FISHERY BULLETIN: VOL. 70. NO. 3 



is $7.36 with a measure of entropy of 130 cent- 

 ibits. (Entropy is defined in the usual way, 

 but measured in centibits rather than in bits 

 owing to the relatively low degree of "random- 

 ness" in these hypothetical examples.) 



Condition II 



The skipper is quite skilled and thus P(Oi 

 = 0.9, P(e2|ei) = 0.1,P(gJ Go) =0.9,P(Gi 



ei) 

 02) 



O.l (say) . The expected value of the branch 

 under this condition is $6.71, and a measure of 

 its entropy is 172 centibits. 



Condition III 



The skipper is unskilled and thus P(6, Gj) = 



0.5 for i = 1,2 and ; = 1,2. The expected value 

 of the branch under this condition is $4.10, and 

 a measure of its entropy is 209 centibits. 



It is important to observe, in respect to the 

 first example, that if nature dealt the G/s with 

 probability of 1 or then entropy would be 0. 

 Nature has not, in our example, chosen to deal 

 the g's deterministically and, therefore, 130 cent- 

 ibits is the lower threshold of entropy, given 

 that probabilistic behavior of nature remains 

 the same. 



Now, we note several interesting features of 

 this analysis which are capable of many simple 

 extensions. First, we have distinguished be- 

 tween the contribution to entropy made by the 

 behavior of nature and the behavior of the fish- 

 ermen. Second, we have quantified the random- 

 ness in the decision problem by measuring the 

 randomness in bits and thus have the opportunity 

 to quantify the required skill of the skipper; be- 

 cause when nature deals a low-entropy proba- 

 bility structure, relatively less skill is required 

 to achieve equivalent results. Third, we can 

 valuate the skipper's decision process as an input 

 to the production function. For example, under 

 Condition III an unskilled skipper can produce, 

 on the average, $4.10 worth of fish in a 209- 

 centibit environment, but a quite skilled skipper 



[skill being measured by P(Gi Igj)] can by his 



skill reduce the entropy 37 centibits. The 37 

 centibits being a difference between entropies 

 is thus a measure of information, and in this 

 example 37 centibits of information are worth 

 $2.61 or roughly 7 cents per centibit. A per- 

 fectly skilled skipper reduces entropy an addi- 

 tional 42 centibits, the additional information 

 yielding 65 additional cents, or about 1.5 cents 

 per centibit. In other words, in this example, 

 the information accrued in moving from un- 

 skilled to quite skilled is about the same as that 

 accrued in moving from quite skilled to perfectly 

 skilled, but the value of a unit of information is 

 4 times greater in moving from unskilled to quite 

 skilled than a unit of information acquired when 

 moving from quite skilled to perfectly skilled. 



DECISION CRITERIA 



Thus, we have considered a model of the way 

 in which the skipper "processes" signals from the 

 fishing environment where the quality of his pro- 

 cessing ability is measured relative to nature- 

 generated entropy in the decision environment. 

 We must now consider how the skipper valuates 

 the signal and the criteria that he places upon 

 these signals. First, consider what might be a 

 traditional approach of where to fish. In this 

 approach we have a field of expected catches and 

 upon examining this field we advise the skipper 

 to fish at the location where the expected catch 

 is highest. A second approach is to examine the 

 field of space-time points and consider the distri- 

 bution of catches at each space-time point. Let us 

 consider a simple aspect of this problem; two 

 space-time points A and B, at which the fisher- 

 man's percei)tion of the catch is that it has an ap- 

 proximately normal distribution. Figure 3 shows 

 these two distributions. The figure also indicates 

 the point on each distribution below which the 

 fishing operation will lose money. If we look at 

 only the expected catch, we would advise fish- 

 ing at A. But if we examine the risk (that is, 



/ 



xf{x)dx, evaluated from — 00 to the break- 



even point) we note that fishing at B will mini- 

 mize risk, and if this were our criterion we would 

 fish at B. We should note further that the fish- 



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