HFGPE (Generalised Peer Evaluation)

HFGPE is a ranking method for when you have a table in which every alternative ("which loan application," "which branch") has been evaluated by all the other alternatives on some efficiency measure, and you want these alternatives placed in a single order. In classical efficiency methods (Data Envelopment Analysis, DEA), each unit evaluates itself by choosing only the weights most favourable to it; this leads many units to score close to one at the same time under "the weighting that shows me in the best light," making it hard to distinguish between them. HFGPE uses a solution known as cross-efficiency: every unit is scored not only by itself but also from the viewpoint of all the other units. This evaluation is carried out at two extremes: a benevolent viewpoint chooses the weights that show the unit as favourably as possible, and an aggressive viewpoint chooses the weights that show it as unfavourably as possible. HFGPE blends these two extremes with a single strategy parameter. Zhou and Xu proposed the method in 2020, and it takes as its direct input benevolent and aggressive peer-efficiency tables that have already been computed.

The idea behind HFGPE is that a unit's true performance is more reliably measured not by its own claim but by how its peers see it. Every unit is evaluated twice by all the other units: once under the assumption "let us look as favourably as possible," and once under the assumption "let us look as critically as possible." The real judgement usually lies somewhere between these two extremes, and HFGPE expresses this with a single strategy parameter. This parameter can be set as a fixed number, or it can be derived from the data by finding the value that best reproduces a ranking experts have actually given in the past (via least squares).

This idea carries a philosophical consequence: HFGPE is a consistency and calibration method. The result depends not on an externally assigned, fixed set of weights, but on how the units evaluate one another and how generously that evaluation is read. Once a strategy parameter has been calibrated to match past expert decisions, the method becomes not merely a mathematical efficiency calculation but a peer-evaluation mechanism consistent with past decisions.

The method proceeds through four steps; these steps take the already-computed benevolent and aggressive peer-efficiency tables as input and do not build these tables themselves from raw production data.

First, confirming the two extreme tables. How every unit is scored by all the other units, in the most benevolent way (the maximum peer-efficiency table) and in the most aggressive way (the minimum peer-efficiency table), is held in two separate tables.

Second, determining the strategy parameter. A strategy parameter (between 0 and 1) showing in what proportion these two extremes should be mixed is either supplied as a fixed value, or found from the data, via least squares, as the value that best reproduces a previously recorded ranking (for example, a priority order experts have given in the past).

Third, combining the two tables. The benevolent and aggressive tables are blended in proportion to this strategy parameter: if the parameter is close to the benevolent end, the result resembles the benevolent table more; if close to the aggressive end, it resembles the aggressive table more.

Fourth, the average peer score and ranking. For every alternative, the average of the scores it received from all the peers evaluating it is taken, and alternatives are ranked by this average from highest to lowest.

The formulas behind each step are given on the DecisionMind method page; this card carries no formulas.

The average peer score tells you how efficient or strong an alternative is seen to be by its peers, and nothing more. The score depends on the chosen strategy parameter and peer group; it cannot be compared with the scores of another analysis carried out with a different strategy parameter or a different peer group. The alternative ranked first is generally the one that stays relatively strong under both the benevolent and the aggressive viewpoint, holding a consistent position between the two extremes; scoring high under the benevolent viewpoint alone while collapsing under the aggressive one pulls the average down.

Thus instead of writing:

"HFGPE found the most efficient unit"

the report should read:

"With this strategy parameter and this peer group, the alternative with the highest average peer score is this one; the ranking is sensitive to the strategy parameter"

HFGPE works with crisp numbers; but here what is crisp is not the raw decision matrix but the already-computed benevolent and aggressive peer-efficiency tables. This is what distinguishes HFGPE from other ranking methods: the engine in this scope does not itself build these two tables from raw production data or a fuzzy evaluation; the user must have already computed them through a prior efficiency analysis (classical or fuzzy peer evaluation). DecisionMind holds no extension of this method for other data types; it stands alone in its base form.

