[EM] "Meaning" of a vote (or lack thereof)

[Warren Smith]

On Thu, Sep 8, 2011 at 2:25 PM, Toby Pereira <tdp201b at yahoo.co.uk> wrote:
> I think part of the problem then is that as far as I can see there is no
> clear and easily understandable description of Double range voting in
> existence.

Let epsilon>0 be a constant.

RULES OF DOUBLE RANGE VOTING
1. Each voter supplies two ballots: the "please be honest sub-ballot"
(scoring each candidate with a real number in [0,1]) and another such
ballot this time with no request for honesty,
call that the strategic sub-ballot.
2. From the strategic sub-ballots, determine who the range-voting
winner A, the second-placer B, and the third-placer C (winner is the
one with highest average score)
3. Let L denote the following lottery: With probability p, the winner
is C; otherwise it is B. Here p is the fraction of strat-sub-ballots
which express a clear preference for C over B.
4. If at least half of all range-style sub-ballots score A greater
than the expected rating for L, that is
score_n(A)>p·score_n(C)+(1-p)·score_n(B)    is satisfied by at least
half of all ballots n, then elect A and stop.
5. Randomly-uniformly select a real number q with 0<q<1. If q>epsilon
then elect A and stop.
Randomly select a strat-sub-ballot (all equally likely). If it
expresses a clear preference for C over B, elect C; otherwise elect B.
Stop.


> Also, it's not intuitively obvious to everyone what the different scores
> should mean. Voting A>B>C in a ranked list is clear. I know there are
> strategic considerations that mean you don't necessarily vote in order of
> favourite, but you are essentially telling the ballot that that is your
> preference order, even if it isn't strictly true. That's essentially what it
> means.
>
> I understand about utility and score votes but it wouldn't be clear to
> everyone, and also people wouldn't know in reality what level of utility to
> expect from each candidate.

--the scores on honest-sub-ballots have a clear "meaning."   If you deny it,
then find an example election in which voting any way other than honest
expected utilities, helps that voter.  You cannot.

Voting "A>B>C", while it may be "clear" to you, in fact may cause A to lose,
or C to win, in every deterministic non-dictatorial ranked-voting scheme...
This is the Gibbard-Satterthwaite theorem.
This suggests that the problem is not that A>B>C has meaning and rnage-style
ballots do not.  It is that you have a wrong perception of that.  But the whole
point of my post waas to correct this wrong perception.  If you now say
"but this wrong perception exists!" that does not refute my post.  It supports
my post's raison d'etre.


> It would be very difficult for someone to
 calculate/guess.

--Sure, some people, or even more likely, some lower animals,
may have trouble.   That's just a speculation unsupported by, and in
fact flatly contradicted by, the actual evidence measuring e.g.
elapsed time taken for range-style voters versus rank-order-style
voters (the latter take longer, indicating more mental effort for rank
ordering).

But the question here was not about what a naive uninformed guesser
might think their mental effort would be; it was about the inherent
presence or absence of meaning. And the person involved was not a
lower animal, but in fact a Nobel prize winning expert on Voting, Ken
Arrow, and another Nobelist, E.Maskin.