[EM] Plurality criterion and the "sincere CW"

C.Benham cbenham at adam.com.au
Mon Jul 1 13:32:39 PDT 2019 

Juho,

> If vote A>B=C is not the same as vote A in a three candidate election, 
> then there is an implicit cutoff at the truncation point. (Or maybe 
> someone wants to put the special "given any preference" point after A 
> in the first vote.)
To be clear, I interpret "vote" as meaning vote above at least one other 
candidate and not just any mark or number next to a candidate's name on 
the ballot paper.
> Ranked methods work well only if voters give us their preferences (of 
> all the relevant candidates)
As long as the truncation incentive isn't stronger than the voters like 
and generally the incentives for voters to misrepresent their true
preferences are as low as possible then if voters choose not reveal 
their weaker preferences that should be no problem.

> But when reading the definition, a natural thought is that if you do 
> not rank some of the candidates that you don't like at all, that might 
> improve the chances of your favourite candidates to win.
Yes, it might or it might not. No-one suggests that the Plurality 
criterion should be posted in the polling booth.

> One quite possible (real life?) risk is that competing factions start 
> truncating the candidates of the other factions. That might lead to 
> bad results.
Yes, I suppose it could lead to slightly "bad" results. But I think it 
is more likely to lead to relatively good results. Generally speaking I 
would guess that
pairwise preferences among candidates the voter "doesn't like at all" 
would be weaker, probably less well-informed, if the method meets 
Later-no-Harm
the preferences could be light-minded (almost arbitrary). That could 
result in a winner with relatively low Social Utility and less 
legitimate-looking.

And of course since all Condorcet methods have some Burial incentive, 
preferences among candidates the voter doesn't like are less likely to be
sincere in any case.  So arguably we should err on the side of trying to 
avoid a "garbage in, garbage out" scenario rather than fret about electing
the candidate who would be the CW if only the voters could be induced to 
reveal their sincere full rankings.

>> 46: A
>> 44: B>C
>> 10: C
>>
> To people who are used to methods where the first positions are the 
> key thing, and that's everything that is important in the election, 
> these votes seem to say that A is the strongest of the candidates.
Here you are somewhat missing the point again. It's not just "first" 
positions, it's *any* (above bottom) positions.  And it's not that A is 
"the strongest
of the candidates". It is that A is so much stronger than B that 
electing B can't be justified.  The Plurality criterion says nothing 
about C.

> Since information given in the votes above is very limited, we can 
> imagine various reasons why all A and C supporters truncated their vote.
It would be much more to the point if you instead try to "imagine 
various reasons" why all the B supporters didn't.
> One way to see those votes is to ask what would happen if A, B or C 
> wins. There would be an interest to change B to A, but just a small 
> interest.
That is "one way" which I regard as very stupid and completely reject. 
Instead of scratching your head wondering why the A and C supporters
deprived us of so much "information", why don't you seriously consider 
the possibility that the B supporters' ranking of  C is completely 
insincere?!

With no explicit approval (or any other sort of ratings) information the 
best winner is arguably C.  Then the 46 A voters have no strong complaint: C
pairwise beats A, C is voted above bottom on more ballots than is A.  
The 44 B>C voters have no complaint: if they hadn't ranked C then A 
would have
won, if they really prefer A to C then it serves them right for telling 
lies.

But electing B and then telling the A supporters "If only two of you 
later change your A>B preference to B>A then everything will be ok, and 
maybe
the B supporters were all sincere in ranking C and it was just their 
good luck that doing so caused their favourite to be elected instead of 
yours" to
me just doesn't wash.

> I'd like my favourite method to meet all the sensible sounding 
> criteria. Unfortunately that is not possible. My philosophy is that 
> the best method might violate all of the mutually incompatible useful 
> criteria a bit, but only so little that those violations do not cause 
> any problems in practice.

So have I been wrong in assuming that you insist on compliance with the 
Condorcet criterion?

