[EM] Condorcet How? JL

[Juho]

On Apr 13, 2010, at 4:20 AM, Kevin Venzke wrote:

> Hi Juho,
>
> Ok, I'm writing this as quickly as possible due to a lack of time.
>
> --- En date de : Dim 11.4.10, Juho <juho4880 at yahoo.co.uk> a écrit :
>> De: Juho <juho4880 at yahoo.co.uk>
>> Objet: Re: [EM] Condorcet  How?
>> À: "Election Methods" <election-methods at electorama.com>
>> Date: Dimanche 11 avril 2010, 19h57
>> On Apr 11, 2010, at 7:25 PM, Kevin
>> Venzke wrote:
>>
>>>>> 49 A
>>>>> 5 B
>>>>> 19 B>C
>>>>> 27 C>B
>>>>>
>>>>> It remains bad. I can't see what criticism
>> would
>>>> remain of this, other
>>>>> than saying that in a real election we might
>> be lucky
>>>> enough to have
>>>>> some A voters vote A>B and accidentally
>> give the
>>>> election away.
>>>>
>>>> I'm not quite sure that B should win with this set
>> of
>>>> votes. Note e.g. that the sincere opinion of the
>> five "B"
>>>> voters could be "B>C", and then this example
>> says that
>>>> with WV it is ok if those five voters truncate
>> strategically
>>>> and B wins instead of C.
>>>
>>> Yes, it is okay, because B voters should hardly be
>> able to expect that
>>> they will get full support from C.
>>
>> In this scenario I'd use another explanation. B and C are
>> from left wing parties that always support each others and
>> rank the right wing candidates (A) last.
>
> Well that scenario will probably never happen, but continuing:

There must be some common scenarios with two like-minded candidates  
and one that differs.

>
>> This time the
>> election will be arranged using WV. B supporters note that
>> they can win by not supporting C any more. C supporters do
>> not have the same incentive since they are about to win.
>
> That's only true if C voters behave on autopilot and don't consider
> the specific election they're voting in. Otherwise they have exactly
> the same incentive.

In the example I assumed that polls tell clearly that C is more  
popular than B.

>
>> Truncation is also useless as a counter strategy. In a large
>> public election it is probable that also others than B
>> supporters will know about this strategic opportunity and
>> plan. Candidate B could recommend sincere voting to his/her
>> supporters, or maybe not. But many B supporters might vote
>> strategically anyway. C supporters could truncate but that
>> would be just a revenge that could elect A instead of B. The
>> dilemma is thus that B and C could agree before the election
>> that they will recommend sincere voting and the candidate
>> with more support would win (if left has more votes than
>> right), but they can not control the most eager B
>> supporters, and also B might be happy if some of the
>> supporters will truncate. The situation is unstable. If B
>> wins the election with the help of the truncating voters,
>> what can we do before the next election? Maybe change the
>> method. Maybe try to convince all voters that sincere voting
>> is the best approach for all.
>
> The situation is definitely unstable, that's why I don't advise  
> worrying
> too much about the clone situation.
>
> Teaching people that "sincere voting is the best approach for all"  
> will
> not work because it only takes a few voters to break it, who don't  
> agree
> to both candidates. "Few" meaning enough to prevent a united majority.
>
>> My concerns with WV are not that much related to strategic
>> voting but more to how it picks the winner with sincere
>> votes. There is so much noise in the elections that all the
>> fine tuning requiring Condorcet strategies are not
>> practical. Some WV strategies like the one that I discussed
>> above may be easy to apply, maybe easier than with margins,
>> but I ,ay be a bit biased here and I have not done any
>> thorough analysis of these two approaches.
>
> I don't think the strategies you describe are easy anywhere because  
> they
> rely too much on the information that people wouldn't have. "Noise"  
> and
> such.

The strategy works best with accurate polling information. If one adds  
uncertainty and complexity in the thinking patterns that the voters  
may have, that makes the strategy more difficult to apply.

>
> It's strange that you talk as though voters would have so much  
> information
> needed to make strategic decisions and also think the voters wouldn't
> want to do that and couldn't be coordinated...