You need the following: both a benevolent and an aggressive peer-efficiency table for every alternative (two square tables of the same size, with rows and columns corresponding to the same alternatives); and either a fixed strategy parameter or a reliably recorded past ranking (to find the strategy parameter from the data). Applying the same weight vector to both the benevolent and the aggressive table is wrong; these two tables must be computed separately, with different optimisation objectives. If no past ranking exists, the strategy parameter must never be defaulted to 0.5; doing so defeats the method's promise of calibration from data.

HFGPE is a suitable choice if you already have benevolent and aggressive efficiency tables computed through a peer-evaluation (cross-efficiency) analysis and want to turn these into a single consistent ranking. If a reliable expert ranking is recorded from the past, you can calibrate the strategy parameter to that ranking and bring future evaluations into line with the past. Its typical areas include loan-application appraisal, branch and institution performance comparison, and any efficiency analysis requiring peer review.

The situations in which it should not be used are as follows: if you do not yet have benevolent/aggressive peer-efficiency tables, a DEA or similar peer-efficiency analysis should be carried out first, and HFGPE should take that analysis's output as input. If there is no reliable past ranking to calibrate against, and a fixed strategy parameter cannot be defended either, how the parameter was chosen remains unclear and the result may look arbitrary.

Both peer-efficiency tables ready, to be reduced to a single ranking → HFGPE

Raw production/input-output data, no efficiency analysis performed yet → a DEA-like peer-efficiency analysis first

Criteria to be given external weights, not peer evaluation → TOPSIS, SAW, VIKOR

No past ranking, strategy parameter indefensible → HFGPE should not be used without a fixed, justified parameter

HFGPE's greatest strength is that it softens the problem common to classical peer-efficiency methods, "most units score close to one in their own favour," by combining a benevolent and an aggressive extreme (Sexton, Silkman and Hogan, 1986; Wang and Chin, 2010). Working with a single strategy parameter makes the result easy to interpret: if the parameter is close to 0, it is immediately clear that an aggressive evaluation was applied; if close to 1, a benevolent one. Being able to calibrate the strategy parameter to past expert decisions turns the method into a tool consistent with past practice, not merely a mathematical exercise.

Its limitations arise from the general nature of the peer-evaluation approach and from the calibration logic itself. First, how the benevolent and aggressive peer-efficiency tables were computed lies outside this method's scope; if these tables are flawed or inconsistent, HFGPE does not correct this, but inherits it as given. Second, the peer-efficiency and cross-efficiency approach is itself contested; the literature has not settled on a single answer as to which secondary objective (benevolent or aggressive) is the "correct" viewpoint (Doyle and Green, 1994). Third, when the strategy parameter is calibrated to a past ranking, this calibration looks backwards; a parameter that worked well in the past may not reflect future evaluations with the same accuracy once conditions change. Fourth, the ranking can change near certain values of the strategy parameter; the parameter's exact value can be decisive for the order, particularly among closely matched alternatives.

The most common mistake is applying the same weight vector to both the benevolent and the aggressive table; these two tables must be computed separately, with different optimisation objectives.

A second mistake is setting the strategy parameter to a default of 0.5 (half benevolent, half aggressive) when no reliable past ranking exists; this is an arbitrary choice resting on no justification and defeats the method's promise of calibration. A third mistake is confusing the roles of rows and columns: rows represent the alternatives being evaluated, columns represent the peers doing the evaluating, and the final score is the row average. A fourth mistake is assuming this kernel will itself generate the benevolent/aggressive tables from raw production data or a fuzzy evaluation set; these tables must be prepared in advance. A fifth mistake is presenting a single definite ranking without reporting how fragile the ranking is near boundary values of the strategy parameter.

The governing principle is this:

An HFGPE result is a summary of how peers evaluate one another and of the chosen strategy parameter; if the parameter changes, the ranking can change too, particularly among closely matched alternatives.