Fig. 5

The overgeneralization fallacy and category mistake of Grafen’s model. The figure shows the relation between the potential set of honest signalling equilibria maintained by condition-dependent trade-offs (blue set) vs. ‘costly signalling’ sensu economics (yellow set) vs ‘costly signalling’ sensu biology (orange set). (i) When additional postulates are included that unnecessarily constrain a model, a conclusion may be correct, not because of the model, but because of the additional assumptions. When one nevertheless claims that the conclusion is generally true regardless of postulated assumptions, then this is an overgeneralization fallacy. (ii) If removing the constraints switches the conclusion (strongly depending thus on the assumptions), one has also committed a category mistake, incorrectly attributing properties to the model and missing its true nature. (iii) Standard costly signalling assumptions (SCSA = A₁ and A₂, orange set) unnecessarily constrain the model of honest signalling (yellow set), because they exclude a potentially important class of trade-off functions. Nevertheless Grafen overgeneralized the conclusion of his model to all signals of quality (red arrow to blue set; see overgeneralization fallacy, point (i)). (iv) Moreover, biologically relevant assumptions may not be constrained to SCSA , contrary to what Grafen suggested [1] (see the ‘Discussion’ section). Removing SCSA switches the conclusion C of the model to !C: honest signals need not be costly, as we have proved in this paper. That is, the conclusion of Grafen’s model (C= honest signals are costly), stems from its specific assumptions and not from more general properties, leading to tautology and a category mistake (see point (ii)) when Grafen identified his model with the Handicap Principle (red arrow to HP). That is, Grafen’s model is not a model of HP as the HP conclusions do not follow from the general properties of the model (it is a model of condition-dependent signals). Thus, even if honest signals turn out to be costly, the Handicap Principle cannot account for them