[EM] Cranor's method (was unranked IRV, cumulative, etc.)

[Forest Simmons]

Suppose that one block of voters has access to all of the voter utilities,
and they also own a Cranor Strategizer.

Hoping to gain some advantage, they run the program (based on their own
sincere utilities along with those of the other voters) until it spits out
a recommendation for whom they should approve in the election.

Then just for fun, then run the program again, only this time as input
they use everyone's sincere utilities except their own. In place of their
own sincere utilities they input the distorted utilities (zeroes and ones)
that were the final output for their faction in the previous run of
Cranor's program.

This time Cranor's program spits out the exact same recommendations as
before, because it is just giving advice on how to optimise strategy; 
because our friends' strategy is already optimum, they won't get advice on
how to improve it (if I understood you correctly). 

Our friends are disappointed; they were hoping that if they input their
optimum strategy at the beginning (in place of their utilities) they would
gain some advantage over the poor blokes that couldn't afford a Cranor
Strategizer. 

If I understand correctly, this tactic will neither help nor hinder our
friends. It will not hinder our friends because the method is monotonic.
It will not help our friends, because you cannot fool the system by
putting in insincere utilities.

Another thing.  It seems to me that if Cranor advised me to approve AB
but the election went to E (skipping over C and D), I would be pretty
upset, especially if it turned out that everyone voted precisely as
advised by Cranor.

Therefore I assume that once Cranor figures out that E is going to win,
she is going to advise me approve down to E.  Whether I am advised to
approve E itself or not would depend on whether my (faction's ?) failure
to support E would result in someone I considered below E winning.

Suppose that E is destined to win (if everyone votes their optimum
strategy) and that everyone who is advised to vote down to and including E
follows that advice, but that the other folks rebel and refuse to vote
down to just above E. Then E would still have to win, because no other
candidate increases in approval.

Forest

On Mon, 23 Apr 2001, Richard Moore wrote:

> I doubt the method is non-monotonic; the counting is done by Approval.
> 
> The reason you got the A answer the first time is that you fed the other
> voters' information into the simulation of the election. The strategizer in
> the real election only improves your vote over the simulated election if
> the simulated election has incomplete or incorrect information. If the
> information that comes out in the real election is identical you will get
> an A answer again.
> 
> Suppose that your simulation tells you to vote AB. You might then
> change your utilities in the real election to force your strategizer to
> cast an A-only vote. But this will not be a better strategy for you,
> because the AB vote was recommended based on the strength of
> candidate B.
> 
> I'm assuming that the central statistical algorithm in Cranor's method
> only looks at the Approval votes and not the underlying utilities. If it
> were to always give the maximum utility result, then it would be the
> equivalent of CR and voters will vote as they would in CR. It has to
> be non-linear.
> 
> Perhaps a good analogy could be found in a poker game. If everyone
> bets blindly -- not knowing the other players' bets -- the poker game
> is like standard Approval. If, on the other hand, you can observe the
> other players' bets, then you can guess at the strength of their hands
> and adjust your strategy accordingly. Cranor's method would be like
> looking at the players' initial bets and subsequent raises and calls (but
> not their actual hands) and trying to deduce who has the strongest
> hand.
> 
> A better analogy might be found in bidding in a game of bridge, but
> I don't know enough about bridge to conjure one up.
> 
> Richard
> 
> 
> Forest Simmons wrote:
> 
> > I'll be more specific.  Suppose that there are three candidates A, B, and
> > C , of which your favorite is A, and that there are five voters. You ask
> > the other four ahead of time what their utilities for the three candidates
> > are.  They trust that Cranor's method is strategy proof, so they frankly
> > tell you exactly how they intend to vote on the CR ballots.
> >
> > Before you vote in the real election, you run her algorithm based on your
> > sincere utilities, as well as the information that you have received from
> > the other four voters and find that after several iterations of the
> > algorithm, the strategizers have converged to constant advice on whom each
> > of the voters should approve. In particular, the final advice you receive
> > is to bullet vote for A, even though you had a utility of 70% for B.
> >
> > You decide to take a chance of fooling Cranor, and bullet vote A in the
> > actual election.
> >
> > When the election results are in you find out that the other voters voted
> > exactly as they had foretold.
> >
> > But you find out that this time Cranor is advising you to approve AB.
> >
> > That would seem fishy to me.
> >
> > In other, words if you already know the advice that Cranor is going to
> > give you, wouldn't you do just as well or better to use that advice on the
> > initial CR ballot?
> >
> > If giving more relative support to A on the initial ballot decreases A's
> > chances to the point that Cranor's advice changes from "approve only A"
> > to "approve AB", then I would have to conclude that the method is
> > non-monotonic.
> >
> > Forest
> 
>