(a) Every person shall be disqualified from holding any office of profit in this State who shall have been convicted of having given or offered a bribe to procure personal election or appointment.

  (b) Laws shall be made to exclude persons convicted of bribery, perjury, forgery, malfeasance in office, or other high crimes from office or serving on juries. The privilege of free suffrage shall be supported by laws regulating elections and prohibiting, under dequate penalties, all undue influence thereon from power, bribery, tumult, or other improper practice.