The formal introduction is in the text. For reference, here is the particular example that we considered.
Companies (ranking of applicants) ---------- Boeing: Eric, Neil, Ryan, Brian, Mike JHU: Ryan, Mike, Neil, Eric, Brian IBM: Mike, Neil, Brian, Eric, Ryan Anheus: Ryan, Neil, Brian, Eric, Mike Intel: Mike, Eric, Neil, Ryan, Brian Applicants (ranking of companies) ---------- Neil: JHU, Intel, IBM, Boeing, Anheus Brian: IBM, Intel, Boeing, Anheus, JHU Ryan: Boeing, IBM, Intel, Anheus, JHU Mike: Anheus, Intel, IBM, Boeing, JHU Eric: IBM, Intel, Boeing, Anheus, JHU
One stable marriage solution that we identifed, was as follows:
(Boeing, Eric) (JHU, Neil) (IBM, Brian) (Anheus, Ryan) (Intel, Mike)Another such solution was identified as:
(Boeing, Ryan) (JHU, Neil) (IBM, Brian) (Anheus, Mike) (Intel, Eric)Although we have not proven so, it turns out that these are the only two valid solutions for this example. Notice the dramatic difference in results from the perspective of Anheuser, who gets their top candidate in the one solution and their least candidate in the other.
An alternate example from a past year:
Companies (ranking of applicants) ---------- Google: W,X,Z,Y NSA: W,Y,Z,X Boeing: X,W,Y,Z Microsoft: W,Z,X,Y Applicants (ranking of companies) ---------- W: Microsoft,NSA,Boeing,Google X: Microsoft,NSA,Google,Boeing Y: Google,Microsoft,NSA,Boeing Z: NSA,Google,Microsoft,Boeing
The stable marriage solution that we identifed, was as follows:
(Google,X) (NSA,Y) (Boeing,Z) (Microsoft,W)Though we have not proved so, in this particuar instance, this is the only legal solution (more generally, there may be many).