The answer is that you do (together with your attorney).
You as the injured victim have the opportunity to request either a trial by jury or trial by judge. You have the first choice. If you request a trial by jury, that's what you'll get. If you request a trial by judge and the defense disagrees, they will then have the opportunity to request a trial by jury as well.
As an injured victim who brings a claim seeking compensation for injuries you received at the hands of a doctor or hospital, you have an absolute constitutional right to have your case heard by a jury of your peers. In New York state court that means that six jurors will be selected from the community to sit and decide your case. There will be alternate jurors available in case of any one of the main jurors are unable to complete their jury duty.
What's the difference between having the case heard by a jury compared to a judge? There are many.
There are some who believe that a judge may not have enough empathy or sympathy for an injured victim because he sees so many of these cases on a daily basis. There are others who believe that a jury is best able to reach a consensus about whether or not there was wrongdoing and if so, how much compensation to award that represents full and fair justice.
Regardless of which opinion you may have, I guarantee you that every attorney will have their own opinion about which they prefer.
I will tell you that in the greater New York metropolitan area including Brooklyn, Bronx, Queens, Manhattan, Nassau and Suffolk, almost all accident, personal injury cases, medical malpractice and wrongful death cases that go to trial are tried by a jury and not a judge. That says a lot all by itself.