A recent project brought to mind a simple approach to ranking alternatives for facility decision makers.

To prioritize facility investments, the U.S. Coast Guard needed to rank its various missions. The approach it adopted was the Analytical Hierarchy Process (AHP), a well-known decision analysis method. [1] There were eight missions and the rankings were to be determined by a panel of senior officers. Using a web-based survey, each officer was asked to rate the importance of each mission to the other missions, so that 28 pair wise comparisons were required. The survey took an estimated 60 minutes to complete for each officer. The comparisons were combined into a matrix of paired comparisons and then, with a specialized software product, mathematically reduced to a preference score or ranking that ranged from 0 to 100. [2] The results were reasonable, but the process seemed overwrought-particularly if it was to be repeated annually.

An alternative approach would be to skip the arduous pair-wise comparison, and simply ask each officer to assign a rank to each mission, then sum the ranks, and sort from highest to lowest value. Known as the Borda Count Method, this is often used in polls and elections-as examples, a modified version is used to score competitive sailing regattas and to rank Heisman Trophy candidates. How do the results differ between the two approaches? Not much it seems. We approximated Borda scores using the survey responses of the individual officers and compared the results:

_ | AHP | _ | Borda | _ |

Mission | Score | Rank | Score | Rank |

A | 100 | 1 | 100 | 1 |

B | 77 | 2 | 89 | 2 |

C | 42 | 4 | 60 | 4 |

D | 46 | 3 | 80 | 3 |

E | 33 | 5 | 59 | 5 |

F | 26 | 6 | 58 | 6 |

G | 13 | 7 | 22 | 8 |

H | 13 | 8 | 30 | 7 |

The standardized scores differed substantially, but the mission
rankings were almost the same, with a reversal of 7^{th}
and 8^{th} place. In other words, the Borda Method led to
similar results for a lot less effort. Analysts with a critical
bent could debate the merits of other approaches, but for those
looking for a quick and transparent way to rank and prioritize (and
for those whose matrix algebra is a little hazy) the Borda approach
is worth a look. [3]

Postscript: We learned yesterday the Coast Guard has indeed switched to the Borda Count Method.

[1] See Thomas L. Saaty, *The Analytical Hierarchy Process:
Planning, Priority Setting, Resource Allocation*. New York:
McGraw-Hill, 1980.

[2] The scores are the eigenvector of the matrix of pairwise comparisons.

[3] For a detailed discussion of alternative voting methods, see
Donald G. Saari, Explaining all three-alternative outcomes.
*Journal of Economic Theory* 87, 1999; or see a summary of
Saari's article at http://www.economist.com/node/288778 .

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