[Election-Methods] RE : Corrected "strategy in Condorcet" section

[Juho]

Thanks for the explanations. I cut the old material and my responses  
quite a lot to keep the size of the mail manageable. At the end of  
this mail I rewrote the comments in a new way (an attempt to use a  
more structured and generic approach to addressing the discussed  
problems; to avoid losing the central themes in the numerous separate  
discussion points; to rewrite the comments now when I have some  
understanding of the intended sincere votes).

On Aug 2, 2007, at 6:44 , Kevin Venzke wrote:

>> 1000 A>B, 1000 C>D, 1 D>B

> Yes, I do think D is the proper winner.

I have many times said that it is possible to support different  
utility functions. An election method may then implement one of these  
utility functions as accurately as it can. I must thus say that using  
winning votes (or something like it) as the ideal utility function  
must also be ok, although maybe not my first preference.

Do you have a verbal (natural language) explanation why D is better  
than A and C. This scenario could be an election in a school. One  
class has voted A>B (A and B are pupils of that class), another class  
has voted C>D, the teacher has voted D>B. What should the teacher  
tell the C>D voting class when they ask "didn't you count our votes"?  
Maybe this is clear to you. Unfortunately not as clear to me. The  
teacher vote seemed to be heavier than the pupils votes :-).


> You are saying that the election method should respect the C>D voters'
> nearly unanimous belief that C is better than D. If this is not for
> the benefit of the C>D voters then for whose benefit is it?

Yes, but this has nothing to do with the (IRV like or some other  
philosophy) first preferences. These votes could as well have come  
from 10 separate sets of votes of type Xi>C>D (where i is an index  
from 1 to 10). In this case C would have had no first place support  
at all. The pairwise matrix has all the relevant data, and no memory  
of the first places.


>> (I'm not sure but your comment sounds to me a bit like the old
>> argument that use of wv makes Condorcet acceptable while margins keep
>> it unacceptable. My point has been that we should cover all arguments
>> in both directions, and that it is not clear to me why this single
>> argument would be more important and a bigger threat than the  
>> others.)
>
> I still don't know what the others are. You bring up isolated  
> scenarios
> involving order reversal, and you make a point about respecting  
> unanimous
> opinions which in the examples presented would be an annoyance to the
> voters with those opinions.

By now you should know roughly what kind of scenarios I want to  
include in the study but maybe you don't agree with the proposed  
conclusions. Maybe the end of ths mail explains more (although I cut  
down the number of scenarios there).

The probability of the presented reversal scenarios and their threat  
level can be discussed but they clearly exist (in my example threats  
were present in winning votes but not in margins).

Unanimous opinions should generally be respected. Maybe good  
explanations are needed if one does not respect them.

Isolated example cases are no problem if they are examples of  
relatively common situations in real life.

> I believe the "old argument that use of WV makes Condorcet acceptable
> while margins keep it unacceptable" usually has to do with order  
> reversal
> strategies.

Yes.


>> What's the "not catastrophic = OK" doctrine? What is considered  
>> noise?
>
> "Not catastrophic = OK" is the attitude you seem to present in  
> particular
> in response to A winning given 7 A>B, 5 B, 8 C. Basically when a  
> candidate
> loses an intuitively important pairwise contest only by a little,  
> it is
> OK for that candidate to win anyway.

I'd say this is a close race. A wins in margins since it is only two  
votes short of being a Condorcet winner. That is one possible very  
sincere measure of who should win an election where the opinions are  
cyclic. The election of A may leave someone wondering if some  
strategic insincere moves could have changed (falsified) the outcome,  
but despite of this it is easy to claim that the algorithm picked the  
best winner.


(1000 A>B, 1000 C>D, 1 D>B)
> If you agree that C>D voters want D to beat the other candidates, then
> they should be allowed to elect D. From *their* perspective it  
> makes no
> sense to require that D must have some support against C to beat other
> candidates.

Yes, the C>D voters want D to beat A and B. They would be happy if D  
would be elected instead of A or B (unconditionally without  
considering how people voted between D and C). But their next  
question after there is an agreement that D beats A and B would be if  
they could go even further and elect C instead of D. Their feelings  
are quite strong/unanimous here.


>> In this election I don't thing there were candidates that could be
>> called "good compromise candidates" since all voters except one gave
>> support to the candidates of their own party and left all the others
>> tied at the last position.
>
> If an election is tied, isn't it okay for one more voter to break the
> tie?

Yes, but in this example it feels more natural to me to think that A  
and C were tied and consider B and D to be less preferred than the  
other two.


> Wouldn't you *especially* want to listen to a voter whose preferences
> cross parties? I think it would hardly be more encouraging if the
> tiebreaking voter simply voted "A".

No, all votes should be equal. It is also hard to judge who  
represents what party and which candidates should be grouped together  
as representing one uniform set of voters (except in this exaggerated  
example).


