[EM] Condorcet How?

[Juho]

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 :-).

On Apr 10, 2010, at 7:20 PM, Kevin Venzke wrote:

> Hi Juho,
>
> --- En date de : Sam 10.4.10, Juho <juho4880 at yahoo.co.uk> a écrit :
>>> I don't get why people assume that B voters secretly
>> do like C. If I
>>> vote for a left-wing candidate, that doesn't mean I
>> like all left-wing
>>> candidates better than all right-wing candidates.
>>
>> I don't want to make assumptions in one way or another but
>> I'd like to identify some rational explanation to why people
>> voted as they did. This is needed also in order to evaluate
>> if the outcome that the method produces is acceptable or
>> not. The example (at least at first sight) seems to suggest
>> that B and C are close to each others since all the C
>> supporters liked B more than A. I discussed shortly also
>> another natural and simple looking (linear opinion space
>> based) option where C is e.g. clearly to the left of B. In
>> this case the B supporters might think A=C (or split their
>> preferences between these two) but in that case the A
>> supporters (maybe right wing) could think more B>C than
>> they now did.
>
> 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.

> 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).

>
> 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. The method can not  
make any difference between these two paths that lead to identical  
sets of votes.

>
>>>> It seems that the role of non-informed voters
>> and/or
>>>> non-sincere/mutinous voters and the surprising
>> emergence of
>>>> candidate C have a strong role in the story, and
>> all the
>>>> blame (of not following the story (and intended
>> outcome)
>>>> that was discussed above) can not be put on
>> margins alone.
>>>
>>> I don't understand that way of thinking. Uncertainty
>> about the strength
>>> of a candidate is going to exist everywhere.
>> Self-interested strategy
>>> is going to exist everywhere. I guess you could excuse
>> margins from
>>> messing up here, but what's the point?
>>
>> 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.

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). (Later  
in the mail there is also some discussion about truncation because of  
too numerous candidates to rank all of them.)

> 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.

>
>>> I'm aware you can find scenarios where WV offers a
>> strategic incentive
>>> where margins doesn't. I don't think I've seen
>> theories about general
>>> patterns of this, or any particularly relevant and
>> alarming scenarios,
>>> etc.
>>
>> I believe there are also situations where WV in practice
>> (not only in some theoretical scenarios) is more vulnerable.
>> I however tend to think that in real life large public
>> elections all Condorcet methods are quite good and not very
>> vulnerable to strategies.
>
> 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 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.

>
>> 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.

>
>> - 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.

> 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 the way, I do want to maximize the sum of
>> utilities. I just don't
>>> think you can be so direct as to ask for them.
>>
>> Sum of utilities would be a good approach for many uses if
>> we could get the personal utilities. In some non-competitive
>> elections and polls we can get them but political elections
>> may be a more difficult environment.
>
> Well, I have assumptions about what tends to maximize utility. The  
> ideal
> scenario for me is that the median voter has 3+ viable options to pick
> from (and not find the choice obvious).
>
>> (There may also be some extreme situations where the sum of
>> utilities is not what we want. For example it might make
>> sense to improve the utility of all voters worth 10 points
>> rather than improve the utility of all but one voter with 12
>> points and then kill or otherwise cause a major decrease in
>> utility to that remaining one voter. In this case one could
>> btw also consider allowing the voters to give ratings like
>> "minus infinity" to avoid this kind of situations, i.e.
>> ratings would not be based on a fixed range but some wider
>> scale, maybe indicating that 0 means "neutral", 100 means "I
>> like a lot" etc.)
>
> Yes. If we could perceive utility more clearly I might have to clarify
> my opinion.
>
>>> I wonder how the idea of performance given sincere
>> votes applies to WV
>>> and margins for you. If everyone ranks all the
>> candidates, they'd be
>>> the same method. If people are truncating, I do prefer
>> WV for the reason
>>> I've already said, that WV treatment of truncation is
>> better (closer to
>>> what is expected) because it places more weight on the
>> "least abstained"
>>> contests.
>>
>> I read that so that you like the performance of WV in some
>> strategic voting scenarios. Maybe you assume that their
>> differences with sincere votes are not big enough to
>> influence your preferences.
>>
>> I maybe lean somewhat more in the direction that strategic
>> voting probably will not be very widely spread in typical
>> large political elections. In this situation the performance
>> with sincere votes becomes more important.
>
> 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.

>
>> And the way that
>> margins handles sincere votes looks to me more natural than
>> the approach of WV. In margins one can discuss if 45:40 is
>> equal in strength than 15:10 (when there are 100 voters) but
>> it looks more obvious to me that 45:0 should be considered
>> to be a stronger opinion than 46:45 (WV and margins differ
>> here). I believe there are practical situations where this
>> difference between WV and margins may materialize in the
>> results of real life elections (and where WV results could
>> be considered "strange"). I also tend to think that in the
>> realm of strategic voting there are also cases where margins
>> performs better than WV (although these differences may not
>> be that critical if strategic voting in Condorcet methods is
>> difficult enough to keep most voters sincere).
>>
>>> You have probably explained before why you think
>> margins is more
>>> intuitive than WV even given *sincere* votes. I don't
>> remember what the
>>> summary of this is though.
>>
>> Maybe I already gave some answers to this above. The
>> difference between 45:0 and 46:45 maybe points out the
>> nucleus of my thinking in this area. If strategies are not
>> used widely then one should put more weight on performance
>> with sincere votes.
>
> Again I don't think voters will view truncation as a strategy, and  
> will
> always do it (especially with more candidates). The alternative is
> most likely even worse: burial without careful consideration of risks.
> How many voters would really rank their more hated frontrunner ahead  
> of
> unknowns? That really concerns me.
>
> 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. 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).

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. 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.

>
>>> That would be nice, but even if true, it is just a
>> mitigation of the
>>> problem, not a reason to refrain from eliminating the
>> problem.
>>
>> 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. If the scenario is likely to occur frequently in real life then  
we should treat it with corresponding seriousness. 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).

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.

>
> If support for C grows then these voters will most likely stop voting
> for B as much. If those 6 B voters actually like C better than A, they
> will be foolish to not vote for C when C is so much stronger.
>
> 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.  
Situations where there would be no correlation are probably rare (one  
often assumes a linear opinion space or a multi-topic opinion space,  
and both of them are based on strong correlation assumptions).

Juho



>
> Kevin Venzke
>
>
>
>
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