[EM] Strategic polls in Approval

[Juho]

Here's one simple strategy for Approval that I don't remember having  
seen on this list.

- three candidates, A, B and C
- a neutral (and correct) opinion poll tells that A and B are the  
leading candidates and C has somewhat less support
- some A supporters publish a new forged opinion poll that says that  
A and C are now the leading candidates and B has somewhat less support
- voters follow some of the known "optimal" Approval strategies or  
use plan their strategy themselves
- some B>A>C supporters approve B and A, some approve B only
- some B>C>A supporters approve B and C, some approve B only
- some C>A>B supporters approve C and A, some approve C only
- some C>B>A supporters approve C and B, some approve C only
- most A>B>C supporters approve A only
- most A>C>B supporters approve A only

Since A is one of the two leading candidates in both opinion polls  
she is likely to get more secondary approval support from B and C  
supporters than the other leading candidate (B) is likely to get.

The key was to fool some B>A>C supporter to approve also A, and some  
C>B>A supporters not to approve B. Some C>A>B supporters may change  
their opinion and not approve A as a result of the forged opinion  
poll, but their number is expected to be smaller than the number of  
the "positively" fooled voters.

As a result of these changes the probability of A winning is now  
higher. Forged opinion polls thus may be used as a strategic tool to  
improve the chances of one's favourite candidate to win. Also other  
efficient propaganda (like paid advertisements and news/articles in  
media and selective distribution of information) that presents C as a  
serious challenger to A (instead of B) may have the same effect. It  
is typical for people to vote for the anticipated winners in any  
election method, but in Approval the combination of "optimal"  
strategies ("approve at least one of the leading candidates",  
"approve candidates above the expected utility") and forged polls  
seems to offer some additional strategic opportunities.

In some suitable circumstances where people use the formal strategies  
actively one could change the winner even quite mechanically  
(carefully planned forged opinion poll results would do it). But of  
course the situation gets more balanced when all the candidates/ 
parties know these tricks. In this base B supporters would maybe  
publish a third opinion poll declaring B and C as the leading  
candidates (if they still have time for that before the election day).

Juho Laatu

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