[EM] Strategic polls in Approval

Juho juho4880 at yahoo.co.uk
Sun Jan 7 13:19:31 PST 2007

On Dec 31, 2006, at 4:55 , Abd ul-Rahman Lomax wrote:
> At 01:59 PM 12/30/2006, Juho wrote:
>>  Im multi-party countries or if parties
>> have more than one candidate that is not exceptional.
> That's right, though the latter situation requires that the party  
> in question have two-thirds of the electorate as supporters,  
> effectively. Such a party would not be likely to run two  
> candidates, for if it did, under some systems, it would risk losing  
> the election. However, with Approval, it could. And if there were a  
> third candidate with parity with the two from the party, party  
> supporters would be well advised to vote for both the party  
> candidates. If even half of them do, there is no chance for that  
> third candidate. What would be strange, indeed, would be for  
> significant party supporters to vote for the third candidate, and  
> that is exactly what it would take for the poll strategy to have an  
> effect....

It is also possible that the three leading candidates would come from  
the same party. Or that there would be smaller parties whose  
supporters would influence the outcome. The strategy may be efficient  
(not as certain but may work) also in the case of two candidates from  
one party and one from the other party in a two-party system (e.g. A  
and B from the same party).

>> In the example it was ok if voters were uncertain of which opinion
>> polls are reliable. The plotters were happy with the confusion (as
>> long as they could avoid having polls where A was not among the
>> leading candidates).
> How could they avoid that? They can't control all the polls, and if  
> they can fake polls, so can someone else.

Surprise attack may work. In the next elections things could be  

It is also not nice if people stop trusting any polls because of the  
fear that they are somehow rigged just to make them vote wrong.

It is btw also possible to advice supporters of some candidate to  
answer the polls in a special way. A supporters might e.g. answer  
that they are going to vote for A and C even if they are not.  
(Another interesting area for study.)

> My point is that this strategem depends upon voters using a voting  
> strategy which is inappropriate for the three-way race that is  
> involved. That strategy is not designed for such races, it is  
> designed for races where there are two and only two frontrunners.

I think the approval strategies that refer to approving candidates  
that are above the anticipated utility don't take position to the  
number of candidates. Also strategies that refer to approving one of  
the two frontrunners candidates do not necessarily need to exclude  
cases where it is not crystal clear who the two lead candidates are.  
Attempts to improve the optimal Approval strategy (like the one that  
you mentioned) are of course always welcome (zero info or others).  
The example only pointed out that the common optimal Approval  
strategies can play a part in a strategic attack (if voters are  
anticipated to use them).

>> In the example the first (correct) poll showed that A and B had more
>> support than C (but only so much that the A supporters could claim
>> that also C could be a lead candidate).
> Right. So all are close to winning. Now, is this "first preference"  
> polling or "approval" polling?

I didn't take position on that but both cases work. Approval polls  
are more accurate when asking opinions before an Approval election.  
Preference order of the approved candidates would provide additional  

> I don't think that the analysis of the stratagem's effect was  
> thorough. To be thorough, one should consider preference strengths,  
> they affect how the voters will respond to the misinformation.

It was not thorough (just a description of the vulnerability). I made  
some calculations also with approving candidates that are above the  
expected utility of the election and the strategy seemed to work at  
least with some reasonable personal utility assumptions (e.g.  
utilities 2-1-0 for all voters).

> Now, if voters have a preferred candidate, I'd think they would  
> listen to that campaign's releases about how the election was  
> going. They would not be terribly likely to be influenced for  
> strategic voting purposes by releases from the campaign of another  
> candidate, not even by supposedly public, disinterested polling  
> organizations.

The A supporters should not hide their involvement in the poll if  
possible. But also a poll signed by A supporters may have sufficient  
impact in a close race.

> I don't think it is possible to distort the polls sufficiently that  
> a rational voting strategy would be seriously affected.

Small changes are sufficient if the margins are small. Of course all  
kind of propaganda will be distributed. Utilizing the Approval  
default optimal strategies is just one of the tricks, not necessarily  
the decisive one. In the example the A supporters managed to publish  
a competing opinion poll that was considered credible by some, and  
that was a sufficient condition for the strategy to work.

> It is only a mindless strategy where voters determine solely who  
> the top two are and don't pay attention to another candidate  
> yapping at the heels of those two. And who is going to advise  
> voters to vote that way? In the context of a true three-way race?

I think the writers on this mailing list have thoroughly discussed  
the optimal Approval strategies. I was assuming that part of the  
voters would follow those rules or some similar logic that they  
developed themselves. One could have also publicly known optimal  
strategies that would treat three-way races and so on in a different  
way than the current optimal strategies. Another path would be to  
rely on party/promoter/media recommendations on how to vote but that  
is another (interesting) story that I didn't yet cover much.

Here is one more explanation on how the example case was supposed to  
work (just to clarify what I maybe left unsaid).
- the first poll (A and B leading) was valid for some time
- C>B>A supporters were recommended to approve C and B because they  
should make a difference between the two leading candidates
- this election was thus at this point a race between the two key  
candidates, A and B
- the second poll was released maybe just one day before the election
- some C>B>A supporters applied the old recommended logic in the new  
situation and approved only C (since it seemed to be one of the  
leading candidates)
- and so on for the other cases
This was thus a surprise attack based on one party using this  
strategy more powerfully than others.

Juho Laatu

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