The Measurement of Housing Preferences in the Analytic Hierarchy Process

Abstract The paper focuses on an adaptation of the AHP method to elicit housing preferences on the rental market. To assess the applicability of the AHP method for residential market analyses, a survey was conducted on a group of students from Cracow University of Economics, Poland. The students were asked to evaluate the importance of particular criteria when selecting an apartment. We identified the major methodological difficulties of the utilization of the AHP method in applied research on preferences and decision-making on the housing market. Potential solutions to the mentioned limitations were also presented.


Introduction
The problem of housing preferences and choices on the real estate market is a complex issue. Preferences and decisions concerning the choice of a specific residential property are an effect of comparing, weighing and assessing a number of various attributes of a real property, and, in consequence, decision options. As the existing research findings show, due to a complex character of problems occurring in such areas as construction (Dytczak, 2010) or the real estate market (Foryś, 2009), multi-criteria decision aiding methods are successfully applied here. In the other area it seems that the methods can also be a useful analytical tool, helping in better understanding of decision-making processes of buyers of flats, being an alternative to the methods like conjoint analysis (Głuszak, 2011). This explains the authors' interest in the AHP method and the conditions for its application in research into housing preferences on the real estate market.
The main objective of the conducted research was to verify the usefulness of the AHP method to study housing preferences on the real estate market. The scope of the research was limited to an analysis of housing preferences expressed by students of the Cracow University of Economics in respect of the choice of residential units for rent.
Three detailed objectives were subordinated to the main objective: (i) structuring a hierarchy of the determinants of decision-making process in the area of the choice of premises for rent by students of Cracow universities, (ii) pre-selection of decision criteria for future structuring of a decision model in this area, (iii) elaborating an optimum way of selecting experts for the planned actual study.

The methods of aiding multi-criteria decision-making processes
The discussed research problem comes from the area of Multi-Criteria Decision Making, MCDM, also called the Multicriteria Analysis, MCA, or Multi-Criteria Decision Aid, MCDA. Mulliner, Smallbone and Maliene (2013, p. 271) quote an MCDM definition created by Zopounidis, who perceives MCDM as "a set of methods which allow the aggregation and consideration of numerous (often conflicting) criteria in order to choose, rank, sort or describe a set of alternatives to aid a decision process". Di Matteo, Pezzimenti and Astiaso Garcia claim that from the methodological point of view "multi-criteria decision making (MCDM) approaches deal with the evaluation of a set of alternatives in terms of numerous decision criteria with the goal of providing a choice highlighting the best alternative among the set of options" (2016, p. 2).
There is a great number of methods of scientific aiding for multi-criteria decision-making processes (see : Trzaskalik 2014, Di Matteo, Pezzimenti andAstiaso Garcia, 2016). The character of the aiding discussed here indicates a possibility to create a hierarchy of decision criteria independent of each other. In the research methods useful in the modeling of decisionmaking processes with hierarchical structure Dytczak and Wojtkiewicz (2010, p. 398 The Analytic Network Process, ANP, is the last of the methods of modeling decision making processes with hierarchical structure. Saaty (2001, p. 34) believes that the fundamental difference between the AHP and the ANP lies in the fact that while the AHP enables to study the influence exclusively on the basis of pairwise comparisons, the ANP enables to analyze interactions of decision criteria (simultaneously, each one with each one). At the same time, the methodological bases of both methods remain identical, the differences occur only in the way of computing the decision supermatrix. Saaty suggests the application of the ANP method only when the creation of a hierarchy of equivalent criteria is difficult. Thus, the ANP method should be understood as the supplementation of the AHP for fuzzy decision-making problems, as it is not subject to so many limitations. Therefore, the AHP method was finally chosen for further analysis. As the results of the existing research with the use of the AHP in the area of housing decisions show, a limitation of the method may consist in imprecise housing preferences of buyers/decision makers (Piwowarski and Matczak, 2010). On the other hand, an example of partial application of the AHP method for the analysis of decision processes on the real estate market can be found in Mulliner, Malys and Maliene (2016), where the functionality of the method was limited to the creation of the supermatrix of decision vectors, while skipping the stage of establishing ranks for individual decision criteria.

The applied research methodology
Research into preferences and decision making processes of buyers of flats in Poland is present in the literature of the subject although it usually has an exploratory and descriptive character. In recent years, a number of studies of housing preferences of young people (Urbańska, 2011;Strączkowski and Suszyńska, 2012) and students (Skotarczyk and Nowak, 2010, Kempa et al., 2015) have been conducted. The previous research findings enabled to build a proper research tool. The authors proposed the construction of a housing choice problem in the form of hierarchical structure, where attributes concerning housing costs, location, the standard of flats, the access to shopping facilities and services, as well as the accessibility of recreational areas were decision criteria. A questionnaire was the main research tool. A group of 153 respondents -lessees of flats from the Cracow University of Economics -was asked for the completion and initial evaluation of the decision criteria. As a result, 125 correctly completed questionnaires were obtained.
The evaluation of the respondents' consistency was conducted in two stages, by means of the analytical and deductive method and by means of the AHP consistency test analysis. In practice, the test of significance was carried out in Super Decisions 2.4.0-RC1 program, and its results are discussed below.

Presentation and discussion of the research findings
The obtained results indicate relatively low consistency of the responses given. 122 responses passed the selection with the use of the analytical and deductive method, which means that 3 responses, namely 2.4%, were rejected. At the next stage, on the level of the tests of significance, the next 84 responses were rejected, that is 68.9 % of those which remained after the first stage. In consequence, 38 responses were obtained which were consistent enough to regard the respondents reliable experts for the planned actual study.

