Scott Aaronson getting Aumann agreement wrong

Scott Aaronson writes-

According to my complexity-theoretic refinement of Aumann’s agreement theorem, which I later published in STOC’2005, two Bayesian agents with a common prior can ensure that they agree to within ±ε about the value of a [0,1]-valued random variable, with probability at least 1-δ over their shared prior, by exchanging only O(1/(δε2)) bits of information—completely independent of how much knowledge the agents have. My conclusion was that, if Aumann’s Nobel-prizewinning theorem fails to demonstrate the irrationality of real-life disagreements, then it’s not for reasons of computational or communication efficiency; it has to be for other reasons instead. (See also my talk on this at the SPARC summer camp.)

This seems reasonable. If 2 people want to ensure they agree surely they can do so in some parsimonious fashion. 

American diplomats used to say about their Indian counterparts- 'they will quickly agree to a sensible proposal but then refuse to agree as to what they have agreed to'. Obviously, this was because the Indians had multiple constituencies to satisfy. However, even in a two person world, an agreement in one context does not necessarily means an agreement to agree as to what the original agreement actually meant in another context. Under Uncertainty, Aumann agreement is always incomplete.

More generally, an Aumann agreement is no agreement at all in the eyes of the Law which will impute 'a common intention' and impose a constructive contract or Trust to prevent unjust enrichment.

In Social Choice, or Public Reason, if there are more than 2 people in the World, and Muth Rationality obtains, an Aumann agreement would be estopped by a prior Aumann Agreement or Social Contract with the force of Law. Why? The answer is that differences in depth of knowledge are not independent of the possibility of Aumann Agreement.  This can easily arise if a certain piece of Knowledge is costly to acquire for at least one party. But, if this is the case, then 'Common Knowledge' can't obtain with respect to any and every bilateral agreement considered as possibly giving rise to unanimity. Why? Because Common Knowledge would become impredicative and contain its own Dictatorial Social Choice Rule. It would cash out as merely a biological tropism or social shibboleth.

 The risk arises that a person with superior Knowledge about something gets everybody to agree to it, thus making it less likely for him to discover he was wrong. This may be catastrophic for him personally in some manner he can't currently foresee.  It is something he may regret. Since we live in a world of radical Uncertainty, if Muth Rationality obtains,  in a three or more agent economy, such agreements would either be substantively meaningless or illegal. Indeed, this is a feature of the law. 

Aumann agreement fails in the real world because Knowledge is costly. Common Knowledge prohibitively so. Bayesian theory has limited purchase because Uncertainty prevails.

 Moreover, there is a regret minimizing reason why we might want to divide up even a small, wholly conventional, corpus of purely conventional knowledge and distribute it across mutually sceptical, protocol bound, epistemic systems which serve as a check upon each other. 

Still, surely, there are good causes where we might speak of bilateral 'Aumann agreements' as seeding some desirable social change?

Consider rape/sexual harassment. That's definitely something we all agree about.

But does this mean we should also agree with Scott's 'Zeroeth Commandment'? Let us see-

Before going any further in this post, let me now say that any male who wants to call himself my ideological ally ought to agree to the following statement.
I hold the bodily autonomy of women—the principle that women are freely-willed agents rather than the chattel they were treated as for too much of human history; that they, not their fathers or husbands or anyone else, are the sole rulers of their bodies; and that they must never under any circumstances be touched without their consent—to be my Zeroth Commandment, the foundation-stone of my moral worldview, the starting point of every action I take and every thought I think. This principle of female bodily autonomy, for me, deserves to be chiseled onto tablets of sapphire, placed in a golden ark adorned with winged cherubim sitting atop a pedestal inside the Holy of Holies in a temple on Mount Moriah.

Scott either has, or will have, post rem, at least one wannabe ideological ally or he has and will have none. In the former case, ought such an ally to have Aumann agreement re. this Zeroeth commandment?

No. Women have never been chattel at any time in human history. Cattle have. Women haven't. Why? They simply are not inferior in any way to men. Some silly writers pretended otherwise and some worthless sociopaths did from time to time get away with treating some women in particular places and particular times in such a manner. But, the same thing happened to some men. But this was not true of all, or most, Humans at any historical epoch.

Scott is saying his ideological ally ought to agree to a stupid lie of his. This ally should not try to reason with Scott and get him to express himself in less hysterical and stupid terms. Scott is describing, not an ally, but a slave or a sycophant. He is the last person one would want on one's team. Sooner or later he's bound to fuck up by demanding everybody agree to some stupid lie he thinks he must write down and post up as a Commandment because otherwise people might think he's a rapist or summat.