Here is a simple model that suggests that non-conformists can have more influence than conformists.

Regarding a one dimensional choice x, let each person i take a public position x_{i}, and let the perceived mean social consensus be m = Σ_{i}w_{i}x_{i}, where w_{i} is the weight that person i gets in the consensus. In choosing their public position x_{i}, person i cares about getting close to both their personal ideal point a_{i} and to the consensus m, via the utility function

_{i}(x

_{i}) = -c

_{i}(x

_{i}-a

_{i})

^{2}– (1-c

_{i})(x

_{i}-m)

^{2}.

Here c_{i} is person i’s non-conformity, i.e., their willingness to have their public position reflect their personal ideal point, relative to the social consensus. When each person simultaneously chooses their x_{i} while knowing all of the a_{i},w_{i},c_{i}, the (Nash) equilibrium consensus is

_{i}w

_{i}c

_{i}a

_{i}(c

_{i}+ (1-c

_{i})(1-w

_{i}))

^{-1}(1- Σ

_{j}w

_{j}(1-c

_{j})(1-w

_{j})/(c

_{j}+ (1-c

_{j})(1-w

_{j})))

^{-1}

If each w_{i}<<1, then the relative weight that each person gets in the consensus is close to w_{i}c_{i}a_{i}. So how much their ideal point a_{i} counts is roughly proportional to their non-conformity c_{i} times their weight w_{i}. So all else equal, non-conformists have more influence over the consensus.

Now it is possible that others will reduce the weight w_{i} that they give the non-conformists with high c_{i} in the consensus. But this is hard when c_{i} is hard to observe, and as long as this reduction is not fully (or more than fully) proportional to their increased non-confomity, non-conformists continue to have more influence.

It is also possible that extremists, who pick x_{i} that deviate more from that of others, will be directly down-weighted. (This happens in the weights w_{i}=k/|x_{i}-x_{m}| that produce a median x_{m}, for example.) This makes more sense in the more plausible situation where x_{i},w_{i} are observable but a_{i},c_{i} are not. In this case, it is the moderate non-conformists, who happen to agree more with others, who have the most influence.

Note that there is already a sense in which, holding constant their weight w_{i}, an extremist has a disproportionate influence on the mean: a 10 percent change in the quantity x_{i} – m changes the consensus mean m twice as much when that quantity x_{i} – m is twice as large.

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