I assume large public elections with independent voters to be the  
default environment. In such environments voters usually have some  
reasonably good polls available (their results may differ somewhat and  
opinions may change before the actual election day). I believe typical  
political elections are competitive enough and therefore there will be  
sufficient number of strategic minded voters and they may act if the  
strategy is easy to apply. Coordination attempts will become public in  
public elections. My assumption was that voters are independent, i.e.  
they can not be told how to vote, or at least many of them will not  
follow such central commands. Societies may differ in how eager the  
voters are to accept/reject "strategic guidance". Additional rules  
like mandatory full ranking under the threat that the vote will be  
rejected should be mentioned as part of the method (if there are such  
rules that force voters towards party controlled behaviour).

>
>> ...
>>> Let me say again that having the method simply bomb as
>> a response to the
>>> BC factions failing to unite is not a good idea.
>>
>> My first preference is to make methods good with sincere
>> votes and then hope that the basic structure is robust
>> enough to resist also strategies. If one starts to optimize
>> some method for strategic defence one may easily spoil the
>> performance with sincere votes, one may need new patches,
>> get a complex method etc. Such fixes may in some cases save
>> a method, but often they may bring more problems than they
>> solve problems.
>
> Maybe this is later in your mail, but I still don't understand what  
> you
> mean by performance with sincere votes.

Simply, given sincere opinions and votes that reflect those opinions,  
does the method elect the best possible winner(s).

> The fact that you don't present
> any scenarios about this

I think I did. For example sincere 49: A>B, 49: C>D, 1: D>B could be  
one such example. WV elects D, and that could be considered less than  
perfect performance with sincere votes.

(I however think that different elections may have different targets  
and therefore the best winner could be different in different  
environments. For example the method might put emphasis on finding a  
winner that all like a lot on average, that is strong or that is not  
too much disliked by any.)

> makes me believe that you consider all
> truncation a strategy that would be eliminated by margins,

Definitely I don't believe that margins would be free of strategic  
temptations, and I don't think "elimination of truncation" is any key  
target in margins. And in some sets of votes margins may be worse than  
in WV. But margins is somewhat more appealing to me with sincere  
votes. Also (contrary to what one often hears) I don't believe that WV  
would be mostly superior in the strategic scenarios. The benefits of  
margins are maybe on its "naturalness" and in the fact that despite of  
not being tailored for strategic situations it nevertheless works  
quite well also in strategic environments (maybe partly thanks to not  
being fiddled in any way).

> and so
> therefore a scenario with sincere votes would be resolved exactly the
> same between WV and margins.

I didn't get this. Do you maybe mean that sincere votes would be  
always fully ranked? (This would explain why you didn't find any  
sincere scenarios among the WV examples that I listed.)

>
> The only other thing I can think of is that you are concerned about  
> WV's
> treatment of people who actually want to abstain from a contest and
> be counted as a schizophrenic in the margins style. In that case I  
> suggest
> that those WV voters flip a coin to simulate the margins treatment of
> their vote.

That'd make margins and WV identical and we would not even have to  
name which one of these approaches to measure preference strength we  
are using. I try not to assume anything special on why some voters  
rank some candidates equal (truncating at the end or otherwise tied  
elsewhere). Technically the methods treat all reasons to rank some  
candidates equal the same way (be it strategy, laziness to rank all  
candidates, sincere opinion that the candidates are equal, opinion  
that the candidates are close enough to equal to rank them equal, or  
equality because the voter simply does not know anything at all about  
those equally ranked candidates). The explanation of the vote set may  
assume something about why people voted the way they did but the  
method can not (unless it contains some guidance to the voters on how  
the method / organizers expect voters to vote when they have certain  
feelings).

