William J. Hurley

The analytic hierarchy process: does adjusting a pairwise comparison matrix to improve the consistency ratio help?

Consider an AHP decision-maker who is uncertain about his or her preferences. In fact, suppose he or she is only able to specify unbiased estimates of these preferences. Then given the decision-makers final pairwise comparison matrix having a consistency ratio less than 0.10, is it possible for the reliability of the analysis to be improved by using some artificial means to lower the consistency ratio (i.e. a minimum perturbation of pairwise comparison matrix elements which reduces the consistency ratio by a given amount)? In this paper we argue that the answer to this question is yes. To make our point, we employ a Monte Carlo simulation of a decision-maker who picks random judgments out of a distribution centered at his or her true judgment. The simulation results suggest that, if the final consistency ratio is less than 0.10, additional artificial manipulation to lower the consistency ratio will improve, on average, the reliability of the analysis.

Transitive calibration of the AHP verbal scale

Abstract One of the strengths of the Analytic Hierarchy Process (AHP) is that it allows decision-makers to specify their preferences using a verbal scale. Yet, as is well known, a strict reliance on the corresponding Saaty 1–9 numeric scale can induce some inconsistency. Hence we argue that, in certain situations, it may be appropriate to calibrate the verbal scale. The result of this calibration is a geometric scale based on a single parameter. We present some limited evidence that this geometric scale marginally outperforms the Saaty 1–9 scale. Moreover, we suggest that this calibration can be used to do a simple sensitivity analysis in cases where judgements are uncertain.

The analytic hierarchy process: a note on an approach to sensitivity which preserves rank order

Abstract Within the framework of the AHP as it applies to multicriteria decisions, it is frequently the case that decision makers are certain about the rank order of the objects for a particular pairwise comparison matrix but uncertain about the precise numerical weights that the AHP produces for that matrix. This uncertainty translates directly into uncertainty about whether the best alternative obtained from the AHP is actually the best alternative. However, if the weights of an AHP pairwise comparison matrix can be varied in a way that preserves the rank order of the objects, and at the same time, this perturbation does not result in the best alternative changing, then the decision maker is typically much more confident about what the AHP recommends. In this paper, I detail a simple approach to sensitivity within the AHP which preserves the rank order of the objects. Scope and purpose In the authors experience with AHP as a multicriteria decision tool, it is frequently the case that decision makers (DMs) are quite certain about the rank order of the objects for a particular pairwise comparison matrix (PCM) but uncertain about the precise numerical weights that the AHP produces for that matrix. This uncertainty translates directly into uncertainty about whether the best alternative obtained from the AHP is actually the best alternative. However, if the weights of a PCM can be varied in a way that preserves the rank order of the objects for that matrix, and at the same time, this perturbation does not result in the best alternative overall changing, then the DM is typically much more confident about what the AHP recommends. In this paper I detail such an approach to sensitivity for the AHP.

The analytic hierarchy process: can wash criteria be ignored?

We define a wash criterion as one where the decision-maker is indifferent among the alternatives when they are compared on that criterion. In view of the Belton-Gear example and other such anomalies associated with the analytic hierarchy process (AHP), we ask whether eliminating a wash criterion will affect the overall ranking of objects. In the case where there is only one level of criteria, the rank-order of objects is unaffected by leaving out a wash criterion. However, in the case where the wash criterion is a subcriterion, the rank order may be affected by leaving it out.

Generalized Markov Dividend Discount Models

3N6). n our Hurley-Johnson [1994] dividend hscount model (DDM), lvidends are assumed to follow a simple Markov process. The firm is assumed to I either maintain the same dividend (with probability 1 p) or increase it (with probability p). Ths process appears to be consistent with the dividend policy of a large number of firms (see Lintner [1956]). We know, however, that not all firms are able to maintain a non-decreasing dividend payout. Many firms run into dfficulty and have to either lower dividends or suspend them entirely. Even if a dwidend stream is increasing, it is rarely the case that each increase can be described by a constant geometric growth rate. To model these and other contingencies, a more complicated Markov process is required. Hence, in this note, we extend the basic Hurley-Johnson approach to more general Markov processes. We also show how to calculate these valuations with a Monte Carlo simulation that is easily implemented on a spreadsheet. Here we employ EXCEL with the add-in @RISK.

Combining expert judgment: On the performance of trimmed mean vote aggregation procedures in the presence of strategic voting

Abstract Analytic group decision techniques for selecting a subset of alternatives range between multicriteria decision analysis techniques such as multiattribute utility theory and the analytic hierarchy process to voting techniques where each member of the decision group submits a ranking of the alternatives, and these individual rankings are then aggregated into an overall ranking. The obvious advantage of voting is that it bypasses the rather intensive data generation requirements of multicriteria techniques. In this paper we compare the performance of trimmed mean rank-order aggregation procedures in the case where a subset of the individuals in the group charged with the decision vote strategically. We employ a Monte Carlo simulation experiment on a specific decision instance and find that trimmed mean aggregation compares favorably with other procedures.

Equitable birthdate categorization systems for organized minor sports competition

In some organized minor sports programs where there is early competitive streaming, players born early in the year are more likely to reach elite levels than those born late in the year. This is generally attributed to the calendar year system most minor sports programs use to group players for the purposes of competition. In this paper I show how to devise more equitable systems based only on player ages. These systems rotate the relative age advantage so that those players born late in the calendar year are not always the youngest players in their age division.

Foreword: special issue on operations research in sport

I am most thankful to Gilbert Laporte for the opportunity to edit this special issue of Computers and Operations Research. I am especially grateful to the authors who submitted. The present collection is a good cross-section of the cutting edge of operations research in sports. It begins with a number of scheduling/timetabling papers. Also included are papers on computing streak probabilities, an analysis of a curling paradox and an ancient Chinese horse race problem, ranking Olympic achievements, and an interesting betting/gambling paper. I have learned a lot from each of these papers. I hope that readers of Computers and Operations Research will also enjoy them. In my view, the heart of OR in sports is providing decision support to practising managers, coaches, and athletes. If I had to define it, a simple variant of Morse and Kimball’s [1] seminal definition would do quite well:

The favourite-longshot bias in parimutuel betting: A clarification of the explanation that bettors like to bet longshots

Abstract One explanation of the favourite-longshot bias in parimutuel betting is that bettors derive utility from betting longshots. The purpose of this paper is to explore the conditions where such an explanation makes sense. We posit a simple two-horse race where there are two groups of bettors: one group always bets the longshot; the other bets on the basis of expected value. The model yields two results. In the absence of transactions costs (track take), there is no favourite-longshot bias. However, if the track take is positive, we would expect to observe the bias. The primary reason is that there is no short-selling mechanism in parimutuel betting markets. Hence, the explanation that bettors like to bet longshots also requires transactions costs and no short-selling.

Are National Hockey League referees Markov

The media and hockey fans have generally criticized National Hockey League (NHL) referees for two biases. One is that fewer penalties are called against the home team. The other is that some penalty calls tend to be ‘even-up’ calls. For instance, if one team receives the first two penalties of a game, it is highly unlikely that it will also receive the third penalty. In this article we find support for both claims, using data from the 2007–2008 NHL season.