[EM] Condorcet How?

[Juho]

On Apr 10, 2010, at 12:39 AM, Kevin Venzke wrote:

> Hi Juho,
>
> --- En date de : Ven 9.4.10, Juho <juho4880 at yahoo.co.uk> a écrit :
>>>>> I more or less despise the election of A in
>> this
>>>> scenario:
>>>>>
>>>>> 49 A
>>>>> 24 B
>>>>> 27 C>B
>>>>>
>>>>> I believe the possibility of this outcome is
>> a
>>>> disincentive for a candidate
>>>>> like C to run.
>>>>
>>>> The story behind these votes seems to be that C
>> is
>>>> ideologically close to B and its nomination makes
>> A win
>>>> instead of B. If C is ideologically close to B why
>> don't the
>>>> "B" voters vote "B>C" (and make C win)?
>>>
>>> Because the story is that C is not considered an
>> established candidate
>>> (or a frontrunner), and the B voters (if they actually
>> prefer C, which
>>> is not something I mean to suggest) will not
>> condescend to rank C.
>>> Depending on the method, they could hand the election
>> to C by ranking C,
>>> and/or alternatively compel C supporters to not vote
>> sincerely.
>>
>> Ok, but the story is not quite flawless yet.
>>
>> Case 1: "B" voters did not notice C. B had 51 supporters
>> before the nomination of C. All that heard of C changed
>> their opinion to "C>B". If C is so obviously better than
>> B then also some of the "A" voters should have voted
>> "A>C" (or "A>C" if they feel the other way around for
>> some reason). But it seems that also they did not notice C.
>> It is also strange that someone can get 27% support (clearly
>> more support than B) and still be unknown to so many of the
>> voters.
>>
>> Case 2: "B" voters did notice C and liked C but didn't want
>> to vote for C. In this case the votes are not sincere but
>> twisted for some psychological reasons. (Also some part of
>> "A" voters should have ranked B or C if they noticed C.)
>
> 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.

>
> Yes, you are right: I am proposing that voters backing more  
> established
> candidates may insincerely decline to give lower preferences to other
> candidates. But this isn't simply because they are mean. It benefits
> candidates like B if the nomination of candidates like C risks  
> wrecking
> the result from the perspective of C voters.

Yes, established parties/candidates may do all they can (including  
psychological games and giving impression that the new parties/ 
candidates are irrelevant) to avoid new parties/candidates becoming  
serious contenders.

>
>> 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.

>
> 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. 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.
- 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.

>
>>> The best scenario is for C to be able to run, be voted
>> for sincerely, and
>>> either win, or not affect the outcome at all.
>>
>> Yes, that would be ideal.
>>
>>>
>>>> If C is
>>>> ideologically far from B then most "B" voters may
>> vote as
>>>> they do now, but then maybe "A" voters should vote
>> "A>B"
>>>> (and make B win) (since C seems to be closer to B
>> than A).
>>>> It is hard to find an explanation to sincere votes
>> like
>>>> this. Or are these maybe strategic votes, e.g. so
>> that
>>>> sincere "A>B" voters have decided to vote "A"?
>>>
>>> The A voters will not vote A>B because A and B are
>> considered the
>>> frontrunners. (i.e. that is the scenario that concerns
>> me.)
>>
>> Yes but also this means that "A" voters are badly
>> misinformed when none of them have heard of C or believe
>> that C is weak although C has 27% first place support
>> (clearly more than B) and all that heard of C "on the B
>> side" voted for C.
>
> You keep saying 27 is clearly more than 24. I don't think it is  
> outside
> the realm of possibility that a candidate expected to place third
> would actually place second.
>
> You can't really conclude A voters are misinformed, not from the votes
> anyway.

Yes, I only talked about one potential explanation (= A and B voters  
misinformed) to why the votes are what they are. There may be also  
other explanations, like A voters having no preference between B and C  
(B=C), or like the one that A and B were from large established  
parties and they wanted to ignore C to make him/her look like  
insignificant. I think the given votes should have at least one  
rational explanation to prove that the method may give unwanted  
results in some real life situations.

> A voters are going to win it, and voting A>B turns B into the
> CW. Notice that C is not really very close to winning.
>
>>>>> Fundamentally, if I said only one thing: I
>> don't
>>>> believe that the margins
>>>>> ranking of defeat strength (resulting from
>> its
>>>> treatment of unranked
>>>>> candidates) is in agreement with what voters
>> would
>>>> expect and want.
>>>>
>>>> What would you consider to be a better approach
>> than
>>>> margins for sincere votes? (winning votes has also
>> scenarios
>>>> that may be questioned)
>>>
>>> Maybe Range? I guess I don't see that question as
>> interesting or useful.
>>
>> Yes, Range could be considered more ideal at least for some
>> uses (when one wants to maximize the sum of utilities)
>> (there are also other alternatives like minimizing harm to
>> some and seeking majority). The problem of course is that it
>> is so difficult to collect sincere ratings. I think the
>> question is important since performance with sincere votes
>> (= elect the correct winner) is important.
>
> It is difficult to collect sincere ratings. But doesn't your question
> assume we can get them?

Ok, my question talked only about sincere votes (but I wanted to  
assume that both components, performance with sincere votes and  
performance with strategic votes, will be considered at some point).

>
> 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.

(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.)

>
> 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. 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.

>
>>>> (Note btw that in another mail I just mentioned
>> also the
>>>> possibility of allowing B and C to formally team
>> up so that
>>>> defeats within their team would not be considered
>> as severe
>>>> as defeats between A and the team.)
>>>
>>> This doesn't interest me much (same as Forest's
>> suggestion of pre-
>>> election agreements in DYN) because I'm not interested
>> in the case that
>>> a single party (for all practical purposes) nominates
>> two candidates.
>>> I don't think that will normally happen or be
>> desirable under any
>>> method. What I'm concerned with is the viability of a
>> "third" option and
>>> voting for the third option.
>>
>> I don't believe such strong methods like teaming would be
>> generally/typically needed. But if there are problems then
>> teaming may be a good way to overcome them (they may e.g.
>> quite efficiently cut out any strategy considerations). I
>> also understand that in some environments all "agreements
>> between parties" may be considered to represent too much
>> some "spirit of old times".
>>
>> In summary, maybe the "third" party explanation is more
>> what you are after than the "not heard of C" explanation. In
>> the example "B" and "A" voters were maybe from some old
>> established parties and they did not want to recognize the
>> emergence of a "third" new strong candidate.
>
> Yes, that's right.
>
>> I believe such
>> problems may well be temporary. If one adopts a new method
>> that allows also "third" candidates to run in a meaningful
>> way and with real chances to win if they have strong enough
>> support, then I'd guess the attitude and problems of
>> ignoring them and not ranking them could fade out very soon.
>> The two main contenders and voters that support them can not
>> pretend any more that other candidates do not exist (one can
>> e.g. not play down a candidate with 27% of the first
>> preference votes).
>
> 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.

Juho



>
> Kevin Venzke
>
>
>
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