LOS ANGELES—“Jeopardy!” needed a host, and Lucille Ball had an enthusiastic suggestion for creator Merv Griffin: The smooth-voiced, debonair emcee of the “High Rollers” game show. That was 1984. Decades later, filling the void left by the late Alex Trebek involves sophisticated research and a parade of guest hosts doing their best to impress viewers and the studio that’s expected to make the call before the new season begins taping later this summer. Think of Sony Pictures Television as clutching the rose, and Mayim Bialik, Anderson Cooper, Katie Couric and “Jeopardy!” champs Ken Jennings and Buzzy Cohen among the suitors so far, with more to come including Robin Roberts, Dr. Sanjay Gupta and LeVar Burton. Sony has “the most robust team of people I have ever seen looking at this and analyzing it in a very cerebral way,” said executive producer Mike Richards. “It’s a real change from the way …