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He was elected to the Knesset on the party's list in 1951 elections, but on 20 February 1952 left the party and formed the Left Faction together with Rostam Bastuni and Moshe Sneh.
Markham received a late endorsement from Premier Bob Carr ahead of the 2002 preselection vote, but this was not enough to sway the right-dominated preselectors, who voted for Noreen Hay, a local left faction figure who defected to the right soon after.
The Prague Trials and the Moscow Doctors' Plot during the years 1952–1953 caused internal dissent within the Mapam and a split where the Left Faction resigned from Mapam and later formed Maki.