[EM] Condorcet How?

[Juho]

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. 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.  
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.

...
> 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.

My best guess is that strategic voting would not be common in  
Condorcet methods in most societies. There may however be some  
societies where people are so used to strategic behaviour in political  
elections that they try to continue that also with Condorcet. In most  
such cases Condorcet might make the voters more sincere after they  
learn that their strategies don't work very well. In some special  
cases (e.g. Australia if they keep the mandatory full ranking rules)  
strategies might even stay widespread.

For truncation due to strategic reasons see previous paragraph.  
Truncation due to laziness / too tedious voting will certainly play a  
role if the number of candidates (and simultaneous elections) is high.

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.

...
> 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.

...
>> 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)  
and another one with another explanation (e.g. interest not to allow  
third parties grow). 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.

...
> 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 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.

Probably it doesn't make much difference to most voters whether the  
used method is IRV or Condorcet. It is just ranking for them.

(I have the Burlington votes somewhere in some Excel compatible format  
in case you need them.)

...
> 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.)

...
>> 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.

...
>>>> - 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. 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 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.

...
>> 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).

...
>> 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.

...
>> 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 gave some that were intended to be such.

...
> I guess you think margins' incentives will stop people
> from truncating without making them do anything *else* insincerely?

?

Juho