[EM] Re: Juho: strategy

[Juho Laatu]

On Apr 26, 2005, at 13:15, James Green-Armytage wrote:

>> 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"

With practical election situations simply referred to the large public 
elections that have been discussed in this mail stream (there are also 
others). This is an election type where many strategies are not so easy 
to apply. US presidential elections are a special case of this generic 
category of elections. This "large public" category is of course a 
quite central category in real life.

Another type of election would be for example this election methods 
community arranging weekly elections (and daily test elections before 
the main election) on which one of a certain set of candidate election 
methods is the best. Negotiations trading with the elections of the 
following weeks would be allowed. I'm sure people would try every 
available strategy. Vulnerability to strategies would in this case be 
much more probable than in the large public election case (because of 
the expertise of the voters, small community, test elections, small 
"parties" that could negotiate their tactics, ability to make deals 
with enemies behind the screens, small number of candidates, known 
preferences of many voters).

> 	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.

Uncertainty has also some positive effects. If strategies lead to 
unexpected and unwanted results, then it is easy to tell voters that 
they should not try to vote strategically since that probably makes 
their situation worse, not better. This is closely related to the 
general very basic (non strategical) observation about Condorcet 
methods that voter whose sincere opinion is A>B>C>D need not vote 
A>C>D>B (to make the situation of the other strong candidate B worse) 
since that change doesn't make the A>B preference any stronger.

> 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)

Maybe this attitude ("my candidate is good, others not good at all") is 
common among people. Maybe one could assume that in some elections 
(e.g. when there is only one candidate from each party) even if the 
voters wouldn't be given the chance to mark ratings in the ballots.

> 	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.

Sounds like some game theoretic situation where both using the strategy 
may lead to a catastrophe to both but one applying it may lead to 
benefits. It is difficult to say to what kind of behaviour this leads 
to. I'm hoping that the risks would be stronger than the benefits and 
as a result people would avoid strategic voting. I'm not sure though.

People are also social creatures, and if the community encourages 
sincere voting, most people will follow that (which is enough to 
eliminate many strategies). Alternatively most voters would go for 
strategic voting, but that situation of the society would then be known 
to all.

Note that natural loops are not common in elections and artificial 
(=strategically created) loops are not that easy to generate. In the 
"no loop" situations Condorcet methods are quite immune to strategies 
and sensible people would vote sincerely. Maybe this would encourage 
sincere voting as a rule in the society.

Wrestler supporters' strategies are also interesting. They have 
different interests depending on which of the D/R strategic voting 
scenarios takes place. Complex mixture of strategic voting could lead 
to electing the "sincere winner".

>> 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.

You almost give the generic simple rule (as an alternative to party or 
press led strategies) for normal voters that I asked for. The rule 
could be "put the serious competitors last in the ballot". This rule 
could help in some situations but maybe (hopefully) it would still 
bring more harm than benefits if used by people who don't know when it 
is likely to bring results.

Btw, it would be good to get some estimates on how probable it is that 
this kind of basic strategies make the results better/worse (when 
applied without coordination and without good understanding about the 
preferences of the voters). Note also that the strategy where people 
intentionally create a loop between the candidates of a competing party 
is quite risk free and from this perspective more problematic than the 
burial type that we are discussing here.

>> 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?

Yes, that is also possible, especially if experts tell that that would 
help.

> It's
> probability of improvement times strength of improvement minus 
> probability
> of harm times strength of harm

Yes, this is a valid formula.

> 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.

Yes. In large elections this probably means that you and a considerable 
number of people who share your opinions will vote in the described way 
to achieve the results.

If there are three candidates with exactly equal amount of support it 
is probably too difficult to guess the direction of the cycle and 
correct strategy (there is  no weak candidate that could be used to 
bury a strong candidate).

> 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...

I can make some mail searches. Not too many mails on this topic yet.

> Smith-efficient
> methods have some extremely significant advantages over all other 
> methods

Smith-minmax excluded or included? I.e. is Smith efficiency the exact 
criterion here?

> they should
> each be assumed to be guilty of extreme strategic vulnerability until
> proven innocent

Fatal strategic vulnerability is of course a show stopper, but it 
appears not to be easy to tell which threats are fatal in real life.

> The problem with margins is that
> the relatively stable counterstrategies like the WV one mentioned above
> don't serve to deter it.

But here I make some probabilistic calculations on how many people 
would be able to apply the correct strategies, and how likely these 
strategies would be needed, and how likely it is that they would cause 
harm, and thereby make difference between margins and WV significant. I 
put also some weight to the sincerity of margins (maybe more because of 
the psychological effects of than because of the fact that it sometimes 
would elect a better candidate).

>> 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.

Agreed. Sincere votes are much better than the need to apply strategies.

Best Regards,
Juho