Relevance and rationality by NICHOLAS ALLOTT

5.2 Optimization under constraints
We have established that no realistic model of reasoning, including therefore the
relevance theoretic comprehension procedure, can be an example of unbounded
rationality. Next I will consider optimization under constraints. This vision of
rationality ‘holds that the mind should calculate the benefits and costs of searching
for each further piece of information and stop search as soon as the costs outweigh
the benefits.’ (Gigerenzer and Todd, 1999, section 2.2)
Therefore a solution is reached without consulting all of the evidence, in contrast
to the way models of unbounded rationality work, using all possible information.
However the requirement that at each stage the costs and benefits of containing the
search be calculated leads to a computational explosion: ‘the paradoxical approach
is to model “limited” search by assuming that the mind has essentially unlimited
time and knowledge with which to evaluate the costs and benefits of future
information search.’ (Gigerenzer and Todd, 1999, section 2.2) This means that
‘optimization under constraints can require even more knowledge and computation
than unbounded rationality.’ (op cit, section 2.2, referring to work by Vriend,
1996; Winter 1975)
As a realistic model of cognition, then, relevance theory cannot rely on
optimization under constraints; indeed it does not, but there are two reasons why
someone might suppose that it does. First, according to the communicative
principle of relevance, ‘Every ostensive stimulus conveys a presumption of its own
optimal relevance’ (Sperber and Wilson 1986/95, p 158). This means that the
hearer is licensed to search for an optimally relevant interpretation: ‘An ostensive
stimulus is optimally relevant to an audience [if] it is the most relevant one
compatible with the communicator’s abilities and preference.’ (Wilson and
Sperber, 2002, section 3) So the relevance theoretic comprehension procedure
looks for the optimal solution, given a particular stimulus in a particular context.
Thus it appears to be an optimizing procedure, but as I shall argue, it is not a kind
of optimization under constraints.
Secondly, as previously noted, relevance is a matter of effort and effects, so the
generalization ‘stop when your expectations of [optimal] relevance are satisfied’
(Wilson and Sperber, 2002, section 3) may seem to be an injunction to calculate at
each stage the costs and benefits of continuing with the search and to stop when
the projected costs in effort outweigh the prospective benefits in cognitive effects.
This is a misinterpretation, however, for two reasons. First, the hearer is licensed
to ‘stop at the first interpretation that satisfies his expectations of relevance,
because there should never be more then one.’ (Wilson and Sperber, 2002, section
3) This follows from the special nature of ostensive-inferential communication: the
speaker ‘wants her utterance to be as easy as possible to understand so that the first
interpretation to satisfy the hearer’s expectations of relevance is the one she
intended to convey.’ (op cit. , section 3) This means that there is no need to
calculate the costs and benefits of continuing the search: what is at issue is rather
whether the cognitive effects are (more than) enough at some time, t, to justify the
processing effort incurred from the beginning of the search to that time.
The second reason why the relevance theoretic comprehension procedure could
not be a species of optimization under constraints is that from the beginning
Sperber and Wilson have been clear that ‘contextual effects and processing effort
are non-representational dimensions of mental processes’ (1986/95, pp 131). We
may sometimes have intuitions about degrees of effort and effect but efforts and
effects – and therefore relevance – are not generally mentally represented and
therefore cannot be used in computations. Thus there is no possibility that future
effort and effects could in general be summed and weighed up against each other
as optimization under constraints requires. p. 77-78

The argument that the relevance theoretic comprehension procedure is a type of
satisficing procedure comes from comparing Gigerenzer’s definition, ‘satisficing
(sets) an aspiration level and ends the search for alternatives as soon as one is
found that exceeds the aspiration level’ (Gigerenzer and Todd, 1999, section 2.3,
referring to work by Simon, 1956, 1990) with the specification of the relevance
theory comprehension procedure:
(a) Follow a path of least effort…(and)
(b) Stop when your expectations of relevance are satisfied. (Wilson and
Sperber, 2002 section 3)

In the case of ostensive-inferential communication,
‘relevance theory claims that use of an ostensive stimulus may create precise and
predictable expectations of relevance not raised by other stimuli.’ (Wilson and
Sperber, 2002, section 3) This is because ‘an ostensive stimulus is designed to
attract the audience’s attention. Given the universal tendency to maximise
relevance an audience will only pay attention to a stimulus that seems relevant
enough.p. 78-79

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