Figure 1. The distribution of the Consistency Ratio (CR) values of experts' ratings
Source: own elaboration When analyzing the distribution of the Consistency Ratio of experts' ratings ( Fig.1), it is worth noting that only small percentage of experts was characterized by large consistency of ratings, thus, the rating Consistency Ratio did not exceed 10%. Those were 38 decision makers, which made up 31.1% of respondents. The biggest number of ratings was in the consistency range between 10 and 15%, so above the consistency threshold limit suggested in the literature.
A relatively large number of ratings was characterized by even lower consistency (CR>0.2).
To assess the influence of consistency on the obtained ratings of the significance of criteria, the table lists the results for all decision makers and the groups of decision makers whose ratings were characterized by a satisfactory consistency level (CR<0.1).  The distribution of experts' (decision makers') ratings is presented in Figure 2. Recreational areas criteria. In the case of the Recreational areas criterion, a few experts were identified who differed significantly from the others in their evaluation of the importance of this feature (including also those for whom the weighing factor of this characteristic was higher than 0.4, thus, a few times higher than the average in the surveyed group of decision makers).
Therefore, we should consider them outliers.
In order to follow carefully the relationship between the consistency of opinions and the significance of individual criteria, the scatter diagrams of the ratings for individual criteria in relation to the level of the Consistency Ratio was analyzed (Fig. 3).

Conclusions
The study results have proven a few interesting properties of the considered objects of lease, as well as the group of experts evaluating the significance -students, in this case. It turns out that a relatively large number of inconsistent responses of experts (namely, those for which the significance coefficient value exceeded 10%, CR>0.1) did not change the ranking of the significance of characteristics influencing the decision to rent a specific flat. Only the power of preferences changed slightly, however, in the discussed decision making process the significance of "Rental cost" and "Location" characteristics decreased insignificantly (from 0.32674 to 0.32066 and from 0.23670 to 0.22234, respectively), whereas the significance of "Retail and services" feature, "Apartment's standard" feature and "Recreational areas" characteristics increased slightly (from 0.09852 to 0.09889, from 0.27493 to 0.28597 and from 0.06312 to 0.07226, respectively).
The conclusion which arises from the above is although a large part of experts did not always give consistent responses, they intuitively made a rational choice of an object of lease.
However, such a situation by no means can be treated as a rule in the modeling of decision making processes with the use of the AHP method. Practical applications of the AHP clearly indicate the disturbance of the distribution of ranks considering pairwise comparisons not fulfilling the condition of the rating consistency (CR<0.1). Hence, it is most probable that there are other reasons for methodological divergences of the applied method and the obtained results.
When analyzing the results of the conducted study, the most probable problem areas which could occur are those mentioned below, grouped according to the declared research objectives.
1. Insufficient precision of the hierarchy of decision criteria:  imprecise nomenclature of the criteria;  non-fulfillment of the condition of reciprocal independence of the criteria and subcriteria.
2. The character of the study:  the study concerned the preferences of potential lessees -students, hence, it is relatively easy to defend the accusation of large divergence of ranks, even in the group of consistent evaluations for individual criteria (N=38);  the reason for the above may be the adopted definition of expert -in the conducted study the "expert" term did not exactly mean a person possessing special knowledge in an evaluated area, with a reputed position, confidently moving in the real estate industry, but rather a person potentially interested in the object of the decisionmaking process -the rent of a flat.

The choice of experts:
 the lack of deep knowledge of the market and specialist industry knowledge in the decision making area signaled above;  random, non-methodical way of choosing experts for the survey;  low reliability of responses given by respondents (no reflection, shame in the face of giving an "incorrect, irrational response", no willingness to participate in the survey, others);  irrational or "pseudo-rational" way of making decisions by young people renting a flat (flat-mate, lemming-like rush, no market analysis, etc.) The proposals of potential solutions or ways to avoid the problems presented below are shown below: Re. 1. Insufficient precision of the hierarchy of criteria:  making the nomenclature of the criteria more precise;  checking whether the criteria for certain are not dependent on each other (do not influence each other);  grouping the criteria according to a different key than the one used in the questionnaire.

Re. 2. The character of the study:
 precise definition of the character of the study and adequate discussion of the adopted threshold consistency level -perhaps in some cases of studies of the preferences of potential lessees where objective, market-rooted opinions are not necessary, it would be justified to increase the acceptable consistency level;  more exact explanation of the sense and the objective of the study, otherwise close observance of the definition of an expert as a person with above average knowledge about the examined phenomenon and its decision making environment.

Re. 3. The choice of experts:
 structuring the way of choosing expertsdeveloping a set of necessary criteria to be fulfilled by an expert, including deeper knowledge of the market of flats to rent, with the simultaneous limitation of the number of experts (e.g. Saaty estimates the optimum number of experts in a study for 5-9 persons);  in the case of studies of potential lessees' preferences, extending the hierarchy of decision criteria, with, for example, "future flatmate's opinion", "fashion/trend" criteria -for the choice of experts which would be more targeted at the objective of the study;  explanatory studiesextending the research methodology with direct explanatory interviews with experts -following the evaluation.
To sum up, the AHP method can be useful in research into housing preferences and choices on the real estate market, on the condition of considering methodological requirements and limitations of this method in the planned research. Special attention should be paid to the issues of the proper selection of determinants and structuring the hierarchy of the decisionmaking process, adjusted to the subject and scope of the research, and the proper choice of experts-respondents.