[EM] A suggested DSV method based on Approval.

[fsimmons at pcc.edu]

Here's an approval based DSV idea that I would like to see tried:

The ballot asks for the following optional information for the purpose of
estimating probabilities of approval wins and ties to be used in the DSV
strategizing:  (1) the voter favorite, and (2) relative scores (on some chosen
range) for the alternatives.  These relative scores can be automatically copied
from a published scorecard if the voter marks such an option.

In addition the ballot asks for (3) an ordinal ranking of all of the
alternatives.  If the voter has left the voter favorite blank in part (1) of the
ballot, the highest ranked candidate from part (3) is filled in as favorite. 
[If a voter doesn't feel the need to strategize, we treat her like a sincere
respondent in a regular poll.]

I. The DSV starts by using the indicated favorites to find the probabilities in
a random favorite lottery.  

II. Then it uses those probabilities to create trial approval ballots from the
combined score information gleaned from part (2) of all of the ballots, by
approving above expected score according to the random favorite lottery.  

III. Let A be the approval winner according to these locally generated
(provisional and unofficial) approval ballots.  Then take many random samples
(with replacement) of size ten from this set of approval ballots.  On the basis
of these samples, for each alternative X, estimate the probability that (in a
sample of size ten) alternative A will be tied for first place with alternative
X.  [Or use combinatorial methods to compute these probabilities, in order to
avoid accusations of "non-determinism!" from the Boetians.]

IV. Finally, on each ordinal ranking from part (3) of the ballot, approve down
to A, and include approval for A if and only if A is more likely to be tied for
first place with an alternative that is ranked below A than with one that is
ranked higher than A in part (3) of the ballot. [These likelihoods are assumed
to be approximately proportional to those based on samples of size ten from the
unofficial approval ballots.]

V.  This second set of approval ballots is the official one, and is used to
elect the winner.

I submit that the method satisfies monotonicity and the FBC with respect to the
ordinal part (3) of the ballot.  Furthermore, for all practical purposes there
is no incentive to submit an insincere ranking in part (3). 

If this version is considered to be too complicated, the provisional approvals
in step (II) can be done on the basis of polled rankings in part (2) of the
ballot instead of scores in a range.

In that case the provisional approval ballots generated in step (II) would
approve each alternative X such that (according to the favorite lottery) an
alternative ranked (in part two of the ballot) below X is more likely to be
elected than an alternative ranked above X.  

In other words, we could use Joe Weinstein's approval strategy as the strategy
for generating the unofficial approval ballots in step (II) instead of the
"approve above expected score" strategy.

What does the sincere voter have to supply? Only one ranking of the
alternatives, and that can be from a published list.  So, for the voter, it is
as easy as any method based on ordinal rankings.

What do you think?