Exhausted-Ballots-First Quota-Filling: Extensions and Applications to No-Quota Systems

Clearly, exhausted ballots should be used to fill as much of the quota as possible before resorting to transferable ballots. But I wonder, can we do better? As I see it, there are two possible rationales for prioritizing exhausted ballots: the obvious (it reduces the number of exhausted ballots) and the less obvious (it’s what the candidate would do, all else being equal). Depending on which of these rationales motivates us, the answer to how best to extend the rule will be different. If the goal is simply to minimize exhausted ballots, we ought simply to remove ballots in reverse order of number of marked hopefuls (i.e. candidates who’ve neither been elected nor eliminated) . But if the goal is to realize the candidate’s prerogative to use those of the votes available to him he chooses (or would choose), I propose quota-filling be governed by the following rules in order of priority:

  1. Candidate’s choice
  2. In reverse order of candidate’s share of MAXes (only applicable if exhausted votes are divided among their maxed choices, who may transfer them freely)
  3. In order of number of marked hopefuls (only applicable if exhausted votes are treated as votes for vacancy)
  4. In reverse order of correlation of scores for hopefuls to candidate’s scores for hopefuls
  5. In reverse order of correlation of scores for winners to candidate’s scores for winners.

We could also apply the above logic to systems without quotas. Phragmen could distribute the winner’s load so as to minimize exhausted ballots while keeping it at least as balanced as it would have been had the runner-up won and maximized balance. In SPAV and its score extensions, only a Porch Quota (i.e. the average of the 2nd through nth highest tallies, n being the number of seats remaining) could be required; scores for the winner could be reduced to 0 on a sufficient number of (current and original) unexhausted ballots to bring the winner’s tally down to the Porch Quota, and the selection of those ballots could be discriminant. Sequential Monroe, which has a vote quota (that is necessarily met) but no score quota, could use a Porch score quota or, at the very least, transfer votes on the cusp of the vote quota discriminately.