[EM] Unranked-IRV, Cumulative, and Normalized Ratings
Richard Moore
rmoore4 at home.com
Mon Apr 23 22:31:59 PDT 2001
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
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