At Protagoras 356a8–c1 Socrates uses the metaphor of weighing to describe how we make choices between different possible courses of action on the basis of the pleasure or pain involved in each. He mentions three tests and gives a recommendation for each based on the outcome. We imagine a pair of scales that registers only which pan contains the heavier material: this is the pan that drops. It does not give a calibrating value to the weight in each pan.
1. Weigh pleasures against pleasures (b3).
Here, choose the option with the most pleasures. (Of two options pick the one that is the heavier; of more than two options pick the one that is heavier than every other option.)
2. Weigh pains against pains (b4).
Here, choose the option with the least pains.
The third, however, seems rather different:
3. Weigh pleasures against pains (b5).
Here, if pleasures outweigh pains then do this praxis. If pains outweigh pleasures then do not do this praxis. (Let's leave aside for now whether this is a recommendation or a description of what people generally do anyway.)
It seems to me that the question settled by 3 is different from the questions addressed in 1 and 2. They are concerned with ranking options, all of which are apparently being considered as possible courses of action. In 3, however, it is being decided whether a course of action should be done or not taking into account that an action will likely involve both pleasures and pains.
Also, the combination of the three will not immediately generate the clear guidance that Socrates seems to want.
We can imagine the procedure as follows. A good maximiser first gathers up the pleasures and pains for a particular action and weighs the pleasures against the pains. Let us imagine the pleasures win out. That course of action is therefore given a recommendation. He will perhaps also consider other courses of action and retain all those for which their respective pleasures outweigh their pains. But now what does he do? He needs to rank the options in order to choose the one in which there is the greatest preponderance of pleasure over pain since he is a maximiser. But the procedures in 1 and 2 will not allow him to settle this question. Imagine two courses of action that are being considered: A and B. Both A and B have both pleasures and pains associated with them. For both A and B, moreover, it is the case that the pleasures outweigh the pains (so both pass the test in 3). But how will the good maximiser then choose between A and B? For example, course of action A may have more pleasure associated with it than course of actions B (A will beat B in test 1) but course of action A may also have more pains associated with it than course of action B (A will lose to B in test 2). The procedure as elaborated here will be unable to adjudicate between such cases since 1 and 2 only register the fact of one set of pleasures being greater than another or one set of pains being greater than another. They are unable to adjudicate between different degrees to which the pleasures of a given option outweigh its pains or, for that matter between different degrees to which the pains of a given option outweigh its pleasures. This is because both pleasures and pains are being considered to have positive mass, as it were. This is helpful because it allows the procedure in 3: pleasures can be weighed against pains. But it prevents us from considering the ‘net’ weight of a given course of action as being the combination of the positive value of pleasures and the negative value of pains.
For example, imagine that course A will produce 8 units of pleasure while course B will produce 6. (So A beats B in test 1.) But course A will produce 6 units of pain while B will produce 5. (So A loses to B in text 2.) Both course A and course B will pass test 3 since in both there is more pleasure than pain produced.
What is needed is a new procedure: a fourth test in which the pleasures of course A are combined with the pains of course B and weighed against the pleasures of course B combined with the pains of course A. The winning course of action is the one whose pleasures are in the heavier pan. (If PleasureA + PainB is greater than PleasureB + PainA, then PleasureA + PainB - PainA is greater than PleasureB, and PleasureA - PainA is greater than PleasureB – PainB.) (Denyer notes the need for such a procedure in his commentary ad 356b1 but I don’t think Socrates makes any explicit reference to it in the description here.)