Comments on: Majority Rule in Social Networks

By: Jeff

Jeff — Sat, 04 Sep 2010 16:55:11 +0000

Hi, Pete
I confess to accepting your logic as correct without close examination because I want to mess with assumptions a bit, specifically that “voter equality” in these circumstances may be assumed socially optimal. You may have followed Errol Morris’s recent series of thought-provoking articles in the New York Times in which, among other things, he considers the “Dunning-Kruger” effect. Loosely put, D-K assert that empirical evidence shows that those who know less about a particular topic more greatly over-estimate what they know than those who know more (who over-estimate, too, just less). It seems to me that many large-scale internet-based voting systems are ripe for the kinds of problems caused by thought- and effort-free consideration by legions of those who know less. (If D-K effects are strong, this is a big problem for democracy based on first-past-the-post voting.)
So, what might we do instead? Leaving aside democracy, can we find ways to sieve for more knowledgeable opinion about trivia in large data sets without a priori insight into what constitutes knowledge? Perhaps surprisingly, the answer is yes – for certain kinds of data collected in certain ways – through use of cultural consensus analysis. CCA doesn’t work all that well for questions of personal preference but it’s Aces for characterizing shared perceptions of a thought world.
CCA is a relatively recent addition to cognitive anthropology, initially worked out to help put ethnographic field research on a more Western scientific basis. Notionally, CCA allows a researcher to tap information in patterns of response across respondents. In addition to culturally correct answers to each question (a cultural answer key), CCA provides a scalar estimate of each respondent’s cultural expertise.

By: Pete Abilla

Pete Abilla — Thu, 26 Aug 2010 15:53:05 +0000

@Greg – I think you’ve found the Wittgenstein-ian (P and ~P) in my argument. Thanks for the feedback. How would you make my argument more cogent?

By: Greg

Greg — Thu, 12 Aug 2010 17:28:33 +0000

Hey Pete, I enjoyed your abstraction of the notions of equity and sensitivity, and their logical equivalence with a majority rule social choice function. Just wondering if this couldn't be proved slightly more easily with some different notation. I'm thinking the following: C is a function that returns the max of |A| and |B|. This set function which is essentially just maximum then obviously ;) respects switching the names of A and B, gives each voter 1 vote, and breaks ties according to a single vote. Conversely any set function which respects switches of names, gives each voter 1 vote, and breaks ties by a single vote is a maximum checker. To prove the claim in that sentence suppose it did something besides return the max of |A|and |B|, in which case it returned the min. Then in the event of a tie, you'd add one vote to, say A, declare it the winner, and then max would win, a contradiction. Am I missing something? In any case, great post. Love to see this type of high quality blogging on the 'net. Regards. GP

By: Julien Couvreur

Julien Couvreur — Thu, 12 Aug 2010 13:10:25 +0000

Since you’re on this topic, you would probably be interested in Arrow’s impossibility theorem: http://en.wikipedia.org/wiki/Arrow's_impossibility_theorem