> how closely the estimated distribution matched the real answers
> A similar analysis applies to answering the second question (the estimates) truthfully.
How does this avoid (or compensate for) downweighting the preferences of people who are legitimately ignorant about what everyone else thinks (and consequently give estimated distributions that hardly match the real answers at all)?
The weights can incorporate a factor (0 < α ≤ 1 in that link) which adjusts the contribution of the prediction's accuracy. When α = 1, we get the zero-sum, purely competitive situation; we can make accurate prediction less important by choosing α < 1.
Although truth-telling is a Nash equilibrium of this setup, it's not the only one. However, as α → 0 the truth-telling equilibrium becomes dominant (i.e. achieves a higher expected payoff).
> A similar analysis applies to answering the second question (the estimates) truthfully.
How does this avoid (or compensate for) downweighting the preferences of people who are legitimately ignorant about what everyone else thinks (and consequently give estimated distributions that hardly match the real answers at all)?