No, it's likely the answer is not somewhere in between the two. The fact that people arguing different sides, if they're interested in convincing others, will moderate their opinion, and that they'll also have their opinion moderated by the prevailing opinions of society, isn't even the cause of this -- but it does make it worse.

Take, for example, estimates of a physical constant. Suppose two people independently estimate a constant. The probability that they'll miss on the same side of the true value is at least 0.5. If the probability of an arbitrary person underestimating the constant is x (and the probability of getting it correct is 0, since it's a real number and there is a continuum of choices), then the probability of both missing on the same side is x^2 + (1-x)^2, which is greater than or equal to 0.5.

Now take those two people and have them talk to one another. If one of them convinces the other their measurement method is more accurate, both will end up agreeing on the same estimate, and thus both will miss in the same direction. It's very unlikely that somebody will look at another person's estimates and reasons for them, and then decide to change their estimate away from that person's. So when they communicate, it's even more likely that the truth will not be in between their estimates. This effect is much worse with politics, where people tend to avoid conflict and everybody grows up in a similar culture.

There is a famous graph somewhere with monotonically increasing estimates of a physical constant over time. Imagine that here.

Now consider politics. Suppose you've got a bunch of people with different kinds of opinions. It might be the case that, over time, the objective truth (when there is one) influences their opinions. Does this increase the probability that the truth is in the middle? It might decrease the variance of their opinions -- with evidence about the truth, they'll end up believing something closer to it. For example, I'd say that evidence about the truth has caused people to have more accurate opinions about the effect of political parties claiming to be Marxist. However, they're still equally capable of overestimating or underestimating the truth.

What conditions might cause the truth to be likely to be in the middle? One would be where the truth is something people can get an approximate idea of, except that the variance in the people's circumstances will make them likely to miss in opposite directions. I suppose this is the kind of situation people often imagine. There's two assumptions here: that the influence of their circumstance outweighs the accuracy with which people generally could have estimated the truth, and that their circumstances would pull them away in opposite directions.

Right now you could compare big government conservatives versus big goverment liberals. Is the truth in the middle there? What about slave-owners versus abolitionists who wouldn't dream of letting their daughter marry a black man? Is the truth in the middle there? And people who think only male landowners should vote versus people who think all males should vote?

Given people's tendency to have opinions almost identical to their neighbors', it's likely the correct answer, for whatever answerable question is being asked, is far outside the contemporary political spectrum. Or are we the chosen generation, right about everything?