Chris Benham

On 1/07/2019 5:38 pm, Juho Laatu wrote:
> I guess the key point that I was referring to is that if you read the 
> definition verbally, it has words "votes in total". Or the wikipedia 
> version of the definition 
> (https://en.wikipedia.org/wiki/Plurality_criterion) has words "given 
> any preference". Usually people talk about "truncation" of the vote. 
> That seems to indicate that the point of truncation has some special 
> meaning (in addition to just indicating that the unlisted candidates 
> should be seen to be in the "shared last" position in the pure rankings).
>>
>> So what is the point of the Plurality criterion?  To my mind it is 
>> simply about not offending obvious fairness and common-sense.
>>
> I believe that is the case. I just don't like the idea of giving the 
> truncation point any special meaning. If vote A>B=C is not the same as 
> vote A in a three candidate election, then there is an implicit cutoff 
> at the truncation point. (Or maybe someone wants to put the special 
> "given any preference" point after A in the first vote.) Different 
> methods may meet this criterion in different ways (some trivially). 
> But when reading the definition, a natural thought is that if you do 
> not rank some of the candidates that you don't like at all, that might 
> improve the chances of your favourite candidates to win. (Also if 
> there is a fourth totally hopeless candidate D, those two votes should 
> be in practice similar, in all typical methods in which the existence 
> of D has no effect on the outcome, or otherwise they seem to have a 
> meaningful implicit cutoff.)
>
> My philosophy is thus that pure ranked votes are pure ranked votes 
> (usually completed so that unlisted candidates are seen as "shared 
> last"). If methods derive some (cutoff like) additional information 
> from the ballots, then I typically prefer methods where that cutoff is 
> explicit (not implicit at the truncation point). And the reason is 
> that I want to see complete rankings (of all the relevant candidates) 
> instead of truncated (= lost) preferences. Ranked methods work well 
> only if voters give us their preferences (of all the relevant 
> candidates). One quite possible (real life?) risk is that competing 
> factions start truncating the candidates of the other factions. That 
> might lead to bad results. For these reasons the idea of rewarding 
> truncation in some cases is not a very good idea. Sometimes it may be 
> acceptable though, just like violations of most criteria sometimes 
> are, if there are no better ways available around the problem in question.
>>
>> 46: A
>> 44: B>C
>> 10: C
>>
> To people who are used to methods where the first positions are the 
> key thing, and that's everything that is important in the election, 
> these votes seem to say that A is the strongest of the candidates. 
> Condorcet methods (that I guess we are mainly discussing here) however 
> can be said to aim at electing the best compromise candidate. That 
> candidate might not have any first preference supporters, and still be 
> a Condorcet winner. Since information given in the votes above is very 
> limited, we can imagine various reasons why all A and C supporters 
> truncated their vote. One way to see those votes is to ask what would 
> happen if A, B or C wins. There would be an interest to change B to A, 
> but just a small interest. One may consider the interest to change the 
> others to some other candidate to be stronger.
>
> If there is a Condorcet winner, as in votes 49: A>>>B>C, 03: B>A>>>C, 
> 48: C>>>B>A, one could ask the voters, would they prefer to change the 
> winner to B, if A or C would win. B may not be very popular, but maybe 
> still a better choice than electing one of the more "extreme" 
> alternatives. If people want the first preferences to have a strong 
> influence, they might prefer methods like IRV (where candidates with 
> small amount of first preferences support may often be eliminated 
> quickly.). Having that kind of a "cutoff" would be another interesting 
> discussion.
>
>> If voters decline to (or don't bother to) express some or all of 
>> their very weak (possibly light-minded) pairwise preferences by 
>> truncating, then I don't classify that as "insincere" voting
>
> I would not call those votes "insincere" either. But they would be 
> "incomplete", and possibly "lazy" in some cases. It is not important 
> to give opinions on the "irrelevant" candidates, but it is important 
> to give opinions on the "relevant" candidates (unless one really 
> thinks they are tied).
>
>> Since therefore there could be several (or even many) alternative 
>> "sincere voting" profiles it follows that there could be more than 
>> one "sincere CW".
>
> I wouldn't say so. There would be only (max) one sincere CW, based on 
