[EM] Re: Juho: strategy

[Juho Laatu]

Hello James,

See embedded comments below.

Best Regards,
Juho



On Apr 17, 2005, at 13:19, James Green-Armytage wrote:

>
> 	Hi Juho. Here is a reply to your April 4 post, where you suggested 
> that
> large scale strategic manipulation in Condorcet methods will be 
> unlikely.
> I like your professional wrestler example almost as much as I like the
> pirates. :-)
> 	I think that I have confronted most of the arguments you raise 
> before. I
> don’t mind going back over old terrain, because the discussion is 
> always
> subtly different each time. But if my reply is too brief, you might be
> able to find more in the archives, or on my web page, or something like
> that.

I have written on practical election situations since it seemed to me 
that that area has not been covered sufficiently on this mailing list. 
Should I read your comment so that strategic manipulation of large 
public Condorcet elections has already been discussed widely on this 
list and proven to be easy? (I'm sure each strategy has been discussed 
in numerous mails but that is not what I'm looking for.)

> 	Basically, you seem to be saying that successful burying strategies 
> are
> difficult to coordinate, and that there is a chance of them backfiring.
> Both of your arguments are valid, and they are shared by many other
> people, but they may not be quite as strong as you think. I’ll address 
> the
> separate issues separately.
> 	As for coordination being difficult, that’s true. The more reversals 
> are
> necessary to create a successful burying strategy, the harder it will 
> be
> to pull off, no question. In my example, a lot of reversals are 
> required.
> If the C faction was larger, the strategy would be easier. E.g., given
> 31: A>>B>C
> 29: B>>A>C
> 15: C>>A>B
> 15: C>>B>A

You introduced now also notation ">>". Does that maybe refer to S/WPO 
or approval or some other particular method? If we are talking e.g. 
about S/WPO, then there are two alternatives. Either voters vote 
sincerely as they do or they could arrange their preferences 
strategically. What did you have in mind?

> … only slightly more than half of the B faction members need to reverse
> (B>C>A) to pull off the strategy.

Yes, in this example less strategic votes are needed. Getting 56% of 
the democrat voters of USA (B party) to vote strategically B>C>A is 
still challenging. I think that doesn't happen in elections whose 
spirit is to vote sincerely or if each voter decides on the strategy 
herself. This would require a massive campaign (by the democrats or by 
the press) that promotes certain strategic voting method.

The higher number of C voters (that don't seem to have any clear 
opinion on whether A or B is better) would make it easier to try to 
achieve victory by influencing the opinions of the C voters.

And if 2 of them would change their opinions from C>B>A to C>A>B, the 
strategy of the B supporters (17: B>C>A) would be lost and A would win 
again.

I note that if the votes were further changed to something like 
27-25-24-24 (from the 31-29-15-15 of he modified example and from the 
46-44-5-5 of the original example), then the strategy would be even 
easier to apply but at the same time risk of electing C would increase. 
This burying strategy thus seems to be seeking place to live between 
the risks of electing C and failing to get sufficient number of B party 
voters voting strategically.

At the same time A party should not vote strategically. If 46% of 
republicans (A party) use the same tactic (as the 56% of democrats) 
voting A>C>B (in the modified example). Then we are about at the 
tipping point to elect either C or A (or B). This of course depends a 
bit on how reliable he opinion polls are and if all of them give the 
same result or not.

In real life elections I think the difficulties and risks are still too 
high for any respectable party to recommend this strategy to its 
voters. It is also quite improbable that after seeing one opinion poll 
saying that republicans are leading, majority of democrat voters would 
make an independent decision to vote strategically while republicans 
would not do anything. Maybe individual voters would hope for the win 
(and activists would fight until the last moment) instead of giving up 
and voting strategically.

> On the bright side, as fewer reversals
> are necessary, one might also expect the A and B candidates to be more
> similar, so that the incentive for burying A would be less likely to be
> strong.
> 	Anyway, let me mention something that you may not have considered. You
> seem to be assuming that strategy will always be planned by some sort 
> of a
> central leadership of a cohesive political unit, and that execution of 
> the
> strategy depends on the obedience of voters at large to their party
> leaders. Actually, this is not my understanding of strategy. I suggest
> that _individual_ voters will use an insincere strategy

I don't want to assume that strategies are always party led. I just 
needed something to explain why in your example only one party applied 
some strategy and why the supporters of that party were so uniform in 
selecting and applying the strategy.

If individuals use the strategies independently, then it is probable 
that also republican (party A) voters would use some strategies. I 
don't know if they would have used exactly the same strategy and 
exactly the same way since the opinion polls promised them victory. But 
despite of the narrow forecasted victory to republicans, the parties 
were pretty much in identical situation in the opinion polls. With good 
probability there was also another opinion poll according to which 
democrats would win.

