Ambiguity of the word 'any'?
Solution 1:
The question
Should any employee of Company X be allowed to assume absolute authority in any project with Company X's name associated?
does indeed permits at least two very different readings. To simplify the analysis, let's consider a similar question that uses any just once:
Should any employee of Company X have the authority to turn off the lights when he or she is the last person to leave the building?
There are two possible ways to read this question. The first is to read it as asking whether every employee should have the authority to turn off the lights if he or she happens to be the last person to leave the building. In short, any = every. The implied alternative answers in this case would be
Yes, every employee of Company X should have the authority to turn off the lights when he or she is the last person to leave the building.
and
No, only certain designated employees of Company X should have the authority to turn off the lights when they are the last person to leave the building.
The second ways to read this question is as asking whether a particular designated employee should have the authority to turn off the lights. In short, any = even one. The implied alternative answers in this case would be
Yes, a particular designated employee of Company X should have the authority to turn off the lights when he or she is the last person to leave the building.
and
No, no employee of Company X should have the authority to turn off the lights when he or she is the last person to leave the building.
In the poster's original example, readers face the same interpretative choice between any as "every" and any as "even one." To avoid the ambiguity, you would have to reframe the question in a way that clarified which sense of any you intended. For example, you might say
Should every employee of Company X be allowed to assume absolute authority over a project that has Company X's name associated with it?
if you had any = every in mind, or you might say
Should no employee of Company X be allowed to assume absolute authority over a project that has Company X's name associated with it?
if you had any = even one in mind.
Solution 2:
The following are three propositions but reworded slightly different. The first proposition is the OP's one
- Should any (whoever) employee of Company X be allowed to assume absolute authority in any (whatsoever) project with Company X's name associated?
In other words, does it matter who has the authority in a project, as long as the person is an employee of Company X, and the project is connected to the company's name?
— Somebody voting "yes" agrees there should be no constriction other than those previously mentioned.
- Should an employee (specific) of Company X be allowed to assume absolute authority in any (whatsoever) project with Company X's name associated?
Is it permissible for an employee of Company X to assume authority in any single project, as long as that project is connected with the company's name on it?
— A person voting "yes" agrees that an employee should be given the opportunity to take charge in a project that has the company's name connected to it.
- Should an employee (specific) of Company X be allowed to assume absolute authority in a project (specific) with Company X's name associated?
Could an employee (under special circumstances) be given the opportunity to take charge in a project, if that project is connected with Company X's name?
— A person voting "yes" agrees there may be instances when this authority may be granted to an individual employee.