Since OP is applying in Surgery I hope your version is accurate for her. It's just that I've never had a chair be involved enough in the day-to-day to even really meet individual candidates, let alone want one. This has been at academic powerhouse programs where the Chairs have been <20% clinical, and less academic regional campus-type programs where the Chairs have been based far away, at the "mothership."
It's an interesting question about what the relative distribution of influence is in different departments.
So, let's say that there is NO scenario where PDs don't have the majority of the influence on the ROL. So, the PD gets somewhere between 51% and 100%.
Could the Chair have as much as 49%? Doubtful.
My experience is that my PC actually has significant influence on the process. She has met all the applicants (none of my APDs have done that) and she has interacted with them in a way that tells a lot. So, let's give her 5%.
My senior APDs both did a lot of interviewing this year and by the end of the season would say "take this one, don't take that one". They have a lot of influence, but don't see every single candidate. So, let's give them 5% each. 10% total.
My junior interviewers actually have not much influence because, frankly, they are just not good enough at interviewing yet. 1.5% each, say a total of 6%.
My Chief residents/residents who have dinner with the applicants. Hard to rate this, but they will, on occasion, have some crucial piece of information. Let's give all residents 2%.
My Chair actually has met all the in-house candidates and the Chair's style is to comment only on one or two candidates. I'm interviewing and ranking a LOT of candidates, so in my case, the Chair's influence is very small, maybe 1%.
That leaves me 86%. I should also mention some other categories of people.
Current faculty who I don't like and/or don't really interact with: I almost totally ignore their thoughts. 0.1%
Current faculty that I do like and/or work with on a regular basis: Can possibly help an applicant. 1%
Faculty from other schools who have been emailing/calling me: Almost the most annoying people to deal with since etiquette requires polite responses. -0.5%
Practicing physicians who graduated from my program 20 years ago, have no contact with the Department except now their nephew is applying: The *most* annoying people I deal with and almost never help an applicant. -5% to a maximum of 0.001%