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.
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