unable to provide a verdict about which of the two models would be more appropriate. This is the reason why the study explored the cost as the basis for comparing the two choice models, which is the power to replicate the observed preference order. The cost was calculated in greedoid analysis as an indicator to assess the extent to which the LBA rule was applied during the sorting process. In order to make a comparison, the cost in the case of the weighted additive choice strategy was calculated manually, in two steps. First, by summing-up the part-worth utilities of attribute aspects provided by conjoint analysis, we obtained the utility score of each destination card for each respondent. Then we deduced a ranking order for each respondent based on the assumption of the  WADD rule (i.e., destinations with higher utility scores are preferred).
Second, the cost (i.e., weighted number of violated ranking pairs) was calculated for each respondent by comparing the deduced ranking order with the actual observed ranking order. If the respondent followed a perfect weighted additive strategy, the deduced ranking order should be exactly the same as the ranking order provided by the respondent and the number of costs would be zero. Otherwise, the higher the number of costs, the less possibility that a WAAD rule was applied by the respondent.
One point to note is that among the 201 useable questionnaires, 184 respondents provided a full ranking of the 10 stimuli destination cards, while the remaining 17 respondents were able to provide only a partial ranking of the destination cards. Thus, all 201 respondents were processed by greedoid analysis to reveal the preferences based on the LBA model. For the model fit comparison, since the conjoint analysis cannot make estimations based on a partial ranking, only the 184 full ranking orders were used for that part of the analysis.

Preference Estimation Based on a Noncompensatory (LBA) Decision Rule
Among the 11 attribute aspects, the most popular first aspect used by the respondents was price at RMB9,000, which was used by 25% (51) of participants (see Table 4). In other words, for one quarter of respondents, low price (RMB9,000) was the most important criterion (aspect) on which to evaluate alternative destinations. For these respondents, all destinations not meeting this criterion were put aside, no matter how attractive they were in terms of other attributes. For 14% of the respondents (28), a relaxing journey with more free time was the most important criterion, and for yet another 13% (27) an easy visa application (low risk of rejection) was the single most important attribute. Famous country and price at 13,000-17,000 were endorsed by 12% (24) of respondents as their primary criterion. The proportions of the respondents who used the other six aspects as their first evaluation criterion were relatively small (no more than 10% for each aspect).
The hierarchical clustering tree was constructed to identify the clusters which used the same/similar aspect order to make their selections. Because of space limitations, Figure 2 presents only a partial tree with important nodes. These nodes represented the most commonly used attribute aspect(s) at each stage. For example, for the clustering of the first aspect used, only five attribute aspects mentioned above were included since these five aspects were the most commonly used, each accounting for more than 10% of respondents. For the group of respondents (51) who used price as their first criterion, they used 10 aspects as their second important criterion. Only those aspect(s) chosen by more than five respondents as their second criterion were included. This was price 13,000-17,000, which was used by 36 of 51 respondents. Among the 36 respondents, only the aspect(s) used by more than five respondents as the third criterion were presented.

Model Fit Evaluations
For the 184 respondents with complete rankings, the WAAD model predicted about 80% (147) rank orders of the hold-out data correctly, whereas the LBA model predicted a slightly lower proportion correctly (76%, 140 respondents).
The results of the cost indicator for each choice model are presented in Table 5. The average cost of the whole sample is 17.39 for the LBA model and 21.4 for the WAAD model. The standard error of mean and standard deviation for the LBA model are smaller than for the weighted compensatory model. A smaller standard error indicates that the sample mean of the costs more accurately reflects the mean of the costs for the actual population (all Chinese long-haul outbound tourists). A smaller standard deviation indicates that individual costs vary less from the mean.
The maximum value of the cost within the whole sample was 84 for the LBA model and 134 for the weighted compensatory model. Since the theoretical maximum cost is 285, the averaged percentage cost for each model is 6% (17.39/285) LBA and 8% conjoint analysis (21.4/285) respectively (from data in Table 3). In other words, the LBA model could replicate 94% of observed preference orders of the whole sample; the weighted compensatory model could replicate 92%. Based on these statistics, it can be inferred that the LBA model performs slightly better in replicating the observed ranking order than the WADD model.
To further examine the suitability of each model at an individual level, for each respondent the decision rule model that produced the fewest errors (least cost) was assigned to him or her. The frequency statistics of the respondents assigned to the two choice models are presented in Table 6. These tests revealed that 67 respondents (36%) were predicted better by the WADD choice model and 117 respondents (64%) were predicted better by the LBA choice model. Based on this indicator, the LBA model performs better in explaining the preferences of the sample than the weighted compensatory model. A further point to note was that among the 184 respondents, there were 20 respondents (10%) whose observed rankings could be perfectly reproduced (No cost) by the LBA model. Although the number of respondents within this group is too small to produce any significant findings, it is still worth looking at the preference characteristics of this group, since it may provide promising hypotheses for further studies investigating noncompensatory decision making. A frequency analysis was run on the first important aspect used by these 20 respondents. Instead of lowest price, the first aspect most frequently used by these perfect LBA decision makers was a relaxing journey with more free time (7). But there remained a significant number of people (6) who used lowest price as their first choice criterion.