> what we know about the opinions of the voters. Information that is not 
> there is not information to the method. Next day voters might vote 
> differently, but that would be another day, and possibly another CW.
>>
>> Later-no-Help criterion ...
>>
> I'd like my favourite method to meet all the sensible sounding 
> criteria. Unfortunately that is not possible. My philosophy is that 
> the best method might violate all of the mutually incompatible useful 
> criteria a bit, but only so little that those violations do not cause 
> any problems in practice. It is however possible that a method like 
> that would be quite complex. I put some considerable weight also on 
> simplicity and understandability, so I might prefer some simpler 
> method instead of the "theoretically optimal" one. I also often tend 
> to emphasise performance with sincere votes in cases, since in many 
> elections strategic voting may not emerge even if there are some small 
> theoretical possibilities of some strategy possibly being successful 
> sometimes. It is important to elect the best winner (= performance 
> with sincere votes), and not tweak the method to do something else 
> because of some far fetched strategy concerns. Often the situation is 
> thus such that there is no need to defend against strategies that are 
> not likely to emerge and succeed anyway. Different elections have 
> different needs. A repeated competitive poll among few EM strategy 
> experts is different from a public election with millions of voters, 
> clear frontrunners, and a wide mixture of continuously changing opinions.
>
> Juho
>
>
>> On 30 Jun 2019, at 19:00, C.Benham <cbenham at adam.com.au 
>> <mailto:cbenham at adam.com.au>> wrote:
>>
>> Juho (and interested others),
>>
>> The Plurality criterion was coined in 1994 by Douglas Woodall. 
>> Quoting him exactly from then:
>>
>>> The following rather weak property was formulated with single-seat 
>>> elections in mind, but it makes sense also for multi-seat elections 
>>> and, again, it clearly holds for STV .
>>>
>>> Plurality. If some candidate /a/ has strictly fewer votes in total 
>>> than some other candidate /b/ has first-preference votes, then /a/ 
>>> should not have greater probability than /b/ of being elected.
>>> *
>>> *
>> No mention of any "implicit approval cutoff".  I know that at the 
>> time Woodall was only thinking about strict rankings from the top 
>> with truncation allowed.
>> If equal-first ranking is allowed, then for the purpose of this 
>> criterion we should be using the fractional (summing to 1) 
>> interpretation of the number of
>> "first-preference votes".
>>
>> Juho seems to think that the Plurality criterion is a "feature" or 
>> strategy device  that somehow encourages truncation.  It isn't and 
>> doesn't.
>>
>> If the method uses one of the traditional Condorcet algorithms that 
>> are almost the same as each other (Smith//MinMax, Schulze, River, 
>> Ranked Pairs)
>> and uses Winning Votes as the measure of pairwise defeat strength, 
>> then the method meets Plurality and also has, at least in the 
>> zero-info case, a weak
>> *random-fill incentive.
>> *
>>
>> IRV, and IRV modified to meet Smith by before each elimination 
>> checking to see if there is pairwise-beats-all candidate among those 
>> remaining, both meet
>> the Plurality criterion.  In those methods do the voters have any 
>> have any incentive "not to rank the candidates of the competing 
>> groupings" ?  No they
>> don't.
>>
>> So what is the point of the Plurality criterion?  To my mind it is 
>> simply about not offending obvious fairness and common-sense.
>>
>> Juho, try to imagine that you have no interest in or knowledge about 
>> voting algorithms, you've never thought about the split-vote problem. 
>> You are accustomed
>> to voting in plurality elections (or even perhaps Approval elections) 
>> and you've never been interested in doing anything other than voting 
>> for your sincere
>> favourite, who regularly wins.  You are content with the current 
>> voting method and can't see any point in changing it.
>>
>> Now imagine some voting-reform movement succeeds and the new method 
>> is, say, MinMax(Margins).  You hear that voters can now rank more
>> than one candidate and you simply seek assurance that you will be 
>> allowed to go on voting as before and you assume that the government must
>> more-or-less know what it's doing and assume the method won't in any 
>> way be less fair than before.
>>
>> In this election your favourite is A.
>> 46: A
>> 44: B>C
>> 10: C
>>
>> It is announced that the winner is B.  At first you think "A got more 
>> first-preference votes than B, it must have something to do with some 
>> voters'
>> second preference votes", but then you notice that B got the same 
>> number of second-preference votes as A (zero), and then you ask "How 
