I am looking for a definition, a negative one, to describe a politician who is not doing politics in the public interest.
Politicaster: n. 1. A petty politician; a pretender in politics
Highbinder: 2.a dishonest political official or leader.
politician: 2b : a person primarily interested in political offices for selfish or other narrow usually shortsighted reasons.
politician: 3. : one who seeks personal or partisan gain, often by scheming or maneuvering.
politician: 3. : (Goverment, Politic & Diplomacy) derogatory chiefly (US) a person who engages in politics out of a wish for personal gain, as realized by holding a public office.
politician: a person who uses public office to advance personal or partisan interests.
politician: 2. : one who deceives or outmaneuvers others for personal gain.
politician: one who regards elected political office as a career.
politician: (disapproving) : a person who is good at using different situations in an organization to try to get power or advantage for himself or herself.
carpetbagger: a politician who moves to a place where he/she sees an opportunity to promote his/her career.
Here is Reinhard Luthin's definition of a specific type of politician who doesn't do politics in the public interest, namely a demagogue:
What is a demagogue? He is a politician skilled in oratory, flattery and invective; evasive in discussing vital issues; promising everything to everybody; appealing to the passions rather than the reason of the public; and arousing racial, religious, and class prejudices—a man whose lust for power without recourse to principle leads him to seek to become a master of the masses. He has for centuries practiced his profession of 'man of the people'. He is a product of a political tradition nearly as old as western civilization itself.
Source: American Demagogues by Reinhard Luthin (1954), p. 3.