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Because  makes no use of genetic operators it is a plan for adjusting weights independently. Specifically, under this procedure, the probability of occurrence of A = a1a2 . . . al at time t + 1 is just  , where P(ar, t) is the proportion of  in Wr(t). It follows at once that an arbitrary schema x occurs with probability l(x) = IIjP(jx), as would be the case under the equilibrium discussed in section 6.2. Moreover, |
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under the plan . Clearly the weights at distinct positions are chosen independently of each other. Hence if a pair of weights contributes to a better performance than could be expected from the presence of either of the two weights separately, there will be no way to preserve that observation. This can lead to quite maladaptive behavior wherein the plan ranks mediocre schemata highly and fails to exploit useful schemata. For example, consider the set of schemata defined on positions 1 and 2 when W = {w1, w2, w3}. Assume that all weights are equally likely at each position (so that an instance of schema  , say, occurs with probability 1/9), and let the expected payoff of each schema be given by the following table: |
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Table 3: A Nonlinear µx on Two Positions |
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Since all instances are equally likely we can calculate from this table the following expectations for single weights: |
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