Consider a set of politicized disciplines, S1, S2, .. Sn (e.g. climate science, GM foods research). Let P1, P2.. Pn be proponents of prevailing theory in respective discipline, and D1, D2, ...Dn be their detractors.

Define coherence K as cardinality of (P1 & P2 &... &Pn) | (D1 & D2 &...&Dn).

Varjag's conjecture: as n approaches infinity, K asymptotically approaches zero. Therefore if true, the argument from authority is rendered relevant.

(the proof is left as an exercise to a reader)

I'm not sure I follow you.

P_i and D_i are sets of proponenents/detractors for discipline S_i, right?

I so, I assume that the & and | boolean operators you use are substitutes for set union and intersection, respectively.

Assuming that the opinions on the various topics are independent, I would rather see K tend to

    \sum |P_i| == \sum |D_i|

What am I missing?

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Also, for my previous post:

    s/(appeal to authority)/(appeal to potentially corrupt authority)/

The point was: people are incoherent in their dismissal of argument from authority. E.g. many (most?) in anti-GM movement also acknowledge anthropogenic global warming as true, obviously having no issue with IPCC authority on it.

Given enough controversial subjects people care for, no one is going to be knowledgeable in all of them. But people invoke "arguing from authority is a fallacy" only when they are not sided with the said authority.

>The point was: people are incoherent in their dismissal of argument from authority. E.g. many (most?) in anti-GM movement also acknowledge anthropogenic global warming as true, obviously having no issue with IPCC authority on it.

This is just using an ad hominem to attack people who cite the argument from authority fallacy. Science is also based on careful examination of empirical evidence, not unsubstantiated pronouncements by authority figures.

Oh, if only it was that easy!

Consider how long it took to get rid of phlogiston theory in physics, even when falsified by experiments. The physicists of the day were careful and rigorous, honest scientists, and their opponents did not have (initially) any alternative theory to replace it with.

And perhaps we are giving too much credit to most people involved in public debates for examination of empirical evidence. I can say honestly that I tried to read the whole IPCC report, but got barely 1/4th in (it is incredibly thick and dense with facts). Very few of my peers though even glanced as the cover, yet their opinions on it are not any less strong.

In fact, you are correct; argument from authority is not a fallacy. Those who think it is do not understand argument from authority. When the authority is relevant to the subject at hand the argument is relevant. It is appeal to misleading authority which is a fallacy (http://www.fallacyfiles.org/authorit.html).

I wouldn't say I'm particularly convinced of the evils of GM food. I think it's generally harmless, at least from what I've seen.

Still, I would not put as much trust in a study/debunking coming directly from Monsato than I would a study coming from other sources.