The　single-dipped　domain　can　be　used　to　model　any　allocation　problem　where　a　single　output　must　be　chosen　in　an　interval　with　the　assumption　that　agents＇　preferences　have　a　single　most　loathful　point　(the　dip)　in　the　interval,　and　the　preferences　are　increasing　as　one　moves　away　from　that　dip.　Practical　domains　like　this　appear　in　political　voting　system　where　each　voter　has　his　most-hated　candidate　and　alternative　candidates　are　evaluated　by　their　proximity　to　this　candidate　or　in　obnoxious　location　problem,　where　each　agent　prefers　to　have　the　obnoxious　location　to　be　distant　from　his　own　location,　among　others.　We　first　characterize　deterministic　and　anonymous　strategy-proof　and　group　strategy-proof　mechanisms　on　single-dipped　public　policy　domain,　complementing　the　well-known　results　on　single-peaked　policy　domain　first　investigated　by　Moulin　(Pub.　Choice　35:437-455,　1980).　Then　we　consider　the　tradeoff　between　strategy-proofness　and　efficiency　by　applying　our　characterization.　As　concrete　applications　of　our　results,　we　extend　existing　models　and　results,　and　resolve　several　open　questions　related　to　the　obnoxious　facility　location　game　from　the　algorithmic　mechanism　design　literature.