[EM] Juho: strategy

[James Green-Armytage]

	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. 
	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

 only slightly more than half of the B faction members need to reverse
(B>C>A) to pull off the strategy. 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 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. (Taking into account the role of
preference strength in the burying strategy is one of the major
foundations of the CWP and AWP methods.)
	The main problem with strategy in margins is that stable
counterstrategies are often not available. As I tried to illustrate in my
March 14 posting, this instability can be severe. WV tends to avoid the
extreme instability of margins, 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.

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.