Issues Regarding the Noncompensatory Decision Rule
Although the WADD model has been widely employed in many studies of tourism decision making (e.g., Morley 1994;Papatheodorou 2001;Seddighi and Theocharous 2002;Ciná 2012), it is evident that under certain circumstances-notably where the decision maker has limited time, energy, and information-simpler, noncompensatory decision rules are favored (Yee et al. 2007;Hauser, Ding, and Gaskin 2009). However, the use of the noncompensatory strategy model has not previously been quantified within tourism   decision-making contexts, and this exploratory study offers potential for future researchers. The findings of the study suggest that the LBA model can be used to explain a large proportion of respondents' preferences and it offers additional insights to conventional, compensatory model approaches.
For instance, the time schedule is one of the most important attributes used by Hong Kong residents in choosing a package tour (Wong and Lau 2001), and in the study of Chinese outbound tourists conducted by Zhu (2005), the time schedule was also an important attribute. However, the noncompensatory estimation offers the potential for additional insight into how this attribute is preferred. The present study found that a relaxing journey with more free time was the second most popular aspect used by tourists as their firstchoice criterion (and was the most popular among those respondents who followed a perfect LBA strategy). This information can be critical for tour operators to make product improvements to this market.
Moreover, the investigation of the noncompensatory decision rule reveals the nonnegotiable nature of preference on certain attributes under certain circumstances, which provides a different perspective for understanding the mechanisms behind tourist decision making behavior. This nonnegotiable aspect of preferences holds intuitive appeal for some special tourism destination choices such as solar or lunar eclipse tourism (i.e., the destination choice is solely based on one attribute). It could also help us to understand why some destinations come to be rejected, since destinations not containing "must-have" aspects will be automatically dropped from consideration.
The noncompensatory (LBA) decision rule estimated in this research is based on the lexicographic preference first introduced by Georgescu-Roegen (1954) within economics and the greedoid analysis used to infer the LBA model was introduced by Kohli and Jedidi (2007) and Yee et al. (2007) independently in marketing research. The application of the noncompensatory theory and the estimation method from these other disciplines entailed more than a simple process of quantifying theories of consumer decision making, but involved a process of careful knowledge adaption and reflection, based on the particular characteristics of tourism products. Tourism is a useful context to explore how knowledge can be translated across fields and disciplines. The current study advocates the further adaptation of knowledge from economics, psychology and marketing to tourist behavior.
Because of the intangibility of tourism products, some of the choice criteria used by tourists tend to be more abstract and associated with more emotional engagement than those used to select everyday products, such as the color of a cell phone or the amount of computer memory. Therefore, a more careful identification of these choice criteria (attributes) and their values (aspects) was required. The attributes and the aspects of the attributes presented to respondents should be ones that reflect the real performance of the available destinations. This revealed the importance of the qualitative interview stage to ensure the attributes and aspects were genuinely relevant to actual destination packages, and the need for multimethod, multicomponent studies.

Evaluation of Model Fit
The evaluation process assumed by compensatory and noncompensatory decision rules are totally different. To provide advice on which type of decision rule is more appropriate for a certain group of people, we need to derive measurements for assigning individual participants to certain decision rules. This research provides two possible estimation methods to evaluate the predictive ability of different choice strategy models. One is the test on hold-out data, while the other is the power to replicate the real preference order (the "cost"). The former has been widely used in previous studies but the latter is an innovation in tourism research. Although the weighted additive (WAAD) model outperforms the LBA model in terms of the out-of-sample accuracy, it does not perform better on preference explanation of each individual respondent.
The inclusion of the "cost" indicator is necessary and important because it can help us to identify those individuals who can be explained more accurately by a certain choice model. Even for the tourist who does not use a certain decision rule consistently, this indicator is able to suggest to what extent a certain rule is applied. As a matter of fact, this is a promising measurement to estimate the suitability of different models or decision rules at the individual level. It serves the same function as the qualitative methods of process tracing mentioned earlier, but overcomes some important disadvantages (e.g., judgment inconsistency and social desirably bias) identified in the qualitative approaches.
The methods used to calculate the cost was another issue addressed in this study. Although Yee et al. (2007) and Kohli and Jedidi (2007) used different programs to generate their aspect orders, the principles they used to identify the "best" aspect order were identical, which involved finding the aspect order that generates the minimum number of violated pairs (costs). This principle does not consider the fact that the importance of particular pair violations may vary with their position in the observed ranking order. A linearly decreasing weighting was used in this research Whether or not the linearly decreasing weighting is the most appropriate weighting scheme to reflect the actual preference, it does offer a useful starting point for further investigation. An alternative weighting scheme might be developed to give larger weights for all the alternatives within the consideration set and smaller weights for all the other alternatives.

