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Constraint (1) in the game formulation considers the p, as being resource proportions whose sum equals unity. Two simple modifications here will result in greater simplicity and realism in the full model. Firstly, if one defines the activities (farmer alternatives) in terms of acreage units, constraint (1) ensures that the levels of these activities, obtained by solution of the p„ measure the proportion of total acreage to be allocated to each activity. * Secondly, since in farm planning one rarely insists that all available acreage is necessarily utilised, one can further modify constraint (la) to read (lb) E P .

From our four original assumptions concerning preferences held prior + to learning that F has occurred and our fifth assumption relating prior to posterior preferences, it can be proved as a theorem that the decision maker's posterior behavior "should" be governed by the four original The Foundations of Decision Under Uncertainty 25 assumptions reworded to deal with posterior rather than prior preferences; and it can also be proved that the scaled judgment that the decision maker forms concerning any event E0 posterior to learning that E* has + occurred "should" agree with the usual definition of Ρ ( Ε 0 | £ ) · From these results it then follows, by exactly the same reasoning that led to our + original theorem on comparison of acts, that after learning that E has occurred the decision maker "should" choose the act which maximizes the index Π \ Or in other words: even though the decision maker is free to deviate from the act called for by the decision rule which was optimal + when chosen before it was known whether or not E would occur, our fifth basic assumption implies that he should not do so.

47 Maximin Programming that, regardless of which state of Nature holds in practice, the resulting total gross margin will never be less than some minimum value V. Our aim is to determine the values of the p, which maximise V, the maximin return. P. problem; it lacks only a single explicit objective function (V) to be maximised. * For each of the η relationships in system I, introduce a non-negative "dummy" variable, pm + h so as to transform each inequation into an equation. The system then becomes: If Si prevails: c np i +c 2 i p 2+ ··-+c m =V ipm -Pm+i If Sj prevails: dipi + c 2]p 2 + · · · + c m- p m If S n prevails: ^ήρι + ^ „ ρ 2 + · · - + c m np m - p m +J - p m+ n =V (System II) =V and, as before: Pm = l p, ^ 0 (for all i = 1 , .