(20 A, 15 A>B>C, 10 A>C>B, 35 B>C, 20 C>B)
>> Someone called this a game of chicken. Not a nice feature of a voting
>> system. If the newspapers publish the results of the poll and tell
>> that C>B voters have the option to vote strategically C>A>B, what
>> should the B>C voters do? Should they truncate in order to eliminate
>> the risks? Those C>B voters that want C to win more that they fear A
>> to win (utilities e.g. C=100, B=50, A=40) may vote strategically even
>> if there would be a risk of some B>C voters using the counter  
>> strategy.
>
> The same newspapers would say that B>C voters should truncate. And  
> then
> it doesn't work. (This is assuming not just that B voters do plan  
> to give
> that many votes to C, but that C voters trust that they will.)

Do you recommend the "B>C" voters to betary C and vote "B"? Note that  
according to the poll "C>B" voters were not planning to vote  
strategically (not yet at least, although they might decide to do so  
after they hear about this possibility).


>> If this would be the preferred mode of operation, then the "tree
>> voting" style where candidates are organised in a tree like
>> structure. See e.g. my mails on tree structures at March 11th 2007.
>> That is one strong but a bit limiting way of getting rid of the cycle
>> based strategies.
>
> I believe major political establishments would tell you that this is
> indeed the "preferred mode of operation" assuming they understood the
> question.

Did you say that you support the tree structure or that only major  
political establishments would support such a structure? Maybe the  
latter.


>> - I can't really comment the strategies if I don't know what the
>> sincere opinions of the voters were. Could you give some set of
>> sincere opinions that led to these strategic votes.
>
> I did this already. What did you not like? That I didn't clearly  
> specify
> the division of the 24 B voters between B>A sincere and B>C sincere?

I think you didn't do that fully yet. Based on your comment I assume  
that the sincere opinions could be e.g. 12: B>A and 12: B>C. I assume  
that B is a centrist candidate and therefore most C supporters might  
vote C>B (like you said). But this does not explain yet why A voters  
would (in real life) all be of (sincere) opinion A>B=C. Am I correct  
to assume that the majority of the A supporters actually feel A>B>C  
(or is there some explanation why this is not the case).

(See further analysis and possible sincere opinions at the end of  
this mail.)


>> - Why is B considered a frontrunner with less first place support
>> than C had?
>
> Because the election results are only available after the election is
> held.

Then why did the B supporters truncate in a situation where they did  
not know that B is a frontrunner? Why didn't C supportres truncate?

It would be really helpful to have the sincere opinions, and possibly  
also recommended strategic voting patterns stable and clearly listed.  
It is hard to discuss the possibilities if one has only the final  
outcome of the election available (that is expected to contain  
strategic votes).

(Further analysis at the end of this mail.)

> I don't know why you ask this. Information isn't perfect; your  
> modification
> of my scenario to make it "more realistic" seemed to primarily have as
> its goal, to make the point that the results of the election are not
> very certain.

Correct. That is why I keep asking. I don't expect the sincere  
opinions of the voters to be as in the votes in the example (they are  
too extreme), and you seem to agree with this. The sincere opinions  
are expected to be more balanced in large elections. And that has an  
impact on the vulnerability and strategic opportunities in the  
election. My target is to study how high the risks are in real life.  
That is why I put more weight on scenarios that can be from real life.


>> - Why did A supporters decide to truncate? Being one of the
>> frontrunners is not yet a good enough reason.
>
> When I first encountered this scenario the candidates were labeled  
> Bush,
> Gore, and Nader. The situation is that Nader turns out to be oddly  
> strong.
> It makes little sense to me to imagine that a substantial number of  
> voters
> would vote "Bush>Gore" just because Nader is in the race.
>
> I'm not sure why it matters whether A voters truncate. If they vote  
> for
> B, as I've said, then they can make A lose. But this doesn't really  
> save
> the scenario because it directly answers why A supporters should  
> truncate.

I think it is already a partial failure of the Condorcet method if  
voters need to vote (counter) strategically. It looks like the  
recommended general voting strategy is close to:

- If you support the strongest candidate (X) of the party, then you  
should bullet vote
- If you support the second strongest candidate (Y) of the party,  
then you should vote Y>X

What if X and Y are about equally strong? Should all X and Y  
supporters truncate or all rank both candidates? If they truncate,  
the other party is more likely to win. If they both rank each others,  
then the strategic risks appear again. Approval has the strategic  
problem of not allowing the second strongest candidate of a faction  
grow. Is this true for Condorcet too if truncation is widely used?

I think Condorcet methods are at their best in situations where  
voters can vote sincerely, not when strategic considerations start  
stealing space and time. The strategic vulnerabilities of Condorcet  
methods are relatively complex and also relatively ugly but luckily  
they may be quite rare. If the system is able to stay clearly on the  
sincere voting side, then Condorcet methods are very good. I'm not  
confident that the system would stay pleasant and under control if  
use of counter strategies would be widely spread.


