Simple experiment to cover several bases: Present two or three people for assessment, asking for 1 to 10 ratings. (A single measure might be best, given the complexity of the rest of the analysis, but there are other options if you have enough subjects to ask1.)
The two choices always present are Trump and Clinton. The third can be a global (for those asked) single third-party/independent candidate or a main Trump/Clinton rival, or else (with a large enough cadre) J Random Candidate sekected from amongst all those categories. And you present the two/three candidates in the two/six different orders. Because "Having already considered Trump and Clinton, how would you now rate Cruz?" would likely elicit a different result-per-person from "Having already considered Trump and Cruz, how would you now rate Clinton?", etc.
(Note that although dressed up as a simple poll, we're not too bothered about political preferences save that we get enough like-for-like tendencies to discover uplift or depression of opinions from the people of similar views but with switched/salted polls. If we do have enough people to derive that partisan Trump voters rate Cruz higher, say, after asked about Clinton than before, whilst partisan Clintonites work differently with that but the same with Trump/Sanders, say, then that's a result.)
Not going to calculate the numbers you'd need to ask to get statistically significent results across each possibility, maybe stly because I've kept it open. Though anyone able to get a large enough study up prior to this precise question being moot is going to be an established national pollster who probably already is contacting as many people as possible, and doesn't want to complicate their current plans.
1 Namely that you do something like ask for rankings on "Trustworthiness, Capability, Experience, ..., Novelty, Unpredictability, Self-Serving" for half (positive to negative, an arguable ordering that may need further discussion), but ask them in the opposite order (negative to positive) for the other half and see if the nature of the first questions has an observable effect upon the latter ones, also.