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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..

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I think I realized an answer. The Schulze Method traditionally uses BI. But it can be easily modified to use POI instead. All that needs to be done is, when counting how many pairwise preferences there are for candidate A over B, instead of using BI (unranked = preferred less), you use POI (unranked = no preference). Then the rest of the computation goes on as normal.

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