TCASII RA POSSIBLE NMAC ARR LAX BY A320.

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WE WERE DIRECT TO CIVET ON THE LAX MITTS ARR CLRED TO DSND VIA THE MITTS ARR WITH A 250 KIAS SPD LIMIT. PASSING THROUGH FL180 SOCAL APCH CTL ASKED US TO LEVEL AT FL180 FOR TFC. WE GOT THE CALL AT ABOUT 17800 FT; ACKNOWLEDGED; AND CLBED BACK TO FL180. DURING THIS TIME SOCAL WAS HAVING A CONVERSATION WITH ANOTHER NON-ACR ACFT ABOUT HIS ALT BECAUSE HIS XPONDER WAS NOT GIVING HIM SOLID ALT ENCODING INFO. I COULD ONLY HEAR SOCAL'S END OF THE RADIO CONVERSATION. THE OTHER ACFT MUST HAVE BEEN ON ANOTHER FREQ THAT THE SOCAL CTLR WAS COVERING. NO SOONER THAN WE LEVELED OFF AT FL180 WE GOT A TCASII RA TO DSND. THE FO (THE PF) DISCONNECTED THE AUTOPLT TO FOLLOW THE RA WHEN IT CHANGED TO A CLB-NOW-CLB RA. THE FO FOLLOWED THE RA JUST AS SOCAL ISSUED A TFC ALERT FOR VFR JET TFC AT 12 O'CLOCK POS ALT UNKNOWN WITH A BAD XPONDER. I RESPONDED THAT WE DID NOT HAVE THE TFC IN SIGHT AND WERE COMPLYING WITH A TCASII RA TO CLB. THE RA STOPPED AT FL185 JUST AS A BUSINESS JET APPEARED OUT OF THE LA HAZE AT LESS THAN 1 MI; HEAD-ON; EXACTLY OPPOSITE DIRECTION; DOING +250 KIAS. AT THAT POINT TCASII SHOWED HIM BELOW US AT 1000 FT; HOWEVER; IT WAS KNOWN THAT HIS XPONDER WAS INACCURATE AND HE APPEARED TO BE ABOUT 500 FT BELOW US. COULD HE HAVE HAD HIS ALTIMETER SET INCORRECTLY TO 29.92 AND NOT THE LCL METER SETTING? AFTER HE PASSED BY US THE TFC PROCEEDED TO CONFLICT WITH JUST ABOUT EVERYONE ELSE BEHIND US IN THE CIVET ARR. WE TALKED A LITTLE BIT ON THE RADIO TO SOCAL ABOUT THE SIT THEN LANDED UNEVENTFULLY. ONCE ON THE GND I CALLED SOCAL ON THE LAND LINE AND GOT 'THE REST OF THE STORY.' THE ACFT; A HAWKER BUSINESS JET HAD DEPARTED FROM SOMEWHERE IN SOUTHERN CALIFORNIA VFR TO FLY AT 17500 FT VFR TO LAS. THE ACFT HAD JUST CHKED IN WITH OUR SOCAL CTLR REQUESTING VFR TA'S. BECAUSE SOCAL COULD NOT GET GOOD XPONDER INFO OFF THE TFC; AND IT APPEARED HE MIGHT BE A TFC PROB FOR US; AS A PRECAUTION THE CTLR HAD US LEVELOFF AT FL180 UNTIL HE COULD GET THE SIT SORTED OUT. IT WAS DARN GOOD HE DID TOO. I ASKED THE SUPVR TO THANK THE CTLR FOR HIS DILIGENCE. IT DID NOT APPEAR THAT ATC WAS GOING TO FOLLOW UP WITH THE HAWKER JET; EXCEPT THAT THE SOCAL CTR WAS VERY CLR TO TELL THE HAWKER PLT THAT HIS XPONDER APPEARED TO BE INOP AND THAT HE REALLY NEEDED THAT TO BE TOOLING ACROSS THE LAX ARR STARS VFR. WE WERE UNABLE TO HEAR THE PLT'S RESPONSE.