[EM] Voting Criteria 101, Four Criteria

Benjamin Grant benn at 4efix.com
Mon Jun 17 09:07:34 PDT 2013

OK, now on to the questions and responses on the other Criteria:



From: Jameson Quinn [mailto:jameson.quinn at gmail.com] 
Sent: Sunday, June 16, 2013 10:36 PM
Subject: Re: [EM] Voting Criteria 101, Four Criteria

In which case it (I think) becomes even more obvious and pointless as a
criteria (as any system that gave the victory to people who get less votes,
however we are counting and measuring votes, would make no sense, I think.)

>>Name: Participation

>>Description: If a ballot is added which prefers A to B, the addition of
the ballot must not change the winner from A to B

>>Thoughts:  This seems to make sense. If we do not require this, then we
permit voting systems where trying to vote sincerely

>>harms your interests. Also, any voting system that would fail
Participation would be I think fragile and react in not always 

>>predictable ways - like IRV. SO this seems to me to be a solid
requirement, that I can't imagine a system that failed this 

>>Criterion to have some other benefit so wonderful to make failing
Participation worth overlooking - I cannot imagine it.


>You have fairly described the participation criterion. I would ask you to
consider that this criterion focuses only on the 

>direction of preference, not its strength; and so it is inevitably biased
towards preferential systems, and dooms you to live 

>within the limits set by Arrow's theorem. My two favorite systems - SODA
voting and the as-yet-unnamed version of 

>Bucklin - both fail this criterion, though I would argue they do so in
relatively rare and minor ways, and both satisfy some 

>weakened version of the criterion.

 I don't understand how a bias exists here. In every case I can currently
imagine, if an election as it stands has A winning, and one more ballot is
added which still prefers A to B, why should that ever cause the winner to
change to B?

Range/Score Voting: If A is winning, and the following ballot was added
(A:90, B:89) A would still be winning.  If IRV is being used and the
following ballot is added (D first place, A second place, B third place) we
wouldn't want B to suddenly be beating A. (Although in IRV I guess it could
happen, but the point is that we wouldn't want it to, right?)

This seems to be a serious issue. Whatever the voting method, if A is
currently winning, and one more ballot gets added that happens to favor A
with relation to B, how could it EVER be a good thing if B somehow becomes
the winner through the addition of that ballot?

I don't understand what bias has to do with the answer to that question?

Also, how could Bucklin (as I understand it) *ever* fail this one? Because a
ballot added that favors A to B under Bucklin would at minimum increase A by
the same amount as B, possibly more, but would *never* increase B more than
A, else the ballot could not be said to prefer A over B, right?


OK, that's several questions.


When would participation failure ever be a good thing? It wouldn't. But in
voting theory, tradeoffs are common. A system which had other desirable
features could fail a reasonable-sounding criterion, and if that failure is
minor and/or rare enough, that could still be a good system. I'd argue that
that's the case for Bucklin systems and the participation criterion. Though
there are certainly many people here who would argue with me on that
specific point, the fact is that choosing any system involves making


So, how does Bucklin fail participation? Imagine you had the following
votes, giving candidates X and Y grades A-F


49: X:A   Y:D

50: X:F   Y:D


The bloc of 50 voters is a majority, so they set the median. Or in Bucklin
terms, Y reaches a majority at grade D, while X doesn't until grade F, so Y


Now add 2 votes with X:C Y:B. Now, X reaches a majority at grade B, while Y
still doesn't until grade D. So now X wins, even though those votes favored
the prior winner Y.


I find this specific example implausible for multiple reasons, and think
that actual cases of participation failure would be very rare. For instance,
those last two voters could have voted X:F Y:B, and honestly expressed their
preference without changing the result.


OK, first of all, my brain does not seem to be able to handle letters on
both sides of the colon (":"), so with your permission, let me alter the
typography of your example, hopefully functionally changing nothing:


49: X:1st   Y:4th

50: X:5th   Y:4th


So if I understand this right, under Bucklin, we look at all 1st place votes
(we need at least 50), and see if we have over half - we don't, so now we
look at all 2nd, still no, all 3rd, still no, and only when we consider 4th
place do we finally have enough votes for candidate Y to have enough to win.


Now we add two votes:


2: X:3rd   Y:2nd


Now we repeat the process, not enough 1st place votes (we need at least 51),
not enough 2nd place votes, and adding in 3rd place we now have 51,
precisely what we need for X to win.


OK I think I see what you mean.  That does show that with this system,
adding in more ballots, even if those ballots prefer Y to X, can still
change the outcome that would have been Y to X.  I don't like that at all.


It's moments like these that make me want to give up on even trying to
pursue fair voting systems.  Grrr..


I will think about this more, I really hate the idea that even theoretically
it might be possible to add a ballot that prefers a candidate, and have that
hurt the candidate. A lot.


Also, as much as possible, for the sake of my brain, if you can avoid using
letter grades in these examples, it will help me.  Or I can simply try to
translate like I did above to the best of my ability.

 >> IIA, on the other hand, strongly favors evaluative systems, because in
comparative systems the entry of a new candidate 

>>can inevitably change the absolute ranking levels of existing candidates.
I think that IIA is certainly a nice thing to pass, \

>>but I'd hesitate to make it a sine qua non.

Independence of Irrelevant Alternative (IIA): Adding a new candidate B to an
election that previously A would have won must not cause anyone apart from A
or B to win.  That is, if A would have won before B was added to the ballot,
C must not win now.

Again, I seem to be missing something here.  If you are running an election
with whatever method, and A would win, but then B enters the race, I can get
A still winning.  I can get B leaping ahead somehow and winning.  What I
cannot understand is how a candidate that A was beating before B's entry,
somehow A now loses to. At least I cannot understand how any system that
fails this criteria could still be worth considering - how the outcome of A
beating C *until* B enters the race, after which C wins, is desirable. Is
there some example that explain how this turn of events could be somehow
fair or sensible?

Again, it's a matter of tradeoffs. The systems I favor happen to meet IIA,
but some people here think the Condorcet criterion, which is incompatible
with IIA, is more important than it.


Is it a well-established fact that Condorcet is incompatible with IIA? That
you cannot have both?


Independence of Clones: since you are saying that IoC is not equivalent with
IIA, I will take up IoC independently along the way in a later set of

I still am curious about this question:

Question: it seems like the two above criteria - Participation and IIA -
would be related. Is it possible to fail one and not the other? Or does
either wind up mandating the other - for example, a system with IIA must
also fulfill Participation, or vice versa?


They are independent criteria.


OK, then I will take up IoC separately and later.


-Benn Grant

eFix Computer Consulting

 <mailto:benn at 4efix.com> benn at 4efix.com



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