ROTHSCHILD: DEFINITION OF FISHING EFFORT 



EXPECTED CATCH 



Figure 3. — The distribution of catch at two locations 

 showing the average catch and the loss region. 



erman samples the distribution dealt by nature 

 and his sample can be biased and vary in preci- 

 sion. His perception of the correct action de- 

 pends upon his view of how many times he can 

 sample these distributions. This is clear because 

 if the fisherman has only one chance to go fishing, 

 he should choose B to minimize his risk, but if he 

 has many chances to go fishing, he should choose 

 A to maximize his gain since the sampling risk 

 will be decreasing inversely proportional to the 

 square root of the number of chances that the 

 fisherman has. 



A reasonable criterion for choosing a fishing 

 location might be the expected gain less the ex- 

 pected loss; e.g., 



a a 



where f{x) is the distribution function of the 

 fisheries earnings, a is the minimum value of 

 this function, b is the maximum value, and B is 

 the break-even point. Note that this general 

 form can be written in several alternative ways. 

 But even the establishment of such a criterion 

 is not sufficient to measure the skipper's behav- 



ior. We need to know the utility that the skip- 

 per places in any value of the criterion. 



ACKNOWLEDGMENTS 



It is a pleasure to contribute this paper in 

 honor of Dr. 0. Elton Sette who has done so 

 much pioneering work in fishery biology and has 

 provided me with many stimulating discussions 

 during the last several years. 



I would like to thank James Joseph of the In- 

 ter-American Tropical Tuna Commission and 

 Paul Adam of the Organization for Economic 

 Cooperation and Development who encouraged 

 me to write this paper. James W. Balsiger 

 kindly read the manuscript. Much of this paper 

 was written under the Sea Grant, Norfish pro- 

 gram, while I was with the Center for Quantita- 

 tive Science in Forestry, Fisheries and Wildlife 

 at the University of Washington. 



ADDENDUM 



The reader interested in applications of de- 

 cision theory should examine "Marine decisions 

 under uncertainty," by John W. Devanney III, 

 Cornell Maritime Press, 1971, which was dis- 

 covered while the present paper was in proof. 



LITERATURE CITED 



DoRFMAN, R., P. A. Samuelson, and R. M. Solow. 

 1958. Linear programming and economic analysis. 

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 Green, R. E., and G. C. Broadhead. 



1965. Costs and earnings of tropical tuna vessels 

 based in California. U.S. Fish Wildl. Serv., Fish. 

 Ind. Res. 3(l):29-45. 

 Raiffa, H. 



1968. Decision analysis; introductory lectures on 

 choices under uncertainty. Addison- Wesley, Read- 

 ing, Mass., 309 p. 

 Rothschild, B. J. 



1971. A systems view of fishery management with 

 some notes on the tuna fisheries. FAO Fish. Tech. 

 Pap. 106, 33 p. 

 Rothschild, B. J., and J. W. Balsiger. 



1971. A linear-programming solution to salmon 

 management. Fish. Bull., U.S. 69:117-140. 



679 



