[EM] RCIPE version 2

[Kristofer Munsterhjelm]

On 27.07.2021 00:16, Richard, the VoteFair guy wrote:
> On 7/26/2021 6:20 AM, Kristofer Munsterhjelm wrote:
>> ...
>> ... Is that right? ...
> 
> Your calculations are correct.

Then that's just Borda. Congrats, you've reinvented Borda-elimination :-)

Well, it's not quite Borda-elimination since the early elimination of a
Condorcet loser may reshuffle the order of later eliminations, and due
to the same effect that causes nonmonotonicity in elimination methods,
lead someone else to win.

But ordinary Borda-elimination does eventually remove every Condorcet
loser, so it should have little effect on your criterion compliances.

In particular, although if I were selfish I shouldn't point this out,
Borda-elimination passes Condorcet and the Condorcet loser elimination
stage doesn't change that. Since your simulator says that it doesn't
pass Condorcet, I would view its other results with some suspicion,
particularly given how it's also been wrong about clone independence.

But, since your method is pretty close to Borda elimination, and Borda
elimination also eliminates Condorcet losers as a matter of course[1],
you could simplify it (if you want to retain its Borda-elimination
nature) into this:

1. Determine the candidate with the fewest arrows, and eliminate that
candidate. Break ties by IRV (and further ties by Ext-Minmax).
2. Repeat from 1 until a single candidate remains. That candidate is the
winner.

Even if you don't want to, you could run tests comparing this simplified
version to the one with Condorcet loser elimination - though as
mentioned, I wouldn't be too confident of the results.

As for Condorcet winner, what I was objecting to (besides me being a
Condorcetist and preferring Condorcet) is that there doesn't seem to be
a principled approach to your methods' violation of CW. You used a
bicycle metaphor: but the attempt to deliberately avoid Condorcet winner
seems like removing the chain (and subsequently creating a
penny-farthing) just so that you can say that it's not a bicycle,
because the pedestrian organization (FairVote) dislikes bicycles.

If you're deliberately setting out to not make a bicycle because
bicycles aren't liked, you should create something that's consistently
not a bicycle: that gets some kind of return for not being a bicycle,
and then has more of a justification of what a good winner is than "this
isn't Condorcet, but you can see Condorcet from here".

Consider something like a method that explicitly eliminates the
Condorcet loser, and where the base method otherwise does not pass
Condorcet. Then the elimination method will pass Condorcet when there's
an unambiguous order of losers (X is the loser, Y beats only X, Z beats
only Y and X, etc.). The iterated Condorcet losers provide a
straightforward order of candidates from most relevant to least
relevant. But now introduce a cycle somewhere "downstream" of the
winner. Then by introduction of such a cycle, the Condorcet winner may
be eliminated early (depending on how the method is constructed). It's
difficult to see why that should make a difference; I'd say you'd need
some kind of explicit reason for why something that appears irrelevant
(the relation between people who would otherwise be losers) matters.

In any case, I don't think FairVote itself would support your method as
long as it's not IRV. They're first and foremost an advocacy
organization focused laser-like on IRV and STV, and as your method isn't
it, they probably won't support it. But even being generous that their
"Core Support criterion" isn't just a fig leaf (see my post to Forest),
any method that is Condorcet in the "straight line scenario" above must
by necessity fail that criterion.

Now, don't get me wrong: I don't think passing Core Support would win
them over - because again, their thing is IRV. I'm more just
re-emphasizing that a method that fails Condorcet should have some
reason for doing so. (E.g. you can get very close to Condorcet while
still passing the favorite betrayal condition - then passing the FBC
becomes the reason.)

-km

[1] For that matter, every sequential elimination method that respects
majority rule will also pass Condorcet Loser, because in the worst case
that the Condorcet loser remains until the final round, the other
candidate will by definition beat the loser in the final round.