>
> [and as I've read further I have another suggestion as well.]
>
>> ...
>>>> I'm not quite sure what the intended explanation
>> /
>>>> discussed real life case now is. You say now that
>> they
>>>> expected C to be much weaker than it was, so we
>> are back to
>>>> the scenario where C was unknown. Or maybe the
>> explanation
>>>> is that A and B voters thought that C is weaker
>> than it is
>>>> AND they wanted to make C look even more
>> insignificant by
>>>> not ranking C (although C should not be a threat
>> in this
>>>> election).
>>>
>>> I don't understand the distinction you are making.
>>
>> What I'm after is one stable explanation why the voters
>> felt and voted as they did. If there are multiple possible
>> explanations then I like to analyze them one by one. The
>> situation that I try to avoid is one where one feature of
>> the scenario will be explained using one kind of
>> explanation/arguments (e.g. lack of information on the
>> strength of C)
>
> I would say this is more key
>
>> and another one with another explanation
>> (e.g. interest not to allow third parties grow).
>
> I can't believe I need to propose that a major party doesn't want to  
> help
> another party to grow? One going after the same votes even.

Yes, parties are typically competitive and want to "steal" the votes  
of the others. If there is a special historical relation between two  
established parties and new ones that have earlier been unable to win  
and that might suffer also now because of that legacy, this could be  
mentioned in the explanation.

>
>> One
>> explanation (or several separate) is needed to be able to
>> comment on if the explanation is realistic, if the winner is
>> what it should be, whether the voters have incentives to
>> vote strategically, and how to fix the problem.
>
>
>> ...
>>> So there's no plotting against C. It's the default
>> treatment for a
>>> candidate like C.
>>
>> In this case I'd need to know what category of candidates
>> will get what kind of treatment. I'd thus like to see
>> accurate enough definitions of the situation so that we can
>> agree on what the motivation and expected behaviour of each
>> voter is.
>
> Non-frontrunners, non-major-party.

As you said above, all parties/candidates fight for the same voters.  
Behaviour towards non-frontrunners and non-major-party candidates may  
differ in different societies (used tricks, level of aggressiveness)  
but is of course likely to be competitive.

>
>> ...
>>> There's no point optimizing for an end state if the
>> method isn't likely
>>> to get there.
>>
>> I believe Condorcet methods are typically robust enough to
>> take most societies (close) to the end state.
>
> I know you think that, though I'm not actually sure even WV would.
>
>>> Well, I think the incentives of the method are more
>> important than the
>>> society. Even when voters can't understand the method,
>> the parties will
>>> probably communicate to them the best way to vote.
>>
>> Trying to explain IRV or Condorcet strategies to the
>> regular voters may be difficult, and risky too if people
>> don't like "plotting parties". Societies may have different
>> moral codes. (Some societies may allow pre-filled ballots,
>> and that could make the voters just voting machines of some
>> plotting individuals.)
>
> I highly, highly doubt that candidates will be unable to tell their
> supporters how they should best vote. And I don't think moral codes
> will have much voice in this. I mean I don't see how that could be
> considered immoral unless there's a prejudice against political
> organization. Plus I don't believe people will perceive any particular
> strategy of a method to be "immoral" if it's what it takes to win.

I'm quite convinced that there are societies where e.g. a candidate  
that slightly trails the current leaders in popularity and who  
recommends voters to "cheat" and vote strategically in order to win  
despite of having less / decreasing support in a way that is not in  
line with what the society considers fair elections, would actually  
lose more votes than what it would gain with the (partially  
implemented) strategy. Candidates sure can tell the voters how to vote  
strategically but I'm not sure if this message ("try other tricks if  
there is not enough support otherwise") is always a good message to  
send to the potential voters. Need to resort to strategic voting may  
also give the message that this candidate is actually not among the  
potential winners any more, and voters often tend to vote candidates  
that are strong and popular. I again note that societies are  
different. In some societies such plotting might ruin a career while  
in others small tricks are allowed as part of the game.

