[EM] Voting Criteria 101, Four Criteria

Benjamin Grant benn at 4efix.com
Sun Jun 16 09:55:26 PDT 2013

With your kind indulgence, I would like some assistance in understanding and
hopefully mastering the various voting criteria, so that I can more
intelligently and accurately understanding the strengths and weaknesses of
different voting systems.


So, if it's alright, I would like to explain what I understand about some of
these voting criteria, a few at a time, perhaps, and perhaps the group would
be willing to "check my math" as it were and see if I actually understand
these, one by one?


I'll start with what seem to be the simpler ones. (For what it's worth, my
understanding comes from various websites that do not always agree with each
other.  Also, I have the fundamental belief that one cannot consider oneself
to have mastered something until and unless one has the ability to
understand it well enough to explain it to someone else - which is what I
will try to do below, re-explain these criteria as a test to see if I really
get them.)


Name: Plurality

Description: If A gets more "first preference" ballots than B, A must not
lose to B.

Thoughts: If I understand this correctly, this is not a critical criteria to
my way of thinking.  Consider an election with 10 candidates. A gets 13% of
the first place votes, more than any other single candidate. And yet B gets
8% of the first place votes, and 46% of the second place votes. It seems
obvious to me that B "ought" to win. And yet, in this circumstance, this
violates the above Plurality Criterion. Therefor is seems to be that the
Plurality Criterion is not useful, to my way of thinking.


Name: Majority

Description: If one candidate is preferred by an absolute majority of
voters, then that candidate must win.

Thoughts: I might be missing something here, but this seems like a
no-brainer. If over 50% of the voters want someone, they should get him, any
other approach would seem to create minority rule? I guess a challenge to
this criteria might be the following: using Range Voting, A gets a 90 range
vote from 60 out of 100 voters, while B gets an 80 from 80 out of 100
voters. A's net is 5400, but B's net is 6400, so B would win (everyone else
got less).  Does this fail the Majority Criterion, because A got a higher
vote from over half, or does it fulfill Majority because B's net was greater
than A's net??


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.


Name: Independence of Irrelevant Alternatives (IIA)

Description: 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.

Thoughts:  This also seems fairly non-controversial. This I think is the
repudiation of the spoiler effect - that just because Nader enters the race
shouldn't disadvantage the candidate that would have won before that
happened.  This would seem (to me) to also be a good Criterion to hold to in
order to encourage more than just two Candidates/Parties always dominating
the scene.  I wonder what the downside would be to strongly embracing this


Question: It seems to me that another criterion I have heard of -
Independence of Clones(IoC) - is a subset of IIA, that if a system satisfies
IIA, it would have to satisfy the Independence of Clones criterion as well -
is that correct? If not, what system what satisfy IoC but *not* satisfy IIA?


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 mandate the other - for example, a system with IIA must also
fulfill Participation, or vice versa?


So let me stop there for now - I know there are other Criteria, but let me
pause so you guys can tell me what I am getting right and what I am getting




-Benn Grant

eFix Computer Consulting

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


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