[EM] Responses to some of Forest's ideas

[Richard Moore]

LAYTON Craig wrote:

>>Discounting E and F, 255/4 = 63.75, so possible strategic 
>>vote is CBA. Depending how confident this group is in the 
>>information that D will lose, they might truncate to CB or
>>just C, but we don't know for sure. "C only" seems unlikely 
>>to me unless these voters are reasonably sure of D's and A's 
>>defeats.
>>
> 
> You are basically suggesting a slightly enhanced zero info strategy.  It
> should be clear from the polls that the front runners are B and C.
> Generally, strategy in such a situation is to make your approval cuttoff
> point between the two front-runners.


Knowing E and F are out of the running isn't zero-info. But 
if that's the only information that you consider, then you 
can evaluate the remaining candidates using zero-info 
strategy. Actually, I simplified the mean calculation a bit. 
For each candidate I should have used the mean of the other 
candidates' utilities, not including that candidate. So the 
threshold for B would be 170/3 (again discounting E and F) 
and the threshold for C would be 185/3. Still no need to 
truncate. Considering unequal probabilities for A, B, C, and 
D is considerably more difficult. This is where we need the 
Pij for each pair (not just who the front-runners from a 
poll are) and I don't think we can calculate that with 
precision for the reasons I give below.

>>Incidentally, I've long suspected there is (in general) no 
>>such thing as universally available "perfect information" in 
>>Approval voting. 
>>
> 
> If you knew that other voters were rational utility maximisers, perfect
> information would be their sincere utilities.  In a real life situation,
> detailed polls could be close, if the pollsters ask questions like "if x and
> y were the frontrunners, what would be your approval vote?".  Supporters of
> particular candidates would probably have similar enough voting patterns or
> strategies to enable an accurate prediction.  The problem with polling is
> not that it is inaccurate - as a general rule a well designed and adequately
> resourced survey is highly accurate - it is that it is constantly out of
> date, as voters change their minds.


I should have been more clear. To me, "perfect information" 
would mean knowing how everyone else will vote. If "perfect 
information" were merely the knowedge of the sincere 
utilities of all voters, then it is still (usually) 
insufficient for calculating strategy because of the 
circular dependencies I mentioned. Also, in polls for 
Approval elections, there is no reason to believe everyone 
polled will reveal their actual vote. Maybe, to boost 
support for their favorite, they will claim they are going 
to vote "A only", then when they go to the polls they will 
hedge and vote "AB". This means that I agree with your last 
point about polls being "constantly out of date".


None of this should be taken as a strike against Approval. 
No rational voter will reverse a preference in Approval, and 
if a voter collapses a preference in Approval there is 
another preference that gets expanded in exchange (unless he 
foolishly collapses his last preference). The rational voter 
will *exchange* preferences (AB>C for A>BC, e.g.) only if he 
believes he will receive a higher utility expectation in 
return. I believe this is what Forest meant when he called 
Approval strategy "benign".

Richard