>
>> ...
>>>> Sincere:
>>>>>> 49:A, 49:B>C, 1:C>B. B wins.
>> Strategic:
>>>> 49:A,
>>>>>> 49:B>C, 1:C>A. C wins.
>>
>> ...
>>>> What is alarming to me is that a candidate that is
>> so
>>>> massively considered worse than B can win with so
>> few (1)
>>>> strategic votes. WV doesn't seem to measure the
>> opinions of
>>>> the society correctly.
>>>
>>> That last paragraph doesn't really make sense to me.
>> You can't expect WV
>>> to measure the opinions of society correctly when
>> voters successfully use
>>> an obscure strategy. And again I don't understand why
>> you focus so much
>>> on strategy when you don't think voters will normally
>> come up with any.
>>
>> My text was not very good. The basic scenario that I don't
>> like is one where multiple groups rank only the candidates
>> of their own favourite group. The votes could be 100:
>> A1>A2>A3, 100: B1>B2>B3, 100: C1>C2>C3
>> etc. WV seems to think that all candidates are about equal
>> (with these votes that are at least close to sincere) since
>> any additional (strategic or sincere) vote may make any of
>> these candidates win. WV thus seems to ignore the sincere
>> unanimous opinions/rankings within each group, and one could
>> say that WV doesn't measure the opinions as one would
>> expect.
>
> I assume if you add 1 A3 vote, margins elects A1. That strikes me as
> illogical unless you're voting a party list method or something. At
> least in WV you can say that A3 might be the approval winner.

Before the last vote A1, B1 and C1 were tied in margins. Margins will  
not allow any other candidates win without a considerable number of  
new votes. That last vote didn't support A1 but it made the situation  
of B1 and C1 slightly worse. They now lose to a candidate that loses a  
lot to A1 while earlier they didn't lose to any of the candidates.  
That difference is not big but who else should be elected if not A1?  
Also WV gives victory to A1 in this example (if the additional vote  
was "1: A3" and not e.g. "1: A3>C2").

>
>> ...
>>>>>> - Another related but maybe more real life
>> like
>>>> example
>>>>>> with richer variation of votes: 10:A,
>> 22:A>B,
>>>> 17:A>C,
>>>>>> 28:B>C, 23:C>B. B wins. Both A wing
>> and BC
>>>> wing think
>>>>>> that B is better than C. If you add three
>> more
>>>> (sincere or
>>>>>> strategic) C>A votes then C wins in
>> WV.
>>
>> ...
>>>> We may assume that all the votes were sincere. My
>> concern
>>>> is that C was elected although both A wing and BC
>> wing seem
>>>> to like B more than C.
>>>
>>> By a bit I guess? I'm having trouble seeing this as a
>> realistic scenario,
>>> before even getting to whether this is a realistic
>> strategy. The BC
>>> contest is weakened by the abstention of the A
>> truncators. That doesn't
>>> seem like information anyone would have.
>>
>> I tried to make this scenario as realistic as I could while
>> still keeping the example very simple (with only few clear
>> voter groups). The reason why only A supporters truncate is
>> that it is probable in real life that voters rank their
>> favourites and leave the less interesting candidates
>> unranked.
>
> I agree, but I didn't question why only A voters truncate. The  
> question
> is how many strategists would know this was something they could use.

There probably were polls that indicated that many A voters would  
truncate (or the pairwise matrix looks like that). Voters might also  
know that it is typical that voters rank their favourite candidates  
and leave some others unranked. Voters might learn the exact strategy  
from the media. One possible path would be that after some earlier  
election somewhere some journalist revealed that it would have been in  
the interest of the supporters of the losing candidate of the left or  
right wing not to rank the other candidate and thereby win. This  
strategic pattern / political set-up may well be generic enough so  
that voters are able to recognize it when their own political  
environment and candidates follow that pattern. This (or media or  
party/candidate guidance) is required to make it clear to many enough  
voters that the strategy could be applied now.

>
>> Here all voters ranked all the candidates of their
>> own wing. Some didn't rank the candidates of the other wing
>> (this has no impact on the BC wing since the competing wing
>> has only one candidate). I thus claim that this kind of vote
>> sets (or slightly more complex) are quite typical in real
>> life elections.
>
> I think a lot more A voters would truncate, but it doesn't matter.
>
>> ...
>>>> I understand that voters may truncate due to
>>>> laziness (too tedious voting) if there are very
>> many
>>>> candidates but I don't have any better rule to
>> estimate
>>>> those missing opinions than to assume that they
>> were 50% for
>>>> and 50% against, and some possibly "no opinion" or
>> "equal"
>>>> (that give the same end result).
>>>
>>> I guess you just don't think it's a better rule?
>>>
>>> Fundamentally we're trying to rank defeat strengths,
>> not decide how to
>>> split up votes. The WV mentality is that the more
>> people that participate,
>>> the better that information is.
>>
>> Note that vote A>B=C may sometimes mean that this voter
>> didn't want to participate in the B vs. C question, but it
>> may as well be a clear statement that B=C. Non-participation
>> may also mean that the voter wants other voters to decide
>> without him/her. If we don't collect separately information
>> on what the reason behind the equal rankings is we can not
>> assume one way or another.
>
> I wouldn't object so strongly to a method which counted explicitly  
> equal
> rankings according to margins (even though this is strategically
> pointless) but truncated rankings according to WV.

