First, the key terms.

Ideal point
A chosen reference with desired or best criterion values.
Outranking
A structured relation supporting preference under specified evidence rules.
Veto
A sufficiently serious disadvantage that blocks a preference under a method’s rules.

The idea, explained

There is no single MCDA technique best for every decision. A distance-to-ideal approach needs normalization, criterion direction, weights and a distance definition. Some methods also compare with an anti-ideal. Outranking methods can use agreement, disagreement and veto thresholds rather than a single fully compensatory average. They may leave alternatives incomparable or tied. These results can honestly represent conflicting objectives rather than a software failure. Model selection should reflect the decision’s structure, evidence and acceptable trade-offs.

STEP 1

Make scales and direction explicit

A smaller cost is better while a larger reliability score may be better. Distances are meaningless if one raw unit dominates only because of its scale. Normalization changes geometry and may affect results, so document it and test alternatives.

STEP 2

Match compensation to the decision

A weighted distance can permit a major weakness to be offset elsewhere. If some harm is unacceptable, a hard constraint or suitable veto may reflect the decision better. Outranking still requires justified thresholds and stakeholder judgments.

STEP 3

Compare methods transparently

Explain difficulty, implementation burden, data needs and ease of communicating the result. If rankings differ, inspect the assumptions that produced the difference. Do not select whichever method happens to favor a previously preferred option.

Follow a worked example.

On already comparable benefit scales, an ideal is (100,100). Option A is (90,40) and B is (60,80). With equal squared-distance weights, A’s squared distance is 10² + 60² = 3,700; B’s is 40² + 20² = 2,000.

Walk it through, one step at a time

  1. Under that simplified distance rule, B is closer. This conclusion depends on the scales, ideal and distance definition.
  2. If the second criterion must be at least 70, A fails a mandatory threshold regardless of its first score. Exclusion is different from assigning a modest penalty.
  3. An outranking analysis could consider criterion-level agreement and a veto under its chosen variant. Report the specific rules instead of assuming every outranking method uses the same formula.

Where people get stuck

A method that produces a total ranking can conceal genuine incomparability, uncertainty or an unacceptable trade-off.

Now try it yourself.

Pause before opening each answer. Explain your reasoning in your own words.

1. Check the core idea

Is an incomparable pair necessarily a failed analysis?

Reveal the answer & reasoning

No. It can reflect insufficient evidence or conflicting criteria under a method that intentionally permits incomparability. Further deliberation or information may be needed.

2. Apply what you learned

Why should raw dollars and reliability percentages not be inserted unexamined into a Euclidean distance?

Reveal the answer & reasoning

Their units and ranges differ. The resulting distance could mostly reflect numerical scale rather than intended importance; normalization and justified trade-offs are needed.