Sort a table using formulas

[ASJacobsen]

I have a table that summarizes the results of a formal bid:

Rank Bidder Bid
2 Bidder1 $995
1 Bidder3 $1,000
4 Bidder2 $950
2 Bidder4 $995

I want to use formulas to convert the table to one that is sorted by Rank.

Rank Bidder Bid
1 Bidder3 $1,000
2 Bidder1 $995
2 Bidder4 $995
4 Bidder2 $950

My current sort table will do this as long as there are no ties. The first
row looks for the #1 ranked bidder, the second row looks for the #2 ranked
bidder, etc... Has anyone figured out how to sort a table like this using
formulas?