What is the effect of Social Proof on Conversion Rate? I'm wondering to what extent Social Proof helps the Conversion Rate of websites and marketing.

Specifically I'm wondering what effect Social Proof would have on Conversion Rate for a sample task in an online context. Lots of marketing material espouses it's effectiveness but I would like academic research on the matter. 

There's some basic research I've found that shows yes, people do things their friends do (such as some of the studies referenced in the Wikipedia article) but this is not specific to new methods of Social PRoof.

What quantitative research has been done in regards to social proof effects website conversion with modern Social Proof techniques like Facebook likes and Amazon customer reviews?
This is a partial answer, but there are a number of academic studies on this topic.  The findings of the Berkeley article "Long Tail or Steep Tail?
A Field Investigation into How Online Popularity Information Affects the
Distribution of Customer Choices" (Tucker and Zhang, 2007) suggest that 


  evidence of a complementary effect, where
  the steep tail indicates new interest in the most popular vendors from outside, with
  negligible cannibalization of interest for less popular vendors. The ndings suggest
  that popularity information can serve as a powerful marketing tool that facilitates
  product category growth. They also explain the prevalence of rm practices to highlight
  bestsellers.


where 'long tail' refers to customers buying low-volume products and 'steep tail' refers to the flocking to popular products.

A couple of key conclusions from that study:


  We find strong evidence for a steep tail effect, where customers are more likely to click
  on the most popular vendors when the popularity information is publicized and made salient
  through ranking the vendors on the page by popularity.


and that there was little negative effects to less popular product sales


  If a steep tail effect exists, and if it complements the long tail, websites such
  as Google.com and Digg.com can increase overall number of clicks at little cost to the less
  popular listings.


A caveat of sorts is stated in the article "On the Depth and Dynamics of Online
Search Behavior" (Johnson et al. 2004) in that their study showed a bit of 'consumer inertia', in that their study


  show that the amount of online search is actually quite limited.