Making all the democrats understand the burying strategy requires also 
systematic teaching, but that could have been done by the press too. If 
democrats decide to vote strategically individually, then sufficient 
understanding of strategic voting must must be available to others too. 
Let's assume that the yellow press is interested of strategies and 
educates and gives hints to the voters efficiently.

C supporters now probably understand that B supporters are going to 
vote strategically. If they believe that C will not be elected in any 
case, they might drop C out of their ballots and vote shortly A>B or 
B>A (this is maybe the simplest scenario), which would change the 
strategic setting. If C supporters believe that also A voters apply 
similar burying strategy than B voters, they could keep their original 
votes in the hope of C getting elected. B voters might also give up 
strategic voting after realizing that C voters are not going to vote 
for C. And if all these possibilities are known to all voters, I don't 
know what they would do. Maybe they will stop voting, or maybe they 
would campaign for some other voting method than Condorcet to be used, 
or maybe they love plotting :-). Btw, probably there would be both 
working and non-working strategy proposals flying around, as well as 
different scenarios that depend on what other voters are expected to 
do.

An alternative to these multiple strategic voting proposals by the 
press could be to formulate some easy to understand rules that normal 
voters could easily apply whatever the opinion polls say. Any such 
rules available from you or elsewhere?

You could however also make a further modification to the example so 
that C supporters would be completely neutral with respect to A and B. 
Then they wouldn't care whether A or B wins. (Maybe I would then seek 
explanations in the direction of low probability of such uniform 
opinion among the C supporters...)

> not because
> someone tells them to, but because they perceive the probability of
> benefit times strength of benefit to be greater than the probability of
> harm times severity of harm (based on poll information and their own
> understanding of how the tally works). We can also assume that there 
> are
> additional biases weighing in favor of sincerity, e.g. a sense of 
> morality
> and civic pride... Hence, if the scale is near to the balancing point, 
> it
> is likely that it will tip toward a sincere vote.
> 	As to burying strategies backfiring, yes, most burying strategies do
> carry some risk of getting a worse result. However, the direction
> risk/reward inequality will depend in large part on the strength of
> preferences involved. For example, imagine that my favorite candidate 
> is
> Bush (not true in real life), and the other two candidates are Dean and
> Kerry. Let's say that my ranking is B>D>K, but I barely care at all 
> about
> the difference between Dean and Kerry; any Democratic president would 
> be
> just about equally horrible to me, whereas I'm a huge Bush fan. We can
> represent this symbolically as B>>D>K, or sometimes B>>>>>D>K. In this
> case, it seems more or less instinctive to rank Bush's closest 
> competitor
> in third place, i.e. the candidate most likely to win his pairwise
> comparison with Bush. Let's say that this is Kerry. So I vote B>D>K. 
> Yes,
> this might backfire, in that we might have Dean instead of Kerry, but 
> if
> so, I haven't lost much. On the other hand, if the strategy succeeds, 
> then
> I have gained an enormous amount.

Could you give also the details of this example (or is this just a 
general comment that sometimes strategies are quite free of risks). 
Maybe republicans got little less than 50% of the votes. Dean has more 
supporters than Kerry. What then?

> (Taking into account the role of
> preference strength in the burying strategy is one of the major
> foundations of the CWP and AWP methods.)

Your efforts on this front are truly appreciated. It may be that giving 
cardinal preferences just in case there would be a loop is a bit heavy 
for practical elections (or maybe the ballots are about as simple as 
the ordinal only ballots). But seeking the limits of taking voter 
preferences into account as much as possible (and maybe also reducing 
strategy risks) is valuable research.

Btw, have you considered CWP and margins. That would make the method 
more natural to me. Or would you lose too many of the strategy defence 
benefits?

> 	The main problem with strategy in margins is that stable
> counterstrategies are often not available.

Counterstrategies are a bit too rough stuff for my taste. I mean that 
if strategies are generally used and also also counterstrategies to 
defend against them, then we are probably too deep in the world of 
strategies (to be considered for public elections). If the 
vulnerability of Condorcet based methods to strategies is this bad in 
real life, then it might be better to use some simpler and less 
strategy dependent voting methods. Normal voters are hardly capable of 
applying correct counterstrategies unless you have some very simple 
rules for them to follow.

(In approval the best strategy has been widely discussed. Maybe that 
could be close to understandable to general public. This is about the 
acceptable level (or maybe already already too high) of use of 
strategies in public elections.)

> As I tried to illustrate in my
> March 14 posting, this instability can be severe. WV tends to avoid the
> extreme instability of margins

I don't see the "extreme instability" although I understand that in 
some cases WV can eliminate some additional threat. I guess all cases 
where the true winner is replaced with one that clearly should not win 
using a strategy that is implementable are severe.

