Some clarifications (original article can be found here):

1. One of those "not-so-far-fetched assumptions" was that traders have fixed budgets that are stochastically independent of their beliefs. Manski never said that his assumptions aren't far-fetched; he wrote: "These assumptions may or may not be realistic, but they provide a simple baseline for efforts to study more complex situations". I just wanted to cut a long story short...

2. Manski writes that "the price of a contract reveals nothing about the dispersion of traders' beliefs and partially identifies the central tendency of beliefs." He then shows that the mean subjective belief of the traders lies in a symmetric interval around the contract price. He neither made a statement about the usefulness of the mean as a proxy for the likelihood that the underlying event occurs, nor did he say that the contract price is a upward or downward biased estimator for the mean belief of the traders.

Jonathan Falk writes:

<> while this paper proves that the IEM price is not necessarily the mean subjective belief, there is no particular reason we should care what the mean subjective belief is, since it doesn't translate into anything. For example, if there are 100 voters and 55 are determined to vote for Bush, then Bush's probability of winning is not 55 percent, but 100 percent. If there are ten people who know that there are 55 people solid Bush voters, then their subjective probabilities are 100 percent and they are right and the mean subjective probabilities of the uninformed don't matter.<>

Counterstrike (attempt...): But then we are dealing with a degenerate probability distribution with point mass at 1 for the underlying event. That way, the mean subjective belief is downward biased with probability one in any market. In other words: Comparing the mean subjective belief with a final outcome (instead of looking at the outcomes in parallel universes) doesn't make any sense and doesn't tell whether the contract price or the mean belief (if different) is on average a "better" (MSE?) predictor. But the last question could be answered empirically to some extent.

<>The market probability is not the mean subjective probability, it's the dollar weighted risk-neutral aggregation of traders' expectation of the outcome, not their expectation of the current subjective probability.

This is probably a better response. Thanks for your input!