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?