Say there are 5 candidates, A, B, C, D, and E. An election is held using a ranked voting method. That is to say, each voter submits a preference list (the order in which they prefer candidates). E.g. A > B > C > D > E could be my preference list.
For most election schemes, a voter is allowed exclude candidates from their preference list. This usually means that the excluded candidates are their least preferred (with no particular preference between them). E.g. A > B > C implies that both D and E are equally worse than all the other candidates. I will call this the Bottom Interpretation (BI).
However, I think there's another plausible reason one should be able to exclude a candidate: if they are not familiar with that candidate, and therefore do not know how much they prefer it with respect to the candidates they do know. For example, if D and E are movies I haven't watched, then I want excluding them from my list (A > B > C) to signify that they could potentially be ranked anywhere in my list, not necessarily at the bottom. I will call this the Partial-Ordering Interpretation (POI).
Is there any election scheme that uses POI when deciding its winner/ordering for the candidates? For an example of what a election scheme that does this should look like:
- 99 voters say A > B > C > D, leaving out E
- 1 voter says that E > A, leaving out the rest
In this case, a scheme that uses POI will decide upon a final ordering of E > A > B > C > D. On the other hand, a scheme like instant-run-off voting (IRV) will decide on a final ordering of A > B > C > D > E, because IRV uses BI..
