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Introduction to decision aid

Ordinal methods

A decision aid method is said to be ordinal if it keeps producing the same results when all input values vary in the same proportion. This implies that such a method reflects exactly the relative importance of the criteria, and is not dependent on the units or the normalization method used (as the weighting methods are).

de Borda's method

For each criterion, the n actions are sorted from the worst to the best and given a value corresponding to the rank obtained: the worst action for a criterion gets 1, and the best one gets n. All values are then summed by action, and the totals gives the classification of the actions. The actions that are indifferent get as value the average of the values they would have obtained if they had not been indifferent.

This method is very often used in sport competitions.

See DECIDE__Borda() [DECIDE.xls / All functions / Borda] for more information.

See also a demonstration implementation written for SciLab.

Condorcet's method

Condorcet's method compares all couples of actions, and determines the best action of each couple by counting for how many criteria each action is better than the other. The results are placed in a matrix, and the totals give the classification of the actions.

Unfortunately, this method sometimes does not respect the transitivity of the preference, which can be unacceptable.

See DECIDE__Condorcet() [DECIDE.xls / All functions / Condorcet] for more information.

Lexicographical methods

In the lexicographical methods, the criteria are sorted in descending order of their weight. Then, for the criterion with the highest weight, the actions are sorted on their values. If they score identically for this criterion, the actions are sorted on the next one, and so forth.

The alphabetical order is the typical example of a lexicographical method.

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