Joseph "Proposition Joe" Stewart was an East Baltimore narcotics trafficking kingpin and a co-founder of the lucrative New Day Co-Op. Rotund and amiable, Joe's shrewdness and drug connection with the Greeks brought him into conflict with rival kingpins Avon Barksdale and Marlo Stanfield. Like Stringer, Joe errs on the side of caution and seeks non-violent resolutions to conflict.
Joe attended the annual basketball game between East and West Baltimore. Joe plays on Avon's pride, goading him into doubling their wager on the outcome, then bringing in a ringer at the last minute to win the game. That same day, he is visited by stick-up-man Omar Little, who gives Joe some of the Barksdale gang's stolen stash in exchange for Avon's pager number, using the information in an attempt on Avon's life. (Prop Joe's role in Omar's attack is never learned by Avon.) Joe later serves as a neutral go-between, organizing a meeting between Stringer Bell and Omar to discuss a truce. ("Game Day")
In 2003, it is revealed that he relies on The Greek's smuggling ring to bring his drug shipments into the Baltimore ports. Prop Joe is also shown lending assistance to Nick Sobotka at the request of Sergei "Serge" Malatov due to a bad drug deal between Nick's cousin Ziggy and Joe's nephew Cheese. Prop Joe helps Nick get money that was stolen out of respect to Sergei understanding that dimwitted family members such as Ziggy are present and problematic. Joe's heroin supply is much more potent than any other drugs in Baltimore, but Joe lacks good territory to market it. Due to Avon's arrest, the Barksdale crew is cut off from any quality drug supply, relying on weaker heroin to market. Joe offers Stringer Bell his product in exchange for the right to deal in some of the Barksdale towers. Avon vehemently rejects the idea stating that he refuses to give up hard-earned real estate, but Stringer secretly agrees to the deal. Avon, unaware of Stringer's move, brings in Brother Mouzone, to move the East Baltimore dealers in Joe's organization out of the towers much to the fear of Prop Joe. Joe realizes Mouzone's reputation claiming that he once murdered five men at once and is a deadly and skilled hitter and sees him as the one person he wished Avon would not have called in. Joe's nephew and lieutenant, "Cheese", is shot and wounded by Mouzone himself, not realizing Mouzone's will and determination, hence cutting off the drug supply to West Baltimore's towers. Joe comes up with the idea of pitting Omar Little against Mouzone feeling that Omar is the one gunslinger in Baltimore who could effectively drive Mouzone out of the city. He sets up a meeting between Stringer and Omar, where the stickup man is tricked into shooting Mouzone, however non-fatally. The elaborate deception forces Mouzone back to New York and forces Avon to grudgingly agree to the alliance between Stringer and Joe.
Joe continues to insulate himself against investigation by maintaining a strict policy of only meeting face-to-face, refusing to utilize any form of electronic communication. His nephew Drac is targeted as a potential inroad for an investigation by Lieutenant Daniels' major case unit, due to his propensity to talk business over the phone. Daniels' unit arrests Joe's lieutenant Lavelle Mann in an undercover buy-bust operation, hoping that Drac would be promoted to replace him. However Joe chooses someone more reliable, thwarting the unit's efforts without realizing he is being investigated. Daniels tips his hand when he arrests Cheese, believing that he had him on tape discussing a murder. Cheese realizes that the tape is of him talking about shooting his pet dog, and they are forced to release him. He reports the incident to Proposition Joe who is thus forewarned about the investigation, and passes the information on to Stringer. The unit moves their investigation away from Joe and onto the more violent Kintell Williamson when they fail to make further progress.
Joe extends the sharing of his supply to many other drug dealers in Baltimore, forming the New Day Co-Op with Stringer Bell, Fatface Rick and Kintell Williamson, among others. He provides all of these dealers with his package, and they receive a discount for the bulk buying; they also agree to avoid bringing unnecessary police attention by limiting violence. Because of their agreement, Williamson stops killing people, and the police begin investigating a brewing turf war between Avon and up-and-coming Marlo Stanfield.
