[EM] Condorcet How?

[Kevin Venzke]

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. 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:

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.

> >> 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. 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. 

> > 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.

> 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.

> - 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. 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?

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.

> > 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.

> 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.

> > 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.

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).

Kevin Venzke