(49 A, 24 B, 27 B>C)
...
(30 A, 9 A>B, 6 A>C, 14 B, 8 B>C, 2 B>A, 25 C>B, 5 C, 1 C>A)
>> These were intended to be sincere opinions that could be from real
>> life. I thus planned to consider any any possible strategies (and
>> strategic truncations) based on these sincere opinions.
>>
>> (These votes were intended to be a more realistic example of sincere
>> opinions than your original example. Now I learned that the original
>> example was not intended to be sincere. The example is however still
>> valid as a more realistic set of sincere opinions.)
>
> I just don't see the point yet. You've added in some other ballot
> possibilities and you made C a bit more viable.

The point is that when we take into account the inaccuracy of the  
polls, opinions that change in time (before the election day),  
negative reactions to strategic plans, having few such voter groups  
present that have different targets than what are present in the  
simplifies scenarios, and having multiple differing opinion poll  
results available, then the cases become more complex and anything  
can happen. Reliable strategies become less reliable. In such  
circumstances the Condorcet methods are expected to perform better.  
Sincere voting is more often the best strategy to apply. My ideal  
outcome of this kind of analysis would be that in many societies  
Condorcet would be practically strategy free. Strategies and counter  
strategies would not be applied since they would not be considered  
efficient, and they would maybe be considered bad manners that  
everyone would try to discourage (e.g. by explaining that it is more  
likely to lead to worse relults than to better results to the voter  
in question).

I note now that since your original example was actually intended to  
be a result of strategic considerations, the sincere opinions may not  
be like this. This example was an attempt to make the opinions  
sincere. It is valid still but maybe not exactly or close to what the  
sincere opinions behind your example were intended to be. (See end of  
the mail for more discussion.)


>> In the modified scenario that I presented the success of the strategy
>> was one vote away but still the strategic plan appeared to be less
>> than clear due to the numerous uncertainties with controlling the
>> strategy, changes in the opinions before the election day, reactions
>> to the strategic voting plans (counter strategies, reduced support to
>> the plotters) etc.
>
> You are talking like it's a positive thing if the C>B voters decide  
> not
> to use a betrayal strategy. It's not positive; it's the other side  
> of a
> bad coin. Whether they betray C now or just remember to do it in the
> future, an incentive is or will be apparent.

One of my key targets is to seek the limit above which Condocet  
methods would be generally strategy free. Both concerning strategies  
and counter strategies. The confused situation and numerous options  
contribute in this direction. That maybe already became obvious  
towards the end of this mail.

- - - - -

I'll now approach your old example from a somewhat new angle, taking  
also the sincere opinions into account. Maybe this approach explains  
a bit better what I'm after. The idea is that strategic voting with  
margins and winning votes is a sword that has two edges. I now  
understand your original (exaggerated) example (49 A, 24 B, 27 C>B)  
to be a result of strategic considerations in a typical left-centre- 
right set-up.

The original (intended, exaggerated) sincere opinions could have been:
49 A>B>C
12 B>A>C
12 B>C>A
27 C>B>A

Both margins and winning votes would elect B with sincere votes.

In this situation the A and B supporters decide to vote (counter)  
strategically and truncate (with more or less valid reasons). (The  
end result / actual votes are exaggerated, but more realistic votes  
can be discussed later if needed.)
49 A
24 B
27 C>B

Margins will elect A and winning votes will elect B. Your opinion  
seemed to be that winning votes is better since with margins C  
supporters would be tempted to vote B>C and thereby make B the  
winner. (Note that with these numbers at least 48 out of the 49 A  
supporters would have to vote strategically to generate the  
temptation for the C supporters to vote strategically.)

An alternative explanation to these actual votes could be that the  
sincere opinions were:
49 A>B=C
24 B>C>A
27 C>B>A

This is a typical (exaggerated) left-right-right set-up. Both margins  
and winning votes would elect C with sincere votes.

In this alternative the B supporters vote strategically and truncate.  
The actual votes are exactly the same as in the first case - this is  
thus just an alternative explanation to them.

Now the fact that winning votes elects B makes it possible for the B  
supporters to apply the strategy while margins do not encourage  
strategic voting.

It is thus difficult to avoid all the strategic voting scenarios  
whichever preference strength measurement function one uses (margins  
or winning votes). It is possible to try to defend against one kind  
of threat and open doors to others while doing so (the two edges in a  
small space) . What choice should the election method do if there are  
problems in whatever choice one makes?

In principle one needs to evaluate all possible cases and then  
estimate which function is better. And of course one has to add to  
the final election method evaluation also the other factors (e.g.  
performance with sincere votes, ref. the 1000 A>B, 1000 B>C, 1 D>B  
example).

(A third explanation to the actual votes would btw be that the actual  
votes are actually sincere. The election method of course has to  
elect a good candidate also in this case. I will not talk about this  
line further now since the actual votes hat were used above don't  
look like a typical set of sincere opinions.)

(Now my feeling is that you were quite happy with voters regularly  
applying the defensive strategies (truncation). I'd be happier to  
conclude that such voting patterns are generally not needed. Real  
life elections are not as extreme and clear, and controlling  
strategic voting is difficult, opinion polls may vary etc. etc. DOes  
this make Condorcet methods strategy free in practice or should we  
prepare for wide spread strategic voting? Is Condorcet better than  
other methods if strategic voting is widespread?)

Juho



		
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