Does word "truncation" carry a meaning here? (other than the technical  
property of equal ranking of the last candidates) (e.g. "ranked equal  
last since not approved", "using ballots where unranked last do not  
have any markings, so they can be considered not approved", "not  
ranked since it was too tedious to rank them")

>
>> ...
>>>> Note btw that WV may suffer quite a lot if voters
>> truncate
>>>> due to laziness / too tedious voting. That could
>> lead to
>>>> different wings ranking only their own favourites,
>> e.g. 50:
>>>> L1>L2>L3, 50: R1>R2>R3 (maybe also
>> 50:
>>>> C1>C2>C3), and that could lead to electing
>> L2, L3, R2
>>>> or R3 (or C2, C3) with few changes or extra votes
>> in the
>>>> style that I described earlier.
>>>
>>> Any scenario like this is doomed. I doubt it's worth
>> trying to save
>>> even if we could: what's the value of all those
>> clones?
>>
>> This problem will be present already with three candidates
>> (and when two of them are considered to be closer to each
>> others than to the third one).
>
> Well, I see no reason to think that voters under WV would use bad  
> strategy
> in the absence of bad information.
>
>> ...
>>>> Also the message that in WV
>>>> truncation is a good defence strategy would
>> encourage
>>>> similar behaviour. In tight elections (and often
>> elections
>>>> are such) the probability of such problems may not
>> be
>>>> negligible.
>>>
>>> And on the other side, a good defensive strategy in
>> margins is to just
>>> vote the best frontrunner in first place.
>>>
>>> Then decide how sincerely to rank the worse
>> frontrunner (or your allied
>>> near-clone) considering that truncation is useless.
>>
>> I missed this one.
>
> I should split it into two statements perhaps:
> 1. when people are truncating then your defensive strategy in margins
> should be to vote for the best frontrunner, because margins won't
> guarantee that a literal majority can get their way by just voting
> sincerely for the better frontrunner and everyone thought to be  
> better.

I hope that in large public elections people never have to resort to  
defensive strategies. If people start to use defensive strategies  
widely in any large public Condorcet elections then I consider that to  
be a failure of the method. I.e. the best promise of Condorcet is that  
it would allow sincere voting. Strategic Condorcet would not be nice.  
And strategic defensive truncation is not nice if widely spread. That  
means also going towards plurality / bullet voting. I'm not sure if  
semi-controlled truncation where some voters are expected to truncate  
(e.g. the ones that expect to be the victims of a burial attack, or  
those who think they are leading) while some others are expected to  
vote sincerely is much nicer. And as already noted, there may be  
disagreements and misunderstanding on who is supposed and/or allowed  
to truncate. This approach might lead to a big mess.

> 2. when nobody is truncating then you have a mess that we haven't  
> talked
> about in this discussion. I won't get into it because you can defeat  
> it
> by asserting that no one will ever want to insincerely rank the  
> worse of
> two frontrunners.
>
>> ...
>>> I guess you think margins' incentives will stop
>> people
>>> from truncating without making them do anything *else*
>> insincerely?
>>
>> ?
>
> I should have answered above what this means. I assume at this point
> that you have an idealized view of what would happen when nobody ever
> truncated.

I believe yes :-). I try to see Condorcet methods as a group that in a  
suitable environment (very competitive but not pathologically/ 
irrationally competitive and not beyond repair) would allow sincere  
voting as the main rule for all rational voters.

Juho




>
> Kevin Venzke
>
>
>
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