Managerial Implications
The investigation of which choice model is more appropriate for a specific tourism market is of great importance for practitioners (e.g., tour operators and destination organizations) to develop more effective advertising and destination products. For example, for the Chinese long-haul tourists who can be understood better by a lexicographic decision rule, the advertisement should focus on the most important attribute(s) and emphasize their performance (expected attribute aspects). While for the group that can be predicted better by a WADD model, it may be more effective to emphasize the wider range of attributes in combination and their components.
Moreover, the hierarchical clustering based on the aggregation of individual aspect orders can provide valuable guidance for market segmentation and product design. For example, the aspect order "RMB9,000 > RMB13,000-17,000 > less risk (visa)" suggests a preference for cheap price and less risk while the aspect order "relaxing journey with more free time > good for brand shopping" suggests two distinguishable markets. Therefore, the hierarchical preference clustering could yield a range of new product/ market opportunities for destinations.

Concluding Remarks
Tourism is a complex and broad-ranging phenomenon, which may lead to a diverse set of choice contexts, including more comprehensive compensatory decision rules and simpler noncompensatory decisions, each leading to different choice outcomes. Thus, the assertion that all tourism decisions arise through the application of one specific decision-making process (the WADD rule) could create a limitation for tourism research. For the first time, this study adopted a "greedy" algorithm to investigate the applicability of alternative decision making processes for destination choice, which quantified the use of noncompensatory decision rules. At a fundamental level, the study casts doubt on the economic rationality that is implicitly assumed in conventional models of tourist consumer behavior and opens up opportunities for future studies and theorizing of the situational and individual differences in preferential choice processes in tourism contexts.
Although the efficacy that the LBA model estimated by the greedoid method could be used as a replacement of the robust WADD model is doubtful, and this was not the underlying purpose of this research, the use of a noncompensatory decision structure offers great additional potential for understanding tourists' destination choices based on a hierarchical order of attribute aspects. Moreover, together with the measurement of cost, the greedoid method enables a statistical judgment about under what circumstances and for whom the lexicographic model is superior to compensatory decision processing. Exploring the application of cost as an indicator of model fit is another contribution of this research, which provides a promising quantitative measurement to supplement qualitative process tracing methods.
As an exploratory study, this research has a number of limitations regarding methodology as well as research focus. Based on these limitations, recommendations are made for future studies. First, the destinations investigated in this study were not real destinations but stimuli that contain different combinations of destination attributes' aspects. A further link with actual destinations could be undertaken in future studies. Yet the qualitative data were useful to help generate realistic attributes for this specific market. For example, ease of obtaining a visa is relatively fixed for each destination country; Australia or New Zealand are relatively easy as opposed to the United States, for example, which contains a greater risk of visa rejection for Chinese tourists. Besides, the discrete choice experiment method used to elicit preferences can be adopted in future studies to link tourists' preferences with their real choice behavior.
Second, particular decision rules chosen by the individual are context-based (Swait et al. 2002). This research only investigated a specific target market (Chinese long-haul outbound) in which the LBA strategy may be suited. Other tourism-related decision-making scenarios (e.g., choice of other markets with different cultures, choice of short-haul destinations, choice of travel mode, hotel or tour operators, in-destination choices) may be considered and investigated in the future. The number of tourism choice contexts in which noncompensatory approaches could be applied is potentially very wide.
Finally, the main purpose of this research was to emphasize the different preference functions revealed by different decision rules and to explore how to distinguish the use of different types of decision rules. Thus, instead of hybrid model decision rules, single type rules were investigated and compared. However, it has been proposed in previous consumer studies that combining lexicographic and compensatory processes in a two-stage model might be a more realistic approximation of decision making (Gilbride and Allenby 2004). Further studies into the tools to infer and estimate these more complicated hybrid decision-making models could be very interesting for future studies of tourism decision making. This article offers one approach in which these might be developed.

Declaration of Conflicting Interests
The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding
The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The third author would like to acknowledge the financial support of The Hong Kong Polytechnic University (Grand No.: 1-VZHU).

Notes
1. By including hold-out profiles in the design of the data collection, conjoint analysis allows an out-of-sample predictive evaluation, which cannot be achieved by the AHP analysis. Since the purpose of this research is not to investigate the probability of certain choice being made or to improve the predictive power of the WADD model, the simpler but still robust OLS regression was adopted for the estimation rather than the more complicated logit regressions (e.g., hierarchical Bays) used in some DCE studies. 2. With the help of Michael Yee, which the authors acknowledge, this study modified the greedoid program by adding a weighting scheme to the software. 3. Tour guides on international trips and marketing managers for international destinations. 4. Among the top four tour operators in terms of the number of tourists receives in Beijing, this is the only one tour operator (the name can be provided on request) which gave permission to access their customers.