[EM] Re: Juho: strategy

[James Green-Armytage]

Hi Juho. Here is a rather rough and jagged reply to your message...
>
>I have written on practical election situations since it seemed to me 
>that that area has not been covered sufficiently on this mailing list. 

	You'll have to define "practical"... and when you do, I may not accept
your definition. Some methods may be practical in that the rules are
relatively few, but impractical in that they will prove unstable once in
use. On balance, I would call such methods "impractical".
>
>Should I read your comment so that strategic manipulation of large 
>public Condorcet elections has already been discussed widely on this 
>list 

	Yes.

>and proven to be easy? 

	No, not necessarily. There is disagreement on this point, but your view
may be more commonly held than mine among Condorcet fans. The
theoretically-minded IRV fans may tend to have a darker view of strategic
possibilities in Condorcet than the Condorcet people do, though, although
to be fair they are probably thinking of the margins methods more than
anything else...

James:
>> 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
Juho:
>
>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?

	>> can mean a lot of different things. In S/WPO it's a strong preference.
In approval cutoff methods it's an approval cutoff. When talking about
sincere preferences, it's a strong preference. I think that the latter
usage was my intention above.
>
>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.

	Uncertain information is what makes the strategy problem in margins so
bad. If information was certain, then the CW would be known, and this
would simplify things somewhat. But if the true CW is not known, then both
sides have a potential incentive to bury, which is what leads us to
disaster. Keep in mind that if only one side buries, and their candidate
happens to win the primary pairwise contest anyway, the burying doesn't
hurt their cause. However, if they don't bury, but the other side does,
then the pairwise winner doesn't matter; the other candidate wins either
way.

Sincere preferences as known by voters (Dem-Rep contest uncertain), with
utilities
46/44?: Dem >> Rep > wrestler (100, 5, 0)
44/46?: Rep >> Dem > wrestler (100, 5, 0)
5: wrestler >> Dem > Rep (100, 20, 0)
5: wrestler >> Rep > Dem (100, 20, 0)

	Game matrix. Payoffs expressed as (Rep, Dem)

			Dems bury			Dems don't bury
Reps bury		wrestler wins (0, 0)	Rep wins (100, 5)
Reps don't bury	Dem wins (5, 100)	pairwise winner wins (52.5, 52.5 on
average)		

	As far as I know, this game is called "chicken". Can you tell me how
people will vote, and who will win? I don't think that I can tell you who
will win, but I think that the wrestler has a pretty good shot.
>
>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.

	Good question. The idea that one side does it but the other side doesn't
is intended just as a starting point, to show that whichever side loses
the primary pairwise contest can recapture the election through burying,
i.e. to show that the *incentive* to bury in the first place exists no
matter who the sincere winner is... and that this initial incentive to
bury feeds the incentive for the other faction to retaliate. I don't
assume that the strategy would be limited to one side, especially given
uncertainty as to the real CW. In margins, the initial burying strategy is
indistinguishable from the deterrent counterstrategy, so the question of
who started the chicken game can quickly becomes a chicken-and-egg
question. (Too many chicken metaphors in one sentence?) The real ugliness
starts when both sides try the strategy en masse.
>
>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, 

	Not necessarily. Imagine a Bush>>Kerry>John Doe voter, who marginally
prefers Kerry over John Doe but hugely prefers Bush over Kerry. Kerry is
obviously the main competition to Bush. Isn't there something
instinctively unattractive about ranking Kerry in second place? I think
so. Even if you don't understand the method at all, instinct can be to do
as much harm as possible to the main rival to your favorite viable
candidate.

>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. 

	Yes, if the C>A>B voters vote C=A>B, this resolves things. But what if
they prefer C>A strongly enough that they're not comfortable with that?
Maybe they want to wait it out and see if the A and B factions throw the
race to C through mutual order reversal.

>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. 

	Exactly. It's too complex to predict. Therein lies the problem.

>Maybe they will stop voting, or maybe they 
>would campaign for some other voting method than Condorcet to be used, 

	Or perhaps a more strategy-resistant variant such as CWP or AWP?
>
>or maybe they love plotting :-). 

	Haha, yes. The whole election becomes one big game show, like Survivor or
something. I don't think I want that...

>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?

	In margins, no. In WV, maybe. In CWP, usually unnecessary.
>
James:
>> 	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.
Juho:
>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?

