If you are on a hiring committee and find out that one of the applicants is someone you have had a past romantic relationship with, should you recuse yourself?
I will almost guarantee that your university has a Compliance office. Here's the one for my university; you'll notice that it has both a number of links to written guidelines, as well as phone numbers for an Ethics hotline. Your university may not have the exact same thing, but there are people there whose job is to answer these types of questions. Make use of them.
That said, from my completely uninformed standpoint, your situation sounds like a conflict of interest. If I was in a similar situation I would definitely recuse myself.
From my own experiences on faculty search committees, administrators would be very unhappy if we went through the hiring process and I later provided such information, since it could be viewed as a conflict of interest or nepotism, even if you do not see it that way. What do you have to lose by making this information known to others and at least see if the administrators in your department believe that you should or should not continue on the committee.
Also, who doesn't search for a good reason to get out of committee work? LOL.
You almost certainly need to remove yourself from any decision about that candidate, especially if your interactions were recent, and you may need to remove yourself from the whole process. It has nothing to do with whether you can live with it, but if your university wants to risk litigation if the shit hits the fan.
You can simply say "I have a conflict with one of the applicants, and wish to be removed from this committee", and then the nature of the conflict is your business alone, or you can find the appropriate person to discuss the exact nature of the conflict with. I suggest a compliance officer or ombudsman, who will be able to understand the sensitive nature.
My university requires members of search committees to disclose any potential conflict of interest in connection with their evaluation of job candidates. The disclosure form is accompanied by an explanatory text titled "Aspirational Principles and Guidelines Regarding Conflict of Interest on Recruitment Committees", which states in particular (emphasis added by me):
Examples of situations that might create either a real or perceived conflict of interest for a member of a recruitment committee include, but are not limited to, the review of candidates who are current or former students, postdocs, mentees, co-authors, close collaborators or partners in a business or professional practice. Other situations may involve review of a candidate who has or has had in the past, a significant personal relationship with the faculty member, either positive or negative, that might impact the ability of the faculty member to participate objectively in the comparison of the qualifications of that candidate with those of other candidates.
The document goes on to list options for dealing with a potential conflict:
Depending on the nature of the relationship, and based on discussion with the recruitment committee chair, the faculty member may:
Voluntarily recuse him or herself from participation on the recruitment committee or in the review and selection process;
Voluntarily recuse him or herself from discussion and/or voting on the particular candidate with whom there is a potential real or perceived conflict of interest;
Continue to serve on the committee and in the review/selection process, but with full disclosure of the relationship to the committee and, if the candidate is on the short list, to the department;
Thus, at the very least, in the scenario you describe you are certainly required to report the fact of the past relationship to your department chair and other members of the committee. Given the nature of the relationship, I would expect that you would also be asked to recuse yourself from any discussion of the specific candidate, and possibly to recuse yourself entirely from membership in the committee.
All of this is according to my university's specific policy, but this policy is based on currently accepted legal and ethical norms in the United States that I would expect to also apply in any major US university. I also doubt that these norms will be materially different in any western country.
I would, without question. The benefits of being seen to act in a way that leaves no doubt as to integrity will far outweigh the probably-zero benefits of sitting on a committee that's making a career decision on behalf of your employer and for a past romantic flame of yours. I can't see any good whatsoever coming out of putting yourself in that situation, and plenty of respect from being seen to avoid the conflict. Recuse without question, citing "non work previous social friendship with the candidate" or similar (you don't need to give the detailed reason)