The translation I am looking at is in Julia Annas, ed., Voices of Ancient Philosophy (Oxford University Press, 2001), pp. 373-75; reprint from the OUP translation of the Protagoras by C. C. W. Taylor (1996)

The speech Plato puts into the mouth of Protagoras in his dialogue Protagoras is one of the earliest philosophical defenses of democratic institutions, such as allowing the vast majority of adults to vote when key decisions must be made and leaders selected as well as allowing ordinary people to serve on juries.

It is probable that the speech reflects ideas in circulation in Athens in the fifth and early fourth centuries B.C., perhaps ideas of Protagoras himself. Unfortunately, we don't have anything this substantial more directly from Protagoras himself. In what follows, all references to "Protagoras" will refer to Plato's character of this name, in this particular passage.

Most of Protagoras' "great speech" consists of a carefully constructed myth involving the creation of human beings and human cities. On the face of it, the myth, like many myths, serves an explanatory function: "So that is why . . . " (Protagoras 322d)

In an explanation, what follows a phrase like this is a statement of what is to be explained (the explanandum). Typically, the reasoning in an explanation starts from what is to be explained, which is an indisputable fact, and reasons toward the causes of that fact (the explanans, i.e., that which does the explaining). Thus, in the famous speech of Glaucon near the beginning of the second book of Plato's Republic, Glaucon starts from a description of justice (widely accepted), according to which justice is an agreement neither to injure nor be injured, and reasons to its "origins," the alleged (probable) causes of this agreement. In this explanation, the reasoning is from supposed effect to cause.

But overt mythical explanations can also conceal a reasoning process in which what is to be explained, the supposed effect, is justified by the reasoning of a god. This is especially the case when the god is assumed to be benevolent and wise, as Zeus is in Protagoras' myth. Therefore, to a great extent, the reasoning of Zeus in this myth is precisely the reasoning that this Protagoras would give if he were not speaking mythically. In this case, the reasoning is from cause to effect. (We shall see later that Zeus' reasoning encapsulates the pragmatic reasoning of unnamed lawgivers and countless generations of civic leaders.)

In the reconstruction that follows, "P" stands for premise, usually one that is stated more or less explicitly in the text, "IC" stands for intermediate conclusion, "A" for assumption or assumed premise, "FC" for final conclusion.

From the myth itself we can find the following premises:

(1,P) The physical equipment that humans possess is insufficient to assure human survival. (321c)

(2,P) Technical gifts help but do not suffice when humans lack the capacity to cooperate. (321e-322b)

(3,P) Real cooperation among humans requires living together in a city.            (322b5-6)

(4,P) Real cooperation in a city requires conscience and justice among (nearly) all (adult) citizens of the city.            (322c, 322d)

From (1)-(4) the conclusion seems to follow:

(5, IC) survival requires conscience and justice among (nearly) all (adult) citizens of the city.

Zeus' reasoning proceeds in purely mythical fashion thus:

(6,P) I wish human survival.            (assumed throughout the section involving Zeus)

(7,IC) I must send conscience and justice to (nearly) all (adult) human beings. (322d)

Now, return to the third-person perspective of the story:

(8,A) Zeus has overwhelming power.

(9,IC) Justice and conscience must have been sent by Zeus to (nearly) all (adult) human beings. (322c)

Protagoras' probable understanding of this is:

(10, A) Cities have learned how to survive.            (Observed fact)

(11,IC) Most (adult) citizens of cities have conscience and justice, at least to some extent. (from 5 and 10)

(11) is reinforced by a second, entirely nonmythical argument. See "here's an extra bit of evidence" (at 323a).

(12,P) everyone thinks that anyone who does not pretend to be just is insane.            (323b)

(This is in contrast to the situation in the specific professions, e.g., carpentry and medicine, in which the person who falsely pretends to expertise is regarded as insane.)

How 12 supports 11 is not as clear as one might like. Probably "Protagoras" is reasoning somewhat as follows:

(13, IC) Everyone who is tolerated in a city must at least act as if he is just.            (based on 12)

(14, P) Such external justice is itself a minimum form of justice. (He appears to assume this.)

These two steps confirm a view already reached:

(15, IC) Same as 11            (based on 13 and 14)

(16, FC) Democratic institutions can work.             (unstated, based on 9 and 11 (=15) )