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Presentation

Session: Posters
Room: TBA
Time: Fri 13:00-14:30

Presenter: Jaakko Hakula (University of Oulu. Health Sciences)

Abstract

The aim of the essay is to make use of similarities between aggregation procedures in social choice theory and multicriteria decision-making (MCDM), and – despite methodological discrepancies - apply directly formalisms of outranking methods in social choice theory to various health care issues. Differences between conceptions of preferences in social choice and MCDM are not problematized. In Finland, Nurmi and Meskanen have analyzed connections of voting paradoxes and MCDM – partly based on works of the American mathematician, Don G. Saari, who has especially studied properties of positional voting rules, and revealed complexities of voting paradoxes. The basic idea is that alternatives and criteria in MCDM stand for candidates and voters in social choice theory, respectively. Voting methods are numerous, and using different methods the same group of voters can end up with different outcomes. The view chosen here is that of a single decision-maker, e.g. a chief physician, a general practitioner - potentially any other expert in bio-psycho-social, technological and economic contexts of everyday health care activities. In group decision-making and participatory planning, candidates correspond to either decision alternatives or criteria and voters correspond to decision-makers or participants. However, issues concerning multiple actors making decisions cooperatively are not included in this paper.

Substituting decision alternatives for candidates and criteria for voters, I’ll apply the interactive link (http://mathdl.maa.org/mathDL/4/?pa=content&sa=viewDocument&nodeId=1195&bodyId=1339) based on Saari’s work to construct a very preliminary example on the evaluation of electronic patient record systems, with an MCDM inclination contrived by Nurmi . For practical and illustrative purposes, there are initially three alternatives and three criteria. Some aspects of changing the number of alternatives and criteria are considered. The methodological focus here is on pairwise and basic positional voting rules – plurality, antiplurality and the Borda count. The emphasis being on an MCDM solution, criteria are put weights by giving them the more “votes” the more important the decision-maker ranks them.

As a hypothetical example on evaluating some basic properties of electronic patient record systems we have three products A, B and C, which are ranked according to three criteria - usability, system modularity and cost-effectiveness - the criteria having weights 7, 5 and 4, respectively. Using the plurality rule and the weights given to criteria, A is the best product, B and C thereafter. In pairwise comparisons both B and C defeat A with weight scores 7 to 9. On the other hand, B is defeated by C with weights 11 to 5. Thus, C (the Condorcet winner)defeats both A and B. The best alternative using the plurality principle is not necessarily the best in the pairwise sense, the conflict remaining unsolved with or without additional weights.

The plurality rule positions the alternatives according to the rankings defined by each criterion, but makes use of very limited amount of available information, i.e. only the first positions. Another positional rule, the Borda count, gives larger scores to higher ranked alternatives. Consequently, the total scores obtained from each criterion determine the ranking of the alternatives. In the above example, the overall ranking based on the Borda count is C(AB). C is ranked first - A and B get even scores (a tie in voting terms). The antiplurality rule gives all positions the same number of points, except the last one, the ranking being CBA in our example. In conclusion, results by using plurality, antiplurality and Borda rules diverge from each other. The choice of the best product, with criteria left unchanged, depends entirely on the evaluation method used. The right strategy matters, too.

Positional rules are sensitive to variations in alternative sets. In our example, the plurality rule gives the rank ABC. If we leave out C, the plurality ranking between A and B results in BA. Withdrawing B or A the ranking is CA and CB, respectively. In pairwise comparisons an analogous problem emerges when the number of criteria is varied. Cyclic preferences may lead to a total tie, and no (rational) choice between the alternatives can be made.

Key Terms

voting, the Saari triangle, multicriteria decision-making, health care professional

Authors:

Jaakko Hakula (University of Oulu. Health Sciences)

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