TO CONSIDER THE QUESTION OF HOW THE FORM OF THE DEATH PENALTY INFLUENCES THE CERTAINTY OF ITS APPOLICATION, TWO AREAS ARE EXAMINED: (1) EXECUTION RATES FOR HOMICIDE IN STATES THAT HAVE MOVED FROM MANDATORY TO DESCRETIONARY CAPITAL PUNISHMENT FOR THIS OFFENSE; AND (2) EXECUTION RATES FOR DEATH PENALTY JURISDICTIONS THAT VARY IN THEIR STATUTORY PROVISIONS FOR MANDATORY OR DISCRETIONARY CAPITAL PUNISHMENT FOR HOMICIDE. THE STUDY EMPLOYS BOTH LONGITUDINAL AND CROSS-SECTIONAL ANALYSIS, INTRODUCING CONTROL VARIABLES ASSOCIATED WITH EXECUTIONS AND HOMICIDES. THE EIGHT 'CHANGE-OVER' STATES ARE NEW HAMPSHIRE, CONNECTICUT, VERMONT, NEW JERSEY, PENNSYLVANIA, NORTH CAROLINA, NEW MEXICO, AND OREGON. THERE IS NO CONSISTENT SUPPORT FOR ARGUMENTS THAT MANDATORY DEATH PENALTIES EITHER REDUCE OR INCREASE EXECUTION RATES. THE FINDINGS ARE ALSO CLEARLY INCONSISTENT WITH ANOTHER RESEARCHER'S ASSESSMENT OF THE OPINIONS OF LEADING 19TH-CENTURY AUTHORITIES REGARDING HOW THE MANDATORY DEATH PENALTY AFFECTS EXECUTIONS. SUPPORTING TABULAR DATA AND A LIST OF REFERENCES ARE INCLUDED. (LKM)