ERVD (Election Based on Relative Value Distances)

ERVD (Election based on Relative Value Distances) is a ranking method that, given a numerical decision table, places alternatives in a single order. Its output, like TOPSIS's, is a closeness score between 0 and 1 and a rank based on that score. Its key difference from TOPSIS is that, instead of building the ideal and anti-ideal points from the dataset's own best and worst values, it starts from a reference point the decision-maker has set in advance. Shyur, Yin, Shih and Cheng (2015) proposed it; the method carries prospect theory, from behavioural decision theory, into multi-criteria decision-making.

In TOPSIS, the "best" and "worst" alternatives are built from the alternative set itself; when the alternative set changes, these two points shift with it. ERVD asks a different question: "how does this alternative perform relative to the expectation level I have set in advance?" Staying above the expectation level is a gain, falling below it is a loss. Kahneman and Tversky's (1979) prospect theory shows that people feel losses more heavily than equally sized gains; ERVD renders this idea numerically. Falling slightly below the reference on a criterion is penalised more heavily than rising by the same amount above it; this penalty ratio is set by a loss-aversion coefficient (λ). Sensitivity also decreases as both gains and losses grow: the first unit of difference is felt strongly, later units make less difference; this is captured by a curvature parameter (α).

This idea has one consequence. ERVD is compensatory, just like TOPSIS: a weakness on one criterion can be balanced by strength on another. But the balancing is not symmetric: a shortfall below the reference weighs more heavily than an equally sized surplus above it. Because the reference point comes from the decision-maker rather than from the dataset, ERVD's ideal point does not shift as readily as TOPSIS's when the alternative set changes; this is an advantage as long as the reference is held fixed.

The method proceeds through four steps.

First step, sum normalisation. Every column is divided by the sum of the values in that column; each cell thereby becomes its column's share. The reference point is scaled by the same column sum. This normalisation does not take account of direction (whether benefit or cost); direction comes into play at the next step.

Second step, the prospect-theory value function. Every cell is compared against the normalised reference point. For benefit criteria, a value above the reference is a gain and is scaled down by the curvature parameter α; a value below the reference is a loss and is scaled by both α and the loss-aversion coefficient λ, which magnifies it disproportionately. For cost criteria this logic is reversed: below the reference is a gain, above it is a loss.

Third step, two reference points and decomposition. In the value table, the best value on each criterion builds the positive ideal, the worst value the negative ideal. Every alternative's weighted absolute distance to these two points is calculated.

Fourth step, relative closeness. An alternative's distance to the negative ideal is divided by the sum of its two distances. Alternatives are then ranked from the highest score to the lowest.

The formulas behind each step, the intermediate tables and the citation formats are given on the DecisionMind method page; this card carries no formulas.

The relative closeness score tells you how well an alternative stands, relative to the other alternatives in this analysis, given the stated reference point and the stated loss-gain assumptions. This score changes if the reference point is changed; TOPSIS's ideal point is at least consistent within the same alternative set, since it is derived from that dataset, whereas ERVD's reference is a choice made by the decision-maker, and once that choice changes, the whole order may be reshaped. The λ and α parameters default to values from Tversky and Kahneman's (1992) risk experiments; these values are not measured from this decision's own context.

Thus instead of writing:

"ERVD shows this alternative is the best"

the report should read:

"With this reference point and these loss-gain assumptions, the alternative closest to the ideal is this one; the order may change if the reference or λ/α is changed"

Crisp data. DecisionMind currently has no extension of this method. You need a complete table with alternatives in rows, criteria in columns, one number per cell; weights summing to 1 for every criterion (ERVD does not produce weights, it takes them from outside); a reference (expectation) value for every criterion; and, optionally, a loss-aversion coefficient (λ, default 2.25) and a curvature parameter (α, default 0.88). These two constants come from Kahneman and Tversky's (1992) experimental work; different values may be more suitable in a different context.

If you have a clear expectation or minimum acceptable level, and you think falling below it should count as a heavier loss than rising above it, ERVD is a suitable choice. It is especially meaningful in decisions carrying a "must not fall below this line" logic, such as safety, compliance or regulatory standards.

There are situations in which it should not be used. If you have no natural reference or expectation level, and it seems more natural for the ideal point to be derived from the dataset itself, TOPSIS should be preferred. Working with the default values without questioning whether the loss-gain asymmetry is meaningful in this decision context, that is, whether λ and α are specific to this case or drawn from general risk experiments, grounds the result in an unexamined assumption.

A clear reference/expectation level exists, losses should count more heavily than gains → ERVD

No reference exists, the ideal should be derived from the dataset itself → TOPSIS

Not "the best" but "the compromise limiting the greatest regret" is wanted → VIKOR

Not a ranking but weights are needed → AHP, BWM, SWARA (subjective) · Entropy, CRITIC (objective)

ERVD's most important strength is that it carries a well-documented finding of behavioural decision theory (Kahneman and Tversky, 1979), loss-gain asymmetry, into a numerical framework. Because the reference point is set explicitly from outside, it does not shift on its own as the dataset changes the way TOPSIS's ideal point does; as long as the reference is held fixed, the risk that the whole ranking is reshaped when a new alternative is added is reduced. Because the method uses a computational structure similar to TOPSIS's, it is relatively easy to understand and apply.

Its limitations stem from the reference point and the parameters coming from outside. First, the result is highly sensitive to the chosen reference point; a different reference can produce a different order, and this choice usually comes not from the data but from the decision-maker's own judgement. Second, the loss-aversion coefficient (λ=2.25) and curvature parameter (α=0.88) default from Tversky and Kahneman's (1992) individual risk experiments; that these values also hold in a specific supplier-selection or public-sector context is an assumption, not a measured fact. Third, the sum-normalisation step does not take account of direction, leaving direction to be handled in the value function; this is an easy point at which, in practice, where criterion direction is handled can be confused. Fourth, which of α and λ plays which role (α curvature, λ loss-magnification coefficient) can easily be mixed up.

The most common mistake is choosing the reference point at random, or from the alternatives' own average, and presenting it as an external standard; the reference should come from the decision context's own expectation, not from the data. A second mistake is leaving λ and α at their default values without noting in the report that this is an assumption. A third is confusing the default values of the curvature parameter (α) and the loss-magnification parameter (λ); DecisionMind's own technical notes specifically stress how easily this confusion arises. A fourth is reading the relative closeness score the way one reads TOPSIS's, and comparing it with a score from another analysis built with a different reference point. A fifth is looking for criterion direction (benefit or cost) only at the normalisation step and overlooking that it is also handled at the value-function step.

The governing principle is this:

An ERVD result is a reflection of the reference point you set and the loss-gain asymmetry you accept; if either is contested, the order is contested too, and the report must show this.