Why the router with the lowest IP is selected to be the DR?

[Chris]

I have 4 routers connected to one switch with fastethernet， see the following diagram:
http://www.netbraintech.com/share/OSPFDR.gif

but when I did the "show ip ospf neighbor"on R4, it shows that the router with the lowest ip address is the DR and the second lowest is the BDR.
that is okay but my book tells me it should be the router with the highest assigned router interface should be the DR not lowest.

[David.C]

* The router sending the Hello with the highest OSPF priority setting becomes the DR.
* If two or more routers tie with the highest priority setting, the router sending the Hello with the highest RID wins.
* It's not always the case, but typically the router with the second-highest priority becomes the BDR.
* The range of priority values that allow a router to be a candidate are 1 through 255.
* If a new, better candidate comes along after the DR and BDR have been elected, the new candidate does not preempt the existing DR and BDR.

So going from the last point if those two routers were the only routers that could become BDR and DR at the time then regardless of any new aditions to the network a new BDR or DR wouldn't be "elected" untill one goes down.