I have to agree with the deciding in favor of Protagoras. Plato’s ideas make sense if you are in an authoritarian society that wants to curb general knowledge and keep the people stupid and happy. In the case of Athens, it is an emerging society that is experimenting with democracy. For democracy to work, even in the early Athenian form, people have to be educated and be able to voice their opinions.
Plato’s idea of “there is a wrong and right answer for everything” and only the smartest and most capable people should be able to decide what is right and therefore what is wrong is elitist and harmful to a society. The example of the two story house is probably the simplest way to explain why. Plato argued that if everyone can voice their opinions in this matter then eventually they will try to build a house of eggshells. This is ridiculous, but if someone wanted to try that, why not let them. His main point on the matter was that once you find a perfect way you should only repeat it. No more variations, just repeat what works and therefore society will function. Using Protagoras ideas in this situation might cause initial failure and waste of resources, but eventually something much better might come from it. Not only could experimenting with different people’s ideas work, it could be better and lead the way to three story houses or even taller ones.
Plato’s fears of the public are an elitist view that is directly contradictory towards the role of a functioning democracy. It might be easier to only let a few of the philosopher-kings make decisions, but it will harm the specialization of the people. If only one person, or even a handful of people are left to make the decisions than there will be no expertise involved. They might be well rounded thinkers, but by opening the floor to everyone’s opinion you may get really dumb ideas, but you will also let the experts speak as well. The trick to making this system work is by being able to tell what the dumb ideas are and what the smart ones are. This is another whole issue that requires people like Protagoras to teach the public. To make them capable of rational decision making in order for the best ideas to not only be heard, but to be understood and clarified as the best decisions by the general majority.
I rule in favor of Protagoras because it is in the best interest of the democracy and the society.