There are potentially many ways to determine which candidate to eliminate when no candidate has made quota. For example,
The first option is the one most commonly used. But consider a candidate who is no one's first choice but everyone's second choice. They get eliminated on the first round.
I think the last one works if all candidates are ranked. But if there are 10 candidates and every voter but one ranks five with that last voter ranking six candidates, then the one voter gets to determine who is eliminated first – perhaps everyone else's first choice!
I thought that calculating the modified Borda count would solve both problems. It would take into account first, second, etc preferences to arrive at the least popular candidate. But actually implementing it and comparing where it selects differently quickly reveals the fatal flaw. Consider the end of a race where the following candidates remain and we still need to elect two:
|Candidate||1st Pref||2nd Pref||mBorda|
Modified Borda causes large parties to swamp smaller parties.
One could divide by the number of candidates running in the same party, but that seems unsatisfying to me.
It feels like there should be other possibilities here, but no time to research…
The biggest issue, I think, is what to do with only partially ranked ballots.
I wondered about the effect of exhausted ballots on the Representation Effectiveness Scores. I was thinking that someone who didn't bother to list more than, say 2, preferences shouldn't penalize the REI if they didn't elect someone because they didn't really try that hard.
It turns out that the effect was very small. Apparently most people elect someone with one of their first two preferences.