[Election-Methods] [english 92%] Re: a strategy-free range voting variant?

[Warren Smith]

Dear Jobst Heitzig

Your new strategy-free voting idea which you described here
  http://article.gmane.org/gmane.politics.election-methods/13693
(which is a fairly radically innovative new approach to
Clarke-Tideman-Tullock voting, and I am CCing Ed Clarke and N.Tideman
in this email)
looks VERY interesting and might be
an excellent idea.

But I do not fully understand it yet and I think you need to
develop+clarify+optimize it further...  plus I'd like you to unconfuse me!

Here are some questions (I quote you after ">" then my questions about
that quote follow, then repeat):

> Of course, this is far from being a new idea so far, and it is not yet
the whole idea since it has an obvious problem: although it obviously
manages to elect the "better" option (the one with the larger total
monetary value), it encourages both the seller and the buyer to
misrepresent their ratings so that the gap between R2(B)-R2(A) and
R1(A)-R1(B) becomes as small as possible and hence their respective
profit as large as possible. In other words, this method is not at all
strategy-free.

--QUESTION:
if they make the gap small, then the buyer pays little to the seller.
Yes, that is better for the buyer.
But doesn't the seller have the opposite incentive?
It is not clear to me the "incentive" you say exists here, really does exist.
If it doesn't, then you do not need to fix this "problem"
because there is no problem. It'd help to clarify this point.


>5. Finally, the voting accounts are adjusted like this:
a) Each deciding voter's account is increased by an amount equal to the
total rating difference between the winner and the benchmark lottery
among the *other* deciding voters, minus some fixed fee F, say
10*N^(1/2). (Note that the resulting adjustment may be positive or
negative.)

QUESTION:
I'm confused about this whole benchmarking thing.

You said the "benchmark" voters were being benchmarked, but now you
say the "deciding"
voters are being benchmarked.  ???

What does "total rating difference between the winner and the
benchmark lottery among the *other* deciding voters" MEAN precisely???
  This is not clear english...  the winner's rating is a number but
"the benchmark lottery" is not a number.  You need two numbers.

>The compensating voter's accounts are decreased by the same total
amount as the deciding voter's accounts are increased, but in equal
parts. (This may also be positive or negative)

--this seems to hurt poor voters.  I.e. if there are "rich" voters who
vote +-100
and poor voters who vote +-1 then the poor voters will need to pay the same fee
in 5b as the rich voters.  They may therefore have incentive to avoid
being in the electorate at all, in which case the electorate will
become biased (rich-dominated).

Of course, it is no "real money" so maybe this does not matter.
Everybody is initially equally
"rich."   But perhaps that is itself a misrepresentation?

>and the
benchmark lottery will tend to equal the ordinary random ballot lottery
with all voters.

--I do not understand what this means exactly.

>In particular, the method is quite efficient.

--what does "efficient" mean?

>If the fee F is set so that the expected (in a reasonable model)
adjustments of the individual accounts are all zero

--well, I'm not sure what that means, but it seems like F can be
readjusted every election
so over a long sequence of elections accounts balance.
Then F would not be "fixed" but it could be fixed in each election
individually.  Does that matter?

>Finally, if I'm not mistaken, the method is still strategy-free for
these reasons: i) A benchmark voter's "favourite" mark does neither
influence the winner nor the voter's own account, so there is no
incentive to misstate the favourite. ii) A deciding voter's ratings do
influence the voter's account only by influencing the winner; the same
arguments as above show that it is optimal for a deciding voter to
sincerely state her true ratings. iii) A compensating voter's ratings to
not affect anything. Since you don't know in which group you end up,
your optimal vote is the true ratings!

--I think your basic ideas summarized here seem
VERY promising, but as above I am
confused about the details --
and even when I get unconfused
there may be modifications
that may be desirable.
I would like to post this all as a web page on the CRV web site
(credited to you of course) when things clarify, if you permit.

--Warren D. Smith
http://rangevoting.org