[EM] A monotonic DSV method for Range

[fsimmons at pcc.edu]

Jameson, 

I appreciate your comments, especially about the need for a DSV method that
doesn't make the voter feel like her interests were not optimally or even nearly
optimally advocated.

In our case, the DSV converts Range ballots into Approval ballots.

The classical example is

x:ABC
y:BCA
z:CAB

where  max{x,y,z} < (x+y+z)/2 .

Is it possible for the DSV to place the approval cutoff's in such a way that all
of the voters feel like their expressed interests were well cared for by the DSV?

No.  Why not?

Consider the case of A being the winner.

For A to be the winner the DSV would have to place the cutoff below the A in the
third faction

z:CA|B.

The only consolation for the second faction is if the DSV approved C .

y:BC|A

The DSV would be accused of almost giving it away to B unless it put the cutoff
between A and B in the first faction.

x:A|BC

In summary, if A is to win, and the DSV performance is to be seen as
satisfactory by the A and B factions, then the approval configuration has to be

x:A|BC
y:BC|A
z:CA|B

But then the C faction will feel betrayed by the DSV, because in their view the
DSV  played their hand wrong by approving A.

So A winning is incompatible with all parties being satisfied with the way that
the DSV played their hand.

Then by symmetry neither B nor C winning is compatible with DSV satisfaction either.

So what would our method MPASRV do?  It depends on the ratings of the middle
alternatives in each of the factions.  Suppose that all three of them are rated
half way between the two extremes.

The WMA rule would have all three of them approved, as in MCA or three slot Bucklin.

The first rule I gave for MPASRV would give them each half approval since
neither the candidate rated above nor the one rated below has a full majority of
random ballot probability.  So this version of MPASRV picks the Borda winner.

The most recent approval cutoff rule I proposed coincides with the WMA rule in
this case, so the Bucklin winner is preserved.

Here's a simpler statement of that most recent version, which I claimed was
generally more stable than the WMA rule:

On each ballot b, for each rating level r between zero and 100, approve the
alternatives rated at level r iff the alternatives rated strictly above r on
ballot b account for no more than r percent of the random ballot probability.

If the voters can understand this DSV policy, and rate the alternatives
accordingly, then they have nobody but themselves to blame if they think that
the approval cutoff was put in the wrong place. 

In other words, the only role of the DSV is to find out the random ballot
probabilities and make the approval decisions that the voters would have made
had they been told these probabilities by some oracle in advance.

In particular, if I rate alternative x at level 20 (on a scale of zero to 100)
it means that if no more than 20 percent of the random ballot probability
accrues to alternatives that I prefer over x, then I would like alternative x to
be approved, otherwise not.

If the DSV carries out this instruction (and all other similarly encoded
instructions) faithfully, then I can have no complaint against the DSV.

The only complaint against the method (as opposed to the DSV itself) is that it
requires me to think about how much random ballot probability there would have
to be in alternatives I prefer over x before I would be willing to leave x
unapproved.

[Of course, one could always vote above or below the line or copy candidate
cards like they do in Australia with STV.]

>From another point of view, this understanding of MPASRV gives more concret
meaning to the ratings than regular Range voting does.  Many people with serious
doubts about ratings as utilities would welcome a cardinal ratings method where
the numbers have such precise and well defined meanings.

The voters who don't want to think too hard can rate intuitively, and the method
will almost surely improve the effect of their ballot beyond its face value.  In
other words, if the typical voter had to choose at random between having their
raw ballot added into the total or having their ballot as transformed by the DSV
added in, they would more likely than not be better off going with the latter.

Suppose for example that the voter rated above 50 all of the alternatives that
she considered approving on a zero information basis, and below 50 all of the
alternatives that she was not inclined to approve on a zero information basis. 
Would she be better off (1) having the ratings added in, (2) forcing the
approval cutoff at 50, or (3) letting the DSV handle the approval cutoff?    I
think that (2) is better than (1), and (3) is better than (2).  In fact, the DSV
will move the approval cutoff above or below 50 percent depending on the over
all support (as reflected in the random ballot probabilities) for the candidates
rated above 50. In general the more the support among the highly rated
candidates, the higher the cutoff will be.  The less the support, the lower.the
cutoff.  As the potential cutoff gets lower and lower, the support for the
alternatives above the moving cutoff grows until the (random ballot) support
meets and balances with the decreasing cutoff rating.

In regular Range voting the voters have to balance expressivity with strategic
power, which requires ratings at or near the extremes.  If we let the DSV do the
dirty work, then we are free to keep the ratings spread out between the extremes
in a way that more fully expresses the relative esteem we have for the various
alternatives..

My Best,

Forest



----- Original Message -----
From: Jameson Quinn
Date: Tuesday, April 27, 2010 7:59 pm
Subject: Re: [EM] A monotonic DSV method for Range
To: fsimmons
Cc: election-methods

> I like this method a lot. I think that some kind of range-based
> DSV is
> probably the ideal system, as long as it's not too much work for
> the voters
> in question. (I favor Bucklin for similar reasons - it can be
> seen as an
> unsophisticated, but extremely easy, form of DSV).
>
> I don't have much more to say about the method. But I do have
> one comment on
> your justification:
>
> To see how this works, think of a voter located in issue space....
> >
>
> This explanation did help me understand the method. However,
> it's important
> to remember that any simple (unweighted) issue space analysis,
> by nature,
> ignores the possibility of condorcet ties, because they can't
> exist in
> unweighted issue space. That means the task is just to choose
> the candidate
> whose Dirchlet set includes the median voter - and there's a lot
> of methods
> which do that, at least with honest voters. The real test of a
> DSV method is
> how it handles Condorcet ties. Essentially, I think that the
> object of a DSV
> should be to minimize honest voter regret about how their
> virtual DSV ballot
> was counted - that is, minimize the pressure for a dishonest
> strategy. You
> can define regret variously, I'd define it to include a product
> of how
> dishonest/risky the voters' better strategy would have been, and
> the utility
> benefit they would have gotten. Note that both of these numbers are
> definite, not probabilistic - there is a definite winner now,
> and there
> would be a definite winner for any cabal strategy. I don't
> really understand
> how this system would react to a Condorcet tie - it seems it
> would depend
> all-too-much on whether one of the top candidate's first choice
> votes were
> minimized by the shadow of a near-clone who was not part of the
> Condorcettie.
>
>
>
> >
> > 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.
> >
> >
> Well, it's better than the alternative, but I wouldn't exactly
> crow about
> this. The aim of a DSV is to minimize the need for strategy and thus
> minimize its use; the fact that a system allows strategy just
> falls out of
> some combination of Arrow's criteria passed.
>
> JQ