Is this simply the observation that optimizing for 2 variables simultaneously will produce smaller gains than on just 1? 'Credit or influence - choose 1'.
A simple math model of conformity suggests that non-conformists have more influence over a social consensus, unless they are directly down-weighted enough due to their non-conformity. Non-extremist non-conformists have the most influence. https://www.overcomingbias.com/2018/11/non-conformist-influence.html …
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I don't model the possibility to not get credit, so this can't be considered a model of the choice between credit and something else.
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But you still have 2 variables.
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Each person chooses one real parameter x_i. They trade off moving x_i toward their personal ideal point a_i, or toward a group mean m. More conformist people put more weight on moving toward m.
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Yes. Which is 2 variables. The personal point, and the group point.
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Yes this is a model where each agent trades off two things they want against each other. But this model much lot more than merely that agents in such situations tend to choose intermediate outcomes.
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Is it: If you are a non-conformist, then you will probably have more influence? or If you have more influence, then you are probably a non-conformist?
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In my model, it is the former.
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That is the more interesting claim. I'll go ahead and read your post now :D
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Yeah. Interesting argument. If influence is a matter of moving the consensus, then non-conformists have more influence. Though, in a democracy, people might be more likely to grant positions of influence to conformists.
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More likely is giving influence to moderates. In which case it is non-extremist non-conformists who have the most influence.
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I'll have to chew on this some. I'm trying to reconcile this with the contrast principle in social identity theory, and also the modeling of alternative voting systems in this fun piece:https://ncase.me/ballot/
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As a trained mathematician it is intriguing to see some applications of these silly symbols messily piled together. Without knowing anything about your equilibrium and without any descriptions from you this piece of blog means nothing to me so do the conclusions.
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You would have to read the blog post. It uses very standard game theory math.
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To do this kind of math meaningfully, you have to converge the cumulative, normalized weights down to a stationary distribution. I don't understand the second equation, but all seems wrong. You could certainly prove something like this but would need do so with statistical tests.
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I don't know what you are talking about, and I have doubts whether you do. This is a very standard sort Nash equilibrium game theory model.
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Equilibria doesn't prove anything meaningful in this case since it's not a one-dimensional problem. This is opinion dynamics. To prove, you need to come up with a statistical simulation and factor in (many) other variables. Real "consensus" is a stationary distribution.
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Isn't that exactly
@nntaleb point about intolerant minorities? -
Did he give a math model?
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Not in this source https://medium.com/incerto/the-most-intolerant-wins-the-dictatorship-of-the-small-minority-3f1f83ce4e15 … However, I wouldn't be surprised if he did elsewhere
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There are also a ton of examples of this kind of phenomena happening among various swarming models. I can't even begin to list them all. Taleb's talk of those with preferences map to the 'informed/uninformed' fish talked about here: https://www.chronicle.com/blogs/percolator/study-of-fish-suggests-the-value-of-uninformed-voters/28031 …
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Framing consensus / conformity as a swarm foraging behavior + game theory is how I discovered the work from
@icouzin's lab and the people at max plank doing studies on the way information is spread thru swarms. Like this study from 2009 https://www.princeton.edu/~icouzin/Yatesetal2009.pdf … -
With modern computer modeling /machine vision, we're starting to be able to map this stuff in terms of networks of information trust. Literally seeing familial relationships & majority illusions impose group level attractors to how foraging behavior influences entire swarms.
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from that http://chronicle.com article, here's a direct quote highlighting both Taleb's view, and the Hanson's math model. And that was from 2011. We might already have an empirically proven version of it (or a correspondence) sitting in a paper somewhere.pic.twitter.com/vRScskNgCy
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