Bidder Count Impact on Uniform Price Economics Say we have an uniform price auction where 1 really rare stamp is for sale.  Only 5 randomly selected stamp collectors are invited to bid and the stamp ends up selling for 1 million dollars.  Now pretend that auction never happened.

If 6 randomly selected stamp collectors were invited instead of 5 in the previous example (again, original auction never happened), what expected percent increase in revenue should the stamp sell for - 10% more, 15% more?  Similarly, what if only 4 bidders were allowed to the auction?

In short, I'm trying to determine how increasing or decreasing bidder participation by 1 impacts the ultimate selling price on a percentage basis.  I'm sure lots of variables are at play, so am not sure if any economic theory can be used to address this.
It is a known result in Mechanism Design that both first-price as well as second-price auctions yield the same expected revenue, under certain conditions (like independence of valuations, private information, etc). Consult   Jehle, G. A., &amp; Reny, P. J. (2011). Advanced Microeconomic Theory (3d ed.), ch.9 on Auctions and Mechanism Design, for a very accessible exposition of the basics, as well as for the full set of conditions that must hold.  

The answer to your question is bound to be distribution-specific. Assume as an example, that, from the point of view of the seller, all (unknown to him) valuations of the bidders for the object for sale, come from a Uniform $U(0,1)$ distribution: this implies that we have normalized the value of the object for sale and that we express the possible valuations of it as a percentage of its possible maximum value, which is assumed common for all bidders. I.e. What we say here is :"we don't know how much each bidder actually values the object, but we do know that the maximum possible valuation by a bidder will be some $V&gt;0$, and this $V$ is common to all bidders". We do not assert that there exists some bidder that actually values the object at $V$.

In such a setup, the Expected Revenue of the Seller is

$$ER(N) = \frac {N-1}{N+1} \tag {1}$$

where $N$ is the number of bidders. Again, this essentially expresses expected revenue as a fraction of the object (unidentified) maximum value.

Now you can play around with $N$ to see how the expected revenue changes, in absolute, relative and percentage terms. It sure isn't changing linearly, but it is everywhere increasing in $N$, approaching unity (i.e. the object maximum valuation).

This should be intuitive in the framework adopted: the more the bidders are, the more probable becomes to obtain higher and higher valuations of the object, and so also to sell it at a higher value.