[EM] Voting Criteria 101, Four Criteria

[Jameson Quinn]

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

> Re: Majority Criteria:****
>
> ** **
>
> To be honest, I am worried that some (or all) of your history lesson
> regarding Arrow might not have landed as well as it should in my brain.
>

Sorry. Sometimes I tend to try to say things too succinctly, and end up
leaving my meaning a bit locked up in jargon or terminology. If you have
any specific questions about the "history lesson" I'd be happy to expand.


> I can say that one of the things I may need help on is the wording of the
> criteria, so if “preferred” is not the right word, then we should use
> something else.
>

For a rated majority criterion: "top-rated". For a rated mutual majority
criterion: "rated above a given threshold".

> ****
>
> ** **
>
> However, I **think** the base idea is the idea that if over 50% of a
> group want a candidate to win, they should get that candidate.  What is
> more murky to me – and perhaps more than me – is how you decide whether or
> not that is being violated in systems that are more complex.
>

The point is that if I can use any score from 0-100, and yet the majority
gives candidate X only (say) 20, or even 99; even if they give all other
candidates even lower scores, the majority criterion shouldn't apply.

For Score Voting, it doesn't matter, because as you showed, score voting
doesn't satisfy the majority criterion anyway. But for rated Bucklin, it
could matter.

> ****
>
> ** **
>
> I guess I would say at a minimum, that if one is using Range Voting (which
> I think you are saying is called Score Voting by the list);
>

Right. Both "Score" and "Range" are understood, but these days, most prefer
"Score".

 freely assign a score of 0 to the maximum amount to each candidate (say
> 100), the candidate with the greatest aggregate score wins) let me see how
> this might fail.  Let’s say out of 1000 people 550 give candidate A scores
> of “100”. Then let’s say that 700 people give candidate B scores of “80”
> each. Let’s also say that everyone else falls short of either of those
> totals.  A gets 55,000 total, B gets 56,000.  B wins.
>

Right.

> ****
>
> ** **
>
> On the one hand, one could say in one sense this violates Majority, but in
> another sense one could perhaps with even more justification claim that B
> actually has the larger majority.  Or maybe to put another way, Majority
> criteria only applies to voters when the system is one person, 1 vote –
> others perhaps Majority criteria applies to **votes**, not voters.****
>
> ** **
>
> In other words, maybe Majority criteria should be worded thusly: *If one
> candidate is preferred by an absolute majority of *votes*, then that
> candidate must win.*
>

That would be stretching the criterion to the point of meaninglessness. The
majority criterion speaks of voters, and Range doesn't pass, but Bucklin
systems do.

The more controversial case for this criterion is approval. Some try to
define the criterion so that an internal preference which doesn't fit on
the ballot is enough to constitute a "majority"; others prefer to define it
so that a "majority" only means anything in terms of the ballots
themselves. I tend to side with the latter as a matter of definition, but I
certainly understand that as a practical matter approval's passing of the
majority criterion leaves much to be desired.

> **
>
> ** **
>
> 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
tradeoffs.

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
wins.

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.

****
>
> ** **
>
> >> 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.


> ****
>
> ** **
>
> 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
> criteria.****
>
> ** **
>
> 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.


> ****
>
> Thanks for your time and help – and please, anyone who wants to chime in,
> please do so, this is not just a conversation between myself and Jameson,
> but between me and the community her.****
>
> ** **
>
> Thanks! J****
>
> ** **
>
> -Benn Grant****
>
> eFix Computer Consulting****
>
> benn at 4efix.com****
>
> 603.283.6601****
>
> ** **
>
> *From:* Jameson Quinn [mailto:jameson.quinn at gmail.com]
> *Sent:* Sunday, June 16, 2013 4:44 PM
> *To:* Benjamin Grant
> *Cc:* election-methods at lists.electorama.com
> *Subject:* Re: [EM] Voting Criteria 101, Four Criteria****
>
> ** **
>
> ** **
>
> 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
> evaluative.****
>
> ** **
>
> 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.****
>
> ** **
>
> Cheers,****
>
> Jameson  ****
>
>  ****
>
> 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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