Can we quantify how position within search results is related to click-through probability? Suppose, for example, that the first search result on a page of Google search results is swapped with the second result. How much would this change the click-through probabilities of the two results? How much would its click-through probability drop if the fifth search result was swapped with the sixth? 

Can we say something, with some level of assurance, about how expected click-through probabilities change if we do these types of pairwise swaps within pages of search results?

What we seek is a measure of the contribution to click-through rates made specifically by position bias.

Likely, how position ranking would affect the sales in Amazon or other online shopping website? If we cast the sales into two parts, the product quality and its ranking effect.


sales = alpha*quality + beta*position + epsilon


How can we quantify the beta?
you might want to look at this paper
Predicting Clicks: Estimating the Click-Through Rate for New Ads


  Whenever an ad is displayed on the search results page, it has 
  some chance of being viewed by the user. The farther down the 
  page an ad is displayed, the less likely it is to be viewed. As a 
  simplification, we consider the probability that an ad is clicked on 
  to be dependent on two factors: a) the probability that it is viewed, 
  and b) the probability that it is clicked on, given that it is viewed: