[EM] Condorcet How?

[Kevin Venzke]

Hi Juho,

I may not have that much more to say either.

--- En date de : Dim 11.4.10, Juho <juho4880 at yahoo.co.uk> a écrit :
> I think I already said most things
> that I had in my mind about the character of winning votes
> and margins. There are however still plenty of details in
> the answers and comments below (maybe already too many for
> many :-).
 
> > To me the only thing that matters is whether there is
> even one scenario
> > that could realistically arise and which is bad.
> 
> Yes, that is enough to prove the vulnerability in realistic
> situations. Of course after that one must still weigh the
> benefits and problems since in practice all methods will
> have some more or less bad problem scenarios.

Well, I am lacking WV scenarios that alarm me. Even when margins seems
to do better than WV in some strategic scenario, it seems like a mere
accident. And not very easily abused.

> > It seems like there
> > is a hold up with the fact that B voters won't vote
> for C. So feel free
> > to change the scenario to:
> 
> At least I don't require that. I'm happy if there is one or
> two separate scenarios. Your favourite, the case where two
> major parties refused to rank the third party candidate (and
> there are no (or only few) B>C votes) would be good as
> well. My requirement is only that each one of these
> explanations should have a realistic explanation that
> explains why the result is not good and what the voters
> might do in that situation. And of course one should not use
> two explanations simultaneously and use arguments from
> whichever one is more appropriate at each time (this is one
> key reason why we need concrete real-life-like examples).

Well, the explanation for the near-clone scenario is that there are
two near-clones and neither dropped out and they didn't play nice with
each other.

> > 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. This strategy could be used by C as
well (if not, why not?) and the result would be (and probably often would
actually be) a failure to achieve any majority over A despite having a
majority of the voters.

Plus the margins solution to this incentive is to just crash into a wall,
which I find unpromising because it could well be that those B voters
actually don't like C. You'll have some voters who decide they like the
one and don't like the other.

I can't really see where you're coming from ultimately. On one hand you
feel that voters will tend to be sincere and not even truncate, and on 
the other you object to WV resolutions because they are vulnerable to
strategies that appear to work mostly in hindsight.

> >> Yes, there will be considerable uncertainty. In
> the light
> >> that the key story behind these votes is that
> there are two
> >> established parties who want to keep the third
> parties out,
> >> my concern was that the supporters of those
> parties seem to
> >> have a strategy that influences the outcome. If in
> that
> >> situation margins leads to an outcome that some of
> these
> >> strategists do not like, that could be also a
> positive thing
> >> in the sense that maybe in the next elections
> those voters
> >> would not apply the same strategy (i.e. do all
> they can to
> >> make third party candidates look insignificant).
> >> 
> >> In this example the B supporters that felt C>A
> (but did
> >> not vote so) should have voted or could vote next
> time
> >> B>C. Also other A and B supporters could
> reconsider if
> >> bullet voting is what they should do.
> > 
> > However the point in this scenario is that the
> strength of C was
> > incorrectly predicted.
> 
> That is one possible scenario where these votes might
> occur. The method must however perform reasonably well in
> all scenarios where this set of votes might emerge.
> 
> And maybe in Condorcet methods it would be wise to vote
> sincerely (in this case B>C>A) if one doesn't have any
> better ideas. It seems that truncation did hurt B voters in
> this scenario.

If you don't make assumptions about the B voters' actual preferences, the
alternative to truncation is strategically adding another preference
that they may not have.

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. It probably won't work
even if BC are actually clones. And when they're not actually clones, you
are just punishing people for not making up lower preferences they didn't
have. (Or worse and more likely: Giving up on one of the two candidates 
entirely.) The clone scenario isn't salvageable, but it doesn't need to 
be even worse.

> 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.

It sounds like you have a problem with the idea of A+B voters scheming
to make C look worse than it is, if C is not even a strong candidate.
That's not the idea. The idea is that the supporters of the two 
frontrunners have no need to support any other candidates. They can
benefit by not supporting them, and they can harm themselves if they
do support them.

So there's no plotting against C. It's the default treatment for a
candidate like C.

> > If you can predict that C is always going to be
> > strong, then yes, strategy will change. When it's only
> possible (or
> > considered unlikely) you're probably never going to
> get there, because
> > C has to get through this minefield without ruining an
> election before
> > it can happen.
> 
> Ok, your main target case seems to be the evolution of
> two-party systems towards systems where also third parties,
> or later all three or higher number of parties, or
> independents may be successful. I'd optimize the method for
> the end state and not prepare for possible misunderstandings
> in the first elections with the new method, i.e. I'd expect
> that all have pretty good information on how the method
> works and how strong each candidate is. Misunderstandings
> can (so make many kind of) a mess.

Well my response to this is exactly the text you are responding to.
There's no point optimizing for an end state if the method isn't likely
to get there.

> > Even if that is completely true, I don't expect you
> are going to get
> > voters to accurately rank both of two frontrunners,
> when there are other
> > candidates also.
> 
> I turn my eyes to Burlington. There were some bullet votes
> but not too many. Some of them must have been sincere and
> some based on misunderstanding of how the system works
> (LNH).

I haven't seen the Burlington votes. It's odd that you bring up LNH to
say that the bullet votes were mistakes, rather than aiming to dismiss
the importance of LNH in this election.

> I don't believe there were many rational strategic
> votes in Burlington. Burlington used IRV and therefore
> burying is not the same as in Condorcet, but obviously in
> both cases most voters don't care what the tabulation method
> is. There could be more burying if someone would market that
> approach. But I still doubt. Maybe there is just some part
> of the voters that feel strategic or don't understand or are
> too eager to try all the tricks. I believe in most societies
> most voters have a tendency to be sincere if they can.

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.

> >> That is why I put also
> >> considerable weight on how WV and margins perform
> with
> >> sincere votes. Also on this side I believe there
> are real
> >> life situations where WV gives worse results. The
> example
> >> that you gave suggests that there are also
> scenarios where
> >> margins performs worse with sincere votes than WV
> does, and
> >> I tried to analyze if the described scenario may
> happen in
> >> real life in the and if the result is not the
> best
> >> possible.
> >> 
> >> Here are also some example scenarios FYI.
> >> - A simple WV strategic vulnerability example.
> Sincere:
> >> 49:A, 49:B>C, 1:C>B. B wins. Strategic:
> 49:A,
> >> 49:B>C, 1:C>A. C wins.
> > 
> > Ok, I realize that is just an example but I'm having
> trouble being
> > alarmed by that. C trails badly and buries B: More
> than anything this
> > seems likely to make A win. Or do nothing.
> 
> With these votes there is no risk of making A win. In real
> life the information would however be less accurate and
> there would be more risks. There could be also safer
> numbers, e.g. 40-45-15 but that would require more strategic
> C>A votes (11 out of 15 possible).
> 
> 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.

> >> - 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.
> > 
> > Ok, so you have a united {BC} majority, and an {A}
> remainder which is
> > quite torn between B and C as the second preference.
> But most of them
> > express the preference. B is the CW.
> > 
> > If I understand you correctly you're saying that the
> 10 truncators and
> > the B>C group like B better than C.
> 
> No. What I meant is that this set of 100 votes is sincere.
> If you ask from those voters that have A as their first
> preference (the "A wing"), they prefer B to C. If you ask
> from those voters that have B or C as their first preference
> (the "BC wing"), they prefer B to C. A wing truncates (votes
> A>B=C) more than BC wing since they are not that much
> interested in the battle between the BC wing candidates.

Ok.

> > That seems like an odd thing to note
> > particularly with the latter.
> > 
> > And you're saying that the strategic incentive is to
> actually add new
> > ballots?
> 
> Let's say those voters either stayed at home or voted
> C>A. That may be their sincere opinion (i.e. all votes
> are sincere still). C wins although the opinions in favour
> of B both within the A wing and within the BC wing seem to
> be clear. This could cause some discussion after the
> election.
> 
> > If you add three ballots you get a cycle of ABCA where
> B>C is the weakest
> > so C wins. If the new voters fail to vote for A, then
> B is CW.
> > 
> > Are you concerned about this? This plan doesn't work
> if C fails to beat
> > A pairwise.
> 
> 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. And of course the more 
abstentions there are (higher probability of knowing about them in
advance), the less you know about A voters' position, weakening B's claim.

> > While the scenarios I bring up show some strategy, I
> consider the strategy
> > natural and not something consciously plotted in
> advance. In fact if you
> > called the truncating voters strategic, I think they
> would be offended
> > and not see it that way at all.
> 
> Truncation could be strategic or laziness or sincere. A
> good method could encourage sincere voting. A good society
> could discourage strategic voting. I think Burlington was a
> positive example in the sense that I'm not aware of any
> strategic plans there.

I wonder what strategic plans they could have. I may have to look into
this more.

> > Given that, my objection with considering 45:0
> stronger than 46:45 is
> > that (assuming the missing voters in the former
> contest are truncating)
> > you are treating the missing votes as an explicit
> opinion of no difference,
> > where I feel (and more importantly I feel voters will
> feel) that these
> > votes should be treated as missing information.
> 
> Margins can be said to assume a 50% - 50% split of opinions
> on both sides (this gives the same result as assumption "no
> difference"). The implicit assumptions of WV are more
> complex.

But less presumptuous.

> 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. The only reason WV doesn't stick to this
rule as I wrote it, is that it would be nonmonotonic and punish you for
voting for a losing side.

> 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?

> 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.

> >> Yes, problems should be solved in any case (in the
> order of
> >> severity, maybe solving some of the least severe
> problems
> >> only partially or leaving them unsolved since some
> problems
> >> will always remain since no voting system is
> perfect in all
> >> aspects). In this case it was difficult to me to
> say which
> >> one was the root cause, the method or the
> political set-up
> >> and the resulting insincere voting behaviour.
> >> 
> >> There are also many ways to read the different
> examples and
> >> political set-ups. For example in the given
> example the
> >> truncation of the B supporters was in a way
> punished by
> >> margins when A was elected. WV would make it
> possible for B
> >> supporters to continue truncating their vote and
> not
> >> indicate their support to C (assuming that B
> supporters
> >> generally prefer C to A). The support of C could
> grow within
> >> the "BC wing" to 49:A, 6:B, 45:C>B and B would
> still win
> >> with WV if B supporters truncate.
> > 
> > To some extent I have responded to this above.
> > 
> > Does margins punish B voters for truncating C?
> > a. doesn't that assume they like C?
> > b. maybe, but it is also punishing C for being
> nominated. That's what
> > WV doesn't do.
> 
> I still have some doubts about the scenario since on the
> other hand C should be a new candidate that has been
> recently nominated by surprise but on the other hand C has
> already more first place support than B has.

I might call this an "independent candidacy." In the US these candidates
usually just lose.

> If the scenario
> is likely to occur frequently in real life then we should
> treat it with corresponding seriousness.

I think we should want it to occur in real life, except for the disaster
part.

> The main rule for
> me is to optimize the method assuming sincere (and not
> misinformed) votes since there is plenty to do already in
> that case, and in most cases such sincere votes may exist
> (there could however be also some strange vote sets that
> might occur more probably due to strategic voting than dues
> to sincere opinions).

So, why do you not produce scenarios showing that WV is not optimized
for sincere voters? I guess you think margins' incentives will stop people
from truncating without making them do anything *else* insincerely?

> The WV history looks to me a bit like an overreaction to
> some threat scenarios. WV is a good defence against some
> well identified threats but I'm not convinced that those
> threat scenarios would be so common and dangerous that so
> strong defence mechanisms would be needed. The negative
> impact of that preference measurement style may well be
> bigger than the achieved benefits.

I want to point out that I personally never even brought up offensive
strategy.

The way I view margins is that it's sort of elegant, but an unrealistic
oversimplification. The reasonableness of the split vote is apparently
irrelevant because the intention is to make people not truncate, no
matter what may result from that.

> > The problem of mutiny with clones isn't solved by
> threatening a car crash
> > if they don't play nice. It's solved by one of the
> clones dropping out
> > of the race. That's not just design advice: Political
> players will do
> > that on their own. That's why I am mostly concerned
> with candidates who
> > are not clones (in sincere terms).
> 
> There may be also e.g. "left wing clones", i.e. candidates
> that are nominated by different parties but that are clones
> in the sense that they are typically ranked next to each
> others. The borderline between clones and candidates that
> are close to each others is not clear.

Voters (probably with the aid of the media) will have to figure out which
one to drop then, or take the gamble of keeping both.

Kevin Venzke