[EM] Voting Criteria 101, Four Criteria

Jameson Quinn jameson.quinn at gmail.com
Sun Jun 16 13:43:43 PDT 2013

2013/6/16 Benjamin Grant <benn at 4efix.com>

> ...I would like to explain what I understand about some of these voting
> criteria, a few at a time...

Thanks for doing this, and again, welcome.

*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.

I think that most here would agree with what you've said.

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

Presumably, by "preferred", you mean "preferred over all others". This
definition is actually a bit controversial. I'll explain, but I have to go
back a bit. Note that all that follows is my personal opinion; it's far too
opinionated to pass muster at Wikipedia, and though I suspect that some
here would agree with most of it, I'm also sure that others will chime in
to debate me on some points.

The modern science of voting theory begins with Kenneth Arrow in the 1950s.
I happen to be reading Kuhn (*The Structure of Scientific Revolutions*) at
the moment, so I'll use his terms. Before Arrow, the study of single-winner
voting systems was disorganized and unscientific; though figures such as
Maurice Duverger and Duncan Black had important insights into the
incentives of plurality on parties and voters, they could offer little
guidance as to how to improve the situation. Arrow offered the first
paradigm for the field. The Arrovian paradigm is essentially preferential,
and it tends to lead toward Condorcet systems as being "best".

>From its very beginning, Arrow's own theorem marked sharp limits to how far
you could go within his paradigm. Nonetheless, as Kuhn quotes from Bacon,
"error leads to truth more quickly than confusion"; that is, even a flawed
paradigm is immensely more productive than prescientific disorganization.
For instance, the important Gibbard-Satterthwaite theorem on strategy
followed close on the heels of Arrow's result.

Since Arrow, there have been other paradigms advanced. Around 1980, Steven
Brams suggested Approval Voting, a simple idea which prior to that had been
used but never theorized. This was clearly a step out of the Arrovian
paradigm, but it didn't quite yet offer an alternative basis for further
research and refinement. Donald Saari then reacted against approval by
advancing a paradigm based on ordinal ballots and mathematical symmetry
(and thus, Borda voting); in my opinion, his willful ignorance of strategic
issues makes his way of thinking ultimately counterproductive, though some
of the tools he created are useful.

So the first person to offer a truly fertile alternative to the Arrovian
paradigm was, in my opinion, Warren Smith (active on this list), with his
1999 paper on Range Voting. This system, now mostly called Score Voting,
goes beyond approval to allow fractional ratings. The division between
Arrovian, preferential systems, and Score-like systems has been expressed
using multiple terms: ranked versus rated (with rated systems sometimes
further subdivided into rated or graded); ordinal versus cardinal;
preferential versus ???; and my own favorite terms, comparative versus

Since Smith, there has also been work in yet another paradigm, that of
delegation. The DemoEx party in Sweden, the study of Asset voting, liquid
democracy, delegable proxy, delegated yes-no (DYN), the revival of interest
in Dodgson's 19th-century proposal for delegated proportional
representation, and most recently my own proposal Simple
Optionally-delegated Approval (SODA) all lie in this line of inquiry.

Still, as always, there are some who continue to mine the vein of the old
Arrovian paradigm, and it can't be said that that vein is entirely played
out. The new paradigms also remain much less well-established academically;
for instance, Smith's seminal paper has never been published in a
peer-reviewed journal.


So all of that history is a backdrop for the debate over how to apply the
definitions of such criteria as Majority and Mutual Majority to evaluative
systems. Your definition of Majority uses the word "preferred", which
inevitably biases it towards ranked thinking. An advocate for evaluative
systems, like myself, would argue that it would be better to say "voted as
favorably as possible". This distinction makes no difference at all for a
comparative system — a candidate who is preferred over all others is, by
definition, at the very top of any purely comparative ballot — but it
allows a level playing field on which evaluative systems can aspire to pass
this criterion as well. Of course, partisans of the comparative Arrovian
paradigm argue back with what seem to me to be unproductive semantic
arguments: the criteria were originally defined in an earlier era, with
reference to comparative systems, so any extension of them to cover
evaluative ones is argued as illegitimate.

> ****
> *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,

(Note: these days the term Score Voting is preferred.)

>  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??

Your example uses the ranked definition of the majority criterion. In the
rated definition I'd favor, neither group of voters is rating their
candidate at the top rating, so the majority criterion simply does not
apply. But simply change the the rating of A proponents from 90 to 100, and
the rated definition applies, so you've shown that Score voting doesn't
pass majority under any definition. A score proponent would argue that a
win by B would be the best result in this situation, because it would
(probably) maximize total social utility; the large extra utility for the
minority who prefer B is more than the small loss of utility for the
majority who prefer A.

> ** **
> *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.

> ****
> ** **
> *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 criteria?

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.

> ****
> ** **
> *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?

Not quite. A system which satisfied IoC could, in theory, shift from clone
X1 to X2 when another candidate (either an X3 or a Y3) entered the race,
which would violate IIA. And a system which satisfied IIA could, in
principle, shift from clone X1 to a newly-entering clone Y2, even though a
clone Y1 had already been in the race. I'm not offhand aware of which
systems would fall into these corners of the Venn diagram, but you are
mostly right: the large majority of systems which pass IoC also pass 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
> wrong.

Looking forward to your further posts. I encourage you to look next at some
strategic criteria: favorite betrayal, later-no-harm, and later-no-help. I
have strong opinions about which of those are important or not, but I'll
let you take your own look first.


> ****
> ** **
> Thanks.****
> ** **
> -Benn Grant****
> eFix Computer Consulting****
> benn at 4efix.com****
> 603.283.6601****
> ----
> Election-Methods mailing list - see http://electorama.com/em for list info
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