> , although in some scenarios stability still
> may be elusive. S/WPO is the next step up after that, then AWP, and 
> then
> CWP. That's how I see things, anyway.

In those voting methods one could get some strategy defence benefits 
also with sincere votes (that you could also call an "unintentional 
counterstrategy"). And I do find it much better if the sincere opinions 
of the voters are used to define the winner than cases where the method 
deviates from the path indicated by the sincere votes in order to be 
strategy resistant, or when counterstrategies need to be applied.

Our discussion so far was pretty much applicable to all Condorcet 
methods. How will you take the WV benefits and additional preference 
information (S/WPO, AWP, CWP) into use? Should voters apply some 
counterstrategy or do you think sincere votes would be enough in the 
methods you mentioned?

> my best,
> James
>
>
> The text of your message follows...
>
>> I'll write a short story explaining why I see the case of large public
>> elections different from the case of individual strategic manipulation
>> examples.
>>
>> The example you used (in the 3/15 post) was:
>>
>> 	Ex. 1: Sincere preferences:
>> 46: A>B>C
>> 44: B>A>C
>> 5: C>A>B
>> 5: C>B>A
>> 	Ex. 1: Pairwise comparisons:
>> A>B 51-49
>> A>C 90-10
>> B>C 90-10
>>
>> And the B voters then voted strategically 44: B>C>A and as a result B
>> won the election.
>>
>> My arguments are based on probabilities and the public nature and 
>> large
>> scale of the election.
>>
>> Let's say that these elections are some presidential elections in USA
>> after a Condorcet based method has been taken into use. Candidate A
>> could be from the republican party. Candidate B would obviously be 
>> from
>> the democratic party. Candidate C is obviously not some centric
>> compromise candidate since A and B voters seem to hate him. Let's say
>> that he is a professional wrestler.
>
> 	You have a gift for imaginative scenarios! (pirates, pro wrestlers…
> what’s next? :-)
>
>> The numbers obviously represent
>> percentages of the total number of voters. The numbers are based on
>> some opinion poll that has been performed some time before the
>> election.
>>
>> The democratic party is thus planning to vote strategically. I'll give
>> some estimates to involved probabilities.
>> - probability of democrats giving a secret recommendation to all its
>> supporters to vote B>C>A => low
>> - probability of democrats giving a public recommendation to all its
>> supporters to vote B>C>A => low
>> - in both cases: probability of comparable number of republicans and
>> others applying some strategy => high
>>   (one can thus not trust that the outcome will be as planned)
>> - probability of sufficient number of democrats voting as they were
>> told => low
>>   (B will not win if more than 3 out of the 44 will not implement the
>> ordered strategy (3 means a tie => 2 or less to win))
>> - probability of considerable portion of democrats voting sincerely
>> even though they were told to vote strategically => high
>> - probability of many voters not understanding the strategy
>> recommendation right or at all => high
>> - probability somewhat different voting behaviour than anticipated
>> based on the opinion polls => high
>> - probability of some democrats not voting at all or voting 
>> republicans
>> because they didn't play dirty strategy tricks before the election but
>> emphasized the need to vote sincerely => high
>> - probability of C getting elected after everybody applying various
>> strategies => low but increases considerably if democrats can make
>> people vote as told
>> - probability of democrats getting their candidate elected by
>> convincing few republicans to vote B => much higher than with 
>> strategic
>> voting
>> - probability of democrats getting their candidate elected by
>> convincing few C supporters to vote B => much higher than with
>> strategic voting
>> - probability of democrats getting their candidate elected by
>> convincing few C supporters to vote C>B>A instead of C>A>B => much
>> higher than with strategic voting
>>   (1 for a tie, 2 for a win)
>>
>> Maybe there are also other reasons. Maybe some that give support to
>> strategic voting(??). And maybe the probability estimates could be 
>> more
>> accurate. But based on this story the probability of deciding to
>> implement the strategy in general, and the probability of a successful
>> outcome of this strategic voting case is in my opinion not very high.
>>
>> What do you think the probability of a) democrats recommending their
>> voters to use this strategy in these elections and b) probability of
>> success of the strategy if implemented is?
>>
>> My message is that although there exist strategic voting patterns that
>> lead to unwanted results, one has to estimate also how serious those
>> theoretical risks are in real life (in this case in large public
>> elections).
>>
>> If strategies are as difficult to implement and results as hard to
>> achieve as in this story, maybe one could get good results by using
>> some sincere voting method and telling voters that the voting method 
>> is
>> well planned and made sincere to take their sincere votes into account
>> in the best possible way. If one would in addition tell that using
>> strategies most likely harms the voters' intentions rather than
>> supports them and best voting scientists would confirm this, maybe
>> people would be first of all happy with the new method and secondly
>> also vote sincerely.
>
>
>
>