>> on earth
>> did this crazy new method elect B over my favourite A, who very 
>> clearly got more "votes" (marks next to his name on the paper 
>> ballots) all of which
>> were first-preference votes!"
>>
>> On hearing the reply "Oh, that's because B was the fewest votes shy 
>> of being the Condorcet winner" do you (a) say "Oh how silly of me, 
>> obviously
>> that's fair!" or  (b) say .. something much less understanding and 
>> accepting ?
>>
>> This scenario also works if the old method was IRV.  You might also 
>> notice that this first MMM election scenario is also a massive 
>> egregious failure
>> of the Later-no-Help criterion (because if the B voters had truncated 
>> then B wouldn't have won).  Do you like that criterion?
>>
>> If the old method had been Approval, you would then presumably be 
>> understanding and resigned if it is announced that C won.
>> In fact electing A is a failure of the Minimal Defense criterion. Do 
>> you like that one?   So methods that meet both MD and Plurality (such 
>> as Winning
>> Votes and Smith//implicitA) must elect C.
>>
>>> ... methods might not elect the best winner (sincere Condorcet winner). 
>> If voters decline to (or don't bother to) express some or all of 
>> their very weak (possibly light-minded) pairwise preferences by 
>> truncating, then I don't
>> classify that as "insincere" voting.  Since therefore there could be 
>> several (or even many) alternative "sincere voting" profiles it 
>> follows that there
>> could be more than one "sincere CW".  It seems obvious to me that the 
>> one of of those that is based on only the relatively strong pairwise 
>> preferences
>> will have a higher "social utility" than one based on all pairwise 
>> preferences which include a lot of very weak ones.
>>
>> 49: A>>>B>C
>> 03: B>A>>>C
>> 48: C>>>B>A
>>
>> Say these are the sincere preferences. If the voters care to express 
>> all their pairwise preferences then the "sincere CW" is B, but if 
>> they choose
>> what I consider to be an alternative way of sincere voting and 
>> truncate where that will only "conceal" some weak pairwise 
>> preferences then
>> an alternative "sincere CW" is (the apparently higher Social Utility 
>> candidate) A.
>>
>> In fact if the method used was the tweaked IRV  method with an 
>> explicit approval cutoff that I recently suggested and the cast votes 
>> were
>> 49: A>>B
>> 03: B>A>>
>> 48: C>>B
>>
>> then only C would be disqualified (because A both pairwise beats C 
>> and is more approved than C) and then B is eliminated and A wins.
>> I doubt that there would much blood flowing in the streets caused by 
>> the failure to elect the voted CW (B).
>>
>> As consolation for not meeting the Condorcet criterion we would have 
>> a method much more resistant to Burial strategy than any Condorcet
>> method (and maybe more appealing to people who like IRV).
>>
>> *
>> Juho Laatu* juho.laatu at gmail.com 
>> <mailto:election-methods%40lists.electorama.com?Subject=Re%3A%20%5BEM%5D%20What%20are%20some%20simple%20methods%20that%20accomplish%20the%20following%0A%20conditions%3F&In-Reply-To=%3C06DA7FE6-AAF5-4684-B448-7FD93DCA0E35%40gmail.com%3E>
>> /Sat Jun 29 07:43:29 PDT 2019/
>>
>>> P.S. I don't like the plurality criterion. It actually sets an 
>>> implicit approval cutoff at the end of the listed candidates. The 
>>> worst part of that idea is that it encourages voters not to rank the 
>>> candidates of the competing groupings. That (potentially huge amount 
>>> of missing information) is not good for ranked methods. If voters 
>>> learn to use that feature, methods might not elect the best winner 
>>> (sincere Condorcet winner). 
>>
>>
>>
>> The following rather weak property was formulated with single-seat 
>> elections in mind, but it makes sense also for multi-seat elections 
>> and, again, it clearly holds for STV .
>> Plurality. If some candidate a has strictly fewer votes in total than 
>> some other candidate b has first-preference votes, then a should not 
>> have greater probability than b of being elected.
>>
>>
>> <http://www.avg.com/email-signature?utm_medium=email&utm_source=link&utm_campaign=sig-email&utm_content=emailclient&utm_term=oa-4885-b> 
>> 	Virus-free. www.avg.com 
>> <http://www.avg.com/email-signature?utm_medium=email&utm_source=link&utm_campaign=sig-email&utm_content=emailclient&utm_term=oa-4885-b> 
>>
>>
>> <x-msg://13/#DAB4FAD8-2DD7-40BB-A1B8-4E2AA1F9FDF2>
>
>
> ----
> Election-Methods mailing list - see https://electorama.com/em for list info


---
This email has been checked for viruses by AVG.
https://www.avg.com
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.electorama.com/pipermail/election-methods-electorama.com/attachments/20190702/d3da2ce4/attachment-0001.html>

More information about the Election-Methods mailing list