[EM] Range Voting in presence of partial information of a certain character

[Juho]

On May 21, 2010, at 4:13 AM, fsimmons at pcc.edu wrote:

> Thanks for the comments Kevin and Lomax.
>
> Let me start over in the same vein:
>
> Suppose that candidate X was just announced as the winning  
> candidate, and no
> indication was given of how the other candidates fared in the range  
> style election.
>
> How would you wish that you had voted your range ballot?
>
> Personally, I would be mostly satisfied with my ballot if I had  
> given max
> support to everybