ModelWorld:TheGreatDebate—MAUT VersusAHP

1 Vol. 35, No. 4, July August 2005, pp. 308 312issn0092-2102 eissn1526-551X 05 3504 0308informs 2005 INFORMSM odel World: The Great Debate MAUTV ersus AHPSaul I. GassRobert H. Smith School of Business, University of Maryland, College Park, Maryland analytic hierarchy process has gained wide acceptance among academics and words: decision analysis, theory: analytic hierarchy process; utility-preference: multiattribute. The theory of decision analysis (DA) is designedto help the individual make a choice amonga set ofprespecifiedalternatives (Keeney and Raiffa1976, vii). Simply put, the basic DA problem is, Howshould a decision maker select from a given set ofcompeting alternatives that are evaluated against con-flicting objectives?

2 Because operations research (OR)is the science of decision making, OR researchersand practitioners have developed a wide range ofmethods for resolving the basic DA problem andits variations. They base some of these methods onvon Neumann and Morgenstern s (1947) expectedutility theory (EUT) and Savage s (1954) subjectiveexpected utility theory (SEUT), with extensions tomultiattribute utility theory (MAUT) and multiat-tribute value theory (MAVT) (Keeney and Raiffa1976, Edwards 1977, Edwards and Barron 1994).Other procedures they have developed and appliedinclude Roy s (1968, 1996) ELECTRE (election etchoix traduisant la r alit ), PROMETHEE (preferenceranking organisation method for enrichment eval-uations) by Brans et al.

3 (1996), TOPSIS (techniquefor order preferences by similarity to ideal solu-tions) by Hwang and Yoon (1981), and Hwang et ), and the analytic hierarchy process (AHP) (Saaty1977, 1980, 1982). People often refer to ELECTRE andPROMETHEE as representing the European School,and TOPSIS and the AHP (and others) as repre-senting the American School. (Mollaghasemi andPet-Edwards 1997 and Belton and Stewart 2002describe most of these multicriteria decision-making(MCDM) methods.)Since its development 25 years ago, the AHP hasbecome a widely popular MCDM procedure in theUS and in other countries. The AHP has gainedwide acceptance among academics and practitioners(Golden et al.

4 1989, Forman and Gass 2001, Goldenand Wasil 2003). It is the workhorse for solving mul-ticriteria problems that have a finite number of alter-natives to be put in rank order by priority (weight).The AHP seems to have replaced MAUT and MAVTfor solving such real-world MCDM problems. As anexponent of the AHP, I introduced it to my MBA andundergraduate management science students in theearly 1980s and was the first to discuss it in a text(Gass 1985). I am an AHP fan. But as the new kidon the block, the AHP has had to compete againstestablished methods, in particular, MAUT. Many aca-demics schooled in MAUT debated the efficacy ofthe the mid-1980s, MCDM researchers began to com-pare the AHP to MAUT.

5 They found that the AHPdoes not adhere to the basic von Neumann andMorgenstern axiomatic structure of normative util-ity theory as incorporated in MAUT, and they raisedother concerns. I tried to reconcile the criticisms ofthe AHP with my understanding of AHP and MAUTand joined E. Forman in describing our view of thedebate (Forman and Gass 2001). We concluded:The AHP has been tested in the marketplace. Its accep-tance as a new paradigm for decision analysis has beenremarkable The AHP is theoretically sound, readilyunderstood, easily implemented, and capable of pro-ducing results that agree with expectations (p. 485).308 Gass:Model WorldInterfaces 35(4), pp.

6 308 312, 2005 INFORMS309I thought we had laid the matter to rest. But Smithand von Winterfeldt (2004, p. 568) reviewed pastManagement Sciencepapers in DA and made the fol-lowing statement:While many in the decision analysis community(ourselves included) follow Dyer in believing the AHPto be fundamentally unsound, others (including Saaty,Harker, and Vargas) disagree and the AHP is stillwidely used in practice statement sends the wrong message to theOR community. That statement motivated me towrite this column. (Smith and von Winterfeldt werejoint editors ofManagement Science s DA departmentin 2004.)In discussing the AHP, Smith and von Winterfeldt(2004, p.)

7 568) began as follows:One of the more acrimonious debates inManagementSciencehas concerned the Analytic Hierarchy Process(AHP).Management Sciencehas published few papers onthe AHP. For our discussion, the following five are ofinterest: Saaty (1986), Harker and Vargas (1987), Dyer(1990), Saaty (1990), and Harker and Vargas (1990).Saaty (1986) provided a full and detailed set of axiomsthat define the boundaries of the AHP. Harker andVargas (1987) reviewed the theory of the AHP andanswered criticisms of the methodology. Dyer (1990)reviewed the criticisms of the AHP, concluded that theAHP is flawed, and offered a resolution of the diffi-culties by synthesizing the flawed AHP and , Saaty (1990) and Harker and Vargas (1990)rebuted Dyer s arguments.

8 Why the debate?The main criticisms of the AHP concern its mea-surement scale, rank reversal, and transitivity of pref-erences. In Saaty s original AHP paper (1977) and inhis book (1980), he describes a measurement scale(termed the fundamental 1 9 scale) for measuring theimportance of one criterion over another or the pref-erence of one alternative with respect to another eval-uated against a criterion. Rank reversal occurs when,after the decision maker (DM) ranks the given set ofalternatives, the DM adds a new, irrelevant alterna-tive to the set. Upon ranking the modified set, the DMfinds that the previously highest ranked alternative isdowngraded.

9 Transitivity between preferences meansthat if alternative A is preferred to alternative B, andalternative B is preferred to alternative C, then alter-native A is preferred to alternative C. I want to con-centrate on rank reversal and transitivity, as these arethe aspects Smith and von Winterfeldt (2004) high-lighted. They stated:While Saaty (1986) provided an axiomatic foundationfor the AHP, these axioms conflict with the axioms ofexpected utility theory and have met with resistancefrom decision analysts (p. 568).Rank reversal in utility theory is related to the con-cept of irrelevant alternatives as given by the follow-ing axiom:Adding new acts (alternatives) to a decision problemunder uncertainty, each of which is weakly dominated(preferred) by or is equivalent to some old act, has noeffect on the optimality or non-optimality of an old act(Luce and Raiffa 1957, p.)

10 288).For example, when buying a car, you first con-sider and rank three different ones A B C and findthat A has the highest rank. You add a fourth, sayan exact copy of C, and for the new problem, a rank-ing of the four cars now causes B to have the highestrank. MAUT proponents use this type of problem intheir attack on the AHP because rank reversal canoccur under AHP but not under MAUT. (Why anyonewould structure a decision problem in this manneris unclear; in defining decision analysis Keeney andRaiffa 1976 state that the decision problem starts with prespecifiedalternatives. ) Rank reversal can and doesoccur in many real-world decision problems.