	No, it's not a particular example; it's a general point. Very key point,
please don't skim over it. If I very strongly prefer A to B, and very
weakly prefer B to C, and voting A>C>B increases A's chances of being
elected, then I will probably want to do it, even if it increases C's
chances of being elected even more than it increases A's chances. It's
probability of improvement times strength of improvement minus probability
of harm times strength of harm, but since the potential improvement is so
much steeper than the potential harm, the strategy is a good idea given
all but the very steepest probabilities. 
	Here is a particular example...
My ratings and utilities for the three candidates... A>B>C (100, 5, 0)
Probability of each candidate winning if I vote A>B>C... A: 40%, B: 55% C:
5%.
Probability of each candidate winning if I vote A>C>B... A: 45%, B: 40% C:
20%
Total probabilistic utility given A>B>C vote = (100*.4) + (5*.55) + (0) =
42.7
Total probabilistic utility given A>C>B vote = (100*.45) + (5*.4) + (0) =
47
	Even though C gains more probability of winning than A as a result of my
strategy, the overall probabilistic utility goes up, so it's attractive to
me. Of course, in an election with a large number of voters, the change in
probabilities would not be anywhere near so large, but you should get the
idea anyway.
>
>> (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. 

	Thank you.

>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). 

	Well, you could just use cardinal ballots and infer the rankings from the
ratings.
	Cardinal pairwise is impractical for hand-tallied elections. It is
practical for electronically tallied elections with an electronic
interface (e.g. touch screen).

>But seeking the limits of taking voter 
>preferences into account as much as possible (and maybe also reducing 
>strategy risks) is valuable research.

	Thank you.
>
>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?

	Yes, I have considered it, if I get your meaning correctly, i.e. to
measure defeat strength in CWP by general marginal utility rather than
winning marginal utility. I'm quite convinced that it would lose the
anti-strategy benefits and the sincere benefits as well. In short, it
defeats the whole purpose. However, after I proposed CWP and AWP, Chris
Benham took up the idea of a margins version of both, and I haven't been
able to talk him out of the "approval margins" method as yet. I could dig
up some of my postings on the subject if you like...
>
>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. 

	Yes, it might be. And then again, it might not be. Smith-efficient
methods have some extremely significant advantages over all other methods,
especially those that aren't Condorcet-efficient. In the long run, I'm
optimistic about them, but as I wrote recently, I feel that they should
each be assumed to be guilty of extreme strategic vulnerability until
proven innocent, assuming that one wants to use them for serious
elections. As for margins, I feel that it is in fact guilty. As for
cardinal pairwise, I am nearly sure that it is innocent, or innocent
enough. My jury is still gradually deliberating on WV, although other
people's juries may have already rendered a verdict.

>Normal voters are hardly capable of 
>applying correct counterstrategies unless you have some very simple 
>rules for them to follow.

	That may be possible. For example, in an election with two strong
candidates, if WV is used, it usually makes sense to recommend that voters
truncate before ranking their least favorite of the two major candidates.
What about elections with more than two strong candidates?... haven't
figured that out yet :-) ... 
>
>(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.)

	Perhaps the main problem with approval strategy isn't the complexity of
the strategy but the availability of information and the clumsiness of
coordination.
>
>I don't see the "extreme instability" 

	I do.

>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.

	That can theoretically happen in both. The problem with margins is that
the relatively stable counterstrategies like the WV one mentioned above
don't serve to deter it.
>
>In those voting methods one could get some strategy defence benefits 
>also with sincere votes (that you could also call an "unintentional 
>counterstrategy"). 

	Yes! That's one of the best things about cardinal pairwise. Sincere
ratings very strongly tend to make burying strategies unprofitable. 

>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?

	CWP is better than AWP is better than S/WPO(WV) is better than WV is much
better than margins. In CWP and AWP, sincere votes should almost always be
sufficient, but conscious counterstrategy can yield additional benefits in
special cases. In WV, some prophylactic counterstrategy is strongly
recommended when the electorate is sufficiently contentious to become
devious. Most of the benefits of S/WPO probably come as a result of
sincere voting, but in general the protection offered by S/WPO is not
equal to that of CWP and AWP. I'll support this last assertion in a later
post.
>
Sincerely,
James