[EM] A monotonic DSV method for Range

[fsimmons at pcc.edu]

Change the word mx to min in the second step fo the method description so that
it reads ..


(2) A gets the min possible rating (say zero) if more than fifty percent of the
top ratings belong to alternatives rated above A.

----- Original Message -----
From:
Date: Tuesday, April 27, 2010 3:04 pm
Subject: A monotonic DSV method for Range
To: election-methods at lists.electorama.com,

> Median Probability Automated Strategy Range Voting (MPASRV)
>
> It is well known that optimal Range strategy is the same as
> optimal Approval
> strategy. But this optimal strategy is hard to automate because
> (1) it depends
> sensitively on hard to estimate probabilities of winning ties,
> and (2) all
> attempts at automating strategies based on expected ratings have
> turned out to
> violate monotonicity. In fact, most DSV (Designated Strategy
> Voting) methods
> fail Monotonicity.
>
> A near optimal approval strategy which depends less sensitively
> (i.e. more
> robustly) on probability estimates than the optimal strategy
> (and based on
> ordinal information only) is to approve alternative C iff the
> winner is more
> likely to come from among the alternatives that you like less
> than C than from
> among the alternatives that you prefer over C.
>
> Unfortunately, automating this strategy by approximating the winning
> probabilities with random ballot probabilities also yields a non-
> monotonicmethod. But it can be modified slightly to yield an
> automated strategy Range
> method that is monotonic and makes appropriate use of ratings:
>
> Modify each Range ballot so that for each alternative A ...
>
> (1) A gets the max possible rating if more than fifty percent of
> the top ratings
> (taken from all ballots and counted as in a random ballot probability
> computation) belong to alternatives rated (on this ballot) below A.
>
> (2) A gets the max possible rating if more than fifty percent of
> the top ratings
> belong to alternatives rated above A.
>
> (3) Otherwise A's rating is not changed.
>
> Then elect the alternative with the highest average rating,
> where the average is
> taken over all the modified ballots. Settle any ties by use of
> the random
> ballot probabilities, or by random ballot itself.
>
> This method is monotonic. It satisfies Participation and IPDA
> (Independence from
> Pareto Dominated Alternatives) . It is also clone independent
> in the same sense
> that ordinary Approval is.
>
> It may seem that the method would slight candidates lacking in
> first place
> support. However, even when alterantive C has no first place
> support, if
> surrounding candidates are approved on a ballot, our process
> makes sure that C
> is approved also.
>
> To see how this works, think of a voter located in issue space.
> The further the
> options are from her, the lower her respective ratings for them.
> Her approval
> cutoff represents a "sphere" such that
>
> (1) half of the the voters lie inside of the sphere and half
> outside, and
>
> (2) all of the alternatives whose Dirichlet/Voronoi regions are
> containedentirely inside the sphere are approved, and those
> whose regions are entirely
> outside the sphere are disapproved.
>
> (3) those alternatives that lie right on the boundary of the
> sphere get rated
> according to the radius of the sphere (the smaller the radius,
> the higher the
> rating).
>
> The Voronoi/Dirichlet regions are the regions of first place
> support of the
> respective alternatives. In the two dimensional case they are
> the colored
> regions found in Condorcet and Range diagrams of Yee/Bolson
> type, in contrast to
> the wierd shapes found in diagrams of the same type representing
> IRV elections.
> For Range and Condorcet the numbers of voters in the respective
> colored regions
> are precisely proportional to the respective random ballot
> probabilities.
>
> Note that our new method MPASRV automatically respects top and
> bottom ratings,
> so voters who think they have a better strategy can control
> their own approvals
> and disapprovals.
>
>
>