[AreaOfEffect]

Sector's idea is the most appealing to me. It is also the least amount of work to implement. Risk does indeed have a method of play where you need not beat every faction into submission, but instead complete an objective which is half-way toward victory. It always ended a game before it got to that depressingly sad moment where the winner wanted to squash the last player who didn't have a chance.

I think it would be nice if every player was assigned 2 or 3 enemies. And victory was achieved by having your enemies eliminated. So long as everyone has a different enemy the game always remains interesting. For example:

In a four player game each player is given 2 enemies.
-Player 1 has 2 and 3
-Player 2 has 3 and 4
-Player 3 has 4 and 1
-Player 4 has 1 and 2
If player 1 is eliminated then player 3 and 4 only need one more opponent removed. This creates a dynamic game were people help other factions simple to buy the time they need to beat up another faction. If it so happens that two players need the same opponent to lose in order to win, then I suppose the one who kills him wins.

I think it would be more interesting then simply, "gang up on the scary guy".