[EM] Condorcet How? JL

[Kevin Venzke]

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:

> 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.

> 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.

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...

> ...
> > 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. The fact that you don't present
any scenarios about this makes me believe that you consider all 
truncation a strategy that would be eliminated by margins, and so 
therefore a scenario with sincere votes would be resolved exactly the
same between WV and margins.

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.

[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.

> 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.

> ...
> > 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.

> ...
> >> 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.

> ...
> >>>> - 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.

> 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.

> ...
> >> 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.
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.

Kevin Venzke