I think we can all agree that the bounty system in Eve is completely arbitrary and meaningless. Having a bounty has no meaning beyond e-peen, and any sufficiently high bounty added by a wronged party can just be cashed in by the pirate using an alt.
I'd like to propose an overhaul as follows (I'm throwing a lot of this against the wall, so feel free to critique, note that "contract" here means a contract to kill someone and has nothing to do with the current contract system of buying/selling things):
1) Sec status will no longer result in the faction police chasing people around highsec. Pirates will therefore be encouraged to travel around in "safety" in highsec.
2) "Security status" replaced with "Reputation", and instead of a actual number it will be reflected in simple terms - Excellent, Good, Neutral, Suspect, Bad, Terrible, Infamous. The exact scale of how this corrolates to existing sec status numbers would need to be explored, I'd assume 5+ would be Excellent and -10 Infamous.
3) Negative reputation decays over a period of time. A pilot who eshews piratical acts will eventually end up with a Neutral reputation. Someone killing people on a regular basis will remain Infamous. Below Neutral the decay would work similarly to how sec status gains work - i.e. you receive a bigger positive sec bonus the closer to the end of the spectrum you are, and a smaller one when you're close to 0 (Neutral).
4) Aggressing and killing non-hostile (i.e. non GCC/aggressed) targets in highsec and lowsec will contribute to this Reputation score in broadly the same way that sec status penalties work. When below Neutral reputation killing NPCs will NOT improve Reputation.
Now, here's the meat of it:
5) A new station service will be added - called Bounty Hunting. Pilots that are "Suspect" reputation or lower will have a random chance of appearing as a contract (a "mission" in Eve terms) that other pilots (Neutral+ rep?) can receive.
6) The random chance of appearing on the list will be weighted according to reputation (lower = higher chance of appearing) and activity - how often and how long someone logs in for, i.e. someone who is regularly online will appear more frequently.
7) A payout value for the contract will be derived based on the current reputation of the target, how long their contract has gone unclaimed, the Reputation of the pilots the target has aggressed. This payout could decay (or increase) post-collection according to the target's activity and reputation.
8) Multiple people can collect the same contract against one person in exactly the same mechanics as people currently receive missions.
9) A target will not receive any kind of notification that someone has their contract.
10) The kill contract will not specify the pilots name, but it will specify which system they were last seen in. Additionally if a contract is "active" while the target is online the bounty hunter will receive periodical updates as to their location (perhaps with an element of fuzz - restrict location updates to constellations?)
11) If the bounty hunter jumps into the same system as the target, and he/she is online and in space, a warpable beacon will be provided to them. This beacon will also be visible on the solar system map (so you don't end up warping to a POS). A BH will therefore not need combat probes to find their target in space.
12) The BH can shoot the target anywhere without going GCC as per killrights system. Target can respond without punishment directly, but any assistance by either side results in GCC (again this is as per current 1v1 aggression mechanics)
13) Blowing up the targets ship is counted as having completed the contract (perhaps getting the pod too would be a bonus payment? or not allowed?). If someone collects the bounty payout from the contract the other BHs will receive an update saying that it has been completed, and it is removed from their contract list.
14) If a BH fails to kill the target after having aggressed them, they will have an hour (or less?) to finish the job or the will be adjudged to have failed the contract, and it is removed from their journal.
The primary advantage of the above system is that whilst it can still be gamed by advising someone that you have their contract and coming to some agreement to split the payout (though this is fraught with risk itself), it eliminates the obvious "use alt to pod empty clone and receive ISK" abuse.
It also creates a whole new profession. There could even conceivably be skills that increase the number of concurrent contracts you can have, how often you receive periodical location updates, etc.
I'll admit it needs a lot of fleshing out in terms of how payouts scale, whether people in null sec show up as available contracts, etc.