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 <[email protected]> a écrit :
De: Juho <[email protected]>
Objet: Re: [EM] Condorcet How?
À: "Election Methods" <[email protected]>
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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