Joe objects to the police attention, which is interfering with all their business. He meets with Marlo's advisor Vinson to try to negotiate a settlement, but Marlo is unwilling to back out of the war, believing that Avon is weak. Joe gives Stringer an ultimatum - end the war or he will be thrown out of the Co-Op. The ultimatum is diffused when Stringer is murdered, and Avon is arrested, leaving Joe with complete control of the Co-Op.
Joe recruits former Barksdale soldier Slim Charles to supply the independent dealers that have arisen from the Barksdale organization in Western Baltimore. However, problems arise; Stanfield has taken control of much of the Barksdales' prime real estate, and the New York drug organizations are taking over territory in Eastern Baltimore. The Co-Op vote to negotiate with Marlo and strike back against the New York drug dealers.
Joe contacts Marlo, who turns down his first offer. Joe manipulates Omar again, convincing him to rob a card game which Marlo ran, pretending that he wanted to make amends for his involvement in the Stringer Bell / Brother Mouzone incident. After Omar robs the card game, Joe offers Marlo another meeting and claims he could protect him against such surprises in the future. Joe also explains that he has contacts within Baltimore City police department and courts and shares information about police activity with other Co-Op members though much of his information is actually publicly available. It can somewhat be assumed however that Joe has a leak in the Major Case Unit specifically as he is aware of their investigative strategies on the phones and is aware of a case against Kintell Williamson that was suspended and inconclusive. Marlo agrees to work with the co-op. With his help, the New York dealers are chased out of Baltimore. Joe also offers Marlo advice on how to deal with a surveillance camera, and generally seems to be helping Marlo's transition into being less violent and more business-minded.
Soon after, Omar wants to get revenge on Marlo. Omar forces Joe (at gunpoint) to agree to betray Marlo, but Omar ultimately double-crosses Joe and steals the entire drug shipment directly from delivery. When the Co-Op claimed Joe should cover the expense of replacing it, Joe threatened to cut them off from the prime supply, and they backed off. Omar returns to sell the shipment back to Joe for 20% of its worth; ever the opportunist, Joe gets 30% from all the members of the Co-Op. At the end of the season, it seems as if Joe and the rest of the New Day Co-Op, possibly including The Greek, will soon be looking for revenge against Omar. 
Joe uses his unique brand of diplomacy to convince Marlo Stanfield to join the New Day Co Op. In exchange for granting Cheese access to one of his Co-Op enemies, Marlo is able to find Joe. Joe is shot in the back of the head by Partlow as Marlo watches.
|Season 1 appearances|
|"The Target"||"The Detail"||"The Buys"||"Old Cases"||"The Pager"|
|The Wire"||"One Arrest"||"Lessons"||"Game Day"||"The Cost"|
|"The Hunt"||"Cleaning Up"||"Sentencing"|
|Season 2 appearances|
|"Ebb Tide"||"Collateral Damage"||"Hot Shots"||"Hard Cases"||"Undertow"|
|"All Prologue"||"Backwash"||"Duck and Cover"||"Stray Rounds"||"Storm Warnings"|
|"Bad Dreams"||"Port in a Storm"|
|Season 3 appearances|
|"Time after Time"||"All Due Respect"||"Dead Soldiers"||"Amsterdam"||"Straight and True"|
|"Homecoming"||"Back Burners"||"Moral Midgetry"||"Slapstick"||"Reformation"|
|"Middle Ground"||"Mission Accomplished"|
|Season 4 appearances|
|"Boys of Summer"||"Soft Eyes"||"Home Rooms"||"Refugees"||"Alliances"|
|"Margin of Error"||"Unto Others"||"Corner Boys" *||"Know Your Place"||"Misgivings"|
|"A New Day"||"That's Got His Own"||"Final Grades"|
|Season 5 appearances|
|"More with Less"||"Unconfirmed Reports"||"Not for Attribution"||"Transitions"||"React Quotes"|
|"The Dickensian Aspect"||"Took"||"Clarifications"||"Late Editions"||"-30-"|
- Actor Robert Chew appeared in David Simon's previous series Homicide: Life on the Street, in the three part episode "Blood Ties", playing Wilkie Collins, a drug kingpin who hates violence; he provides the police with key information about what drug dealer was shooting at them so that they will not interfere with his business. He and his wife are subsequently murdered for his betrayal; his young son witnesses, and helps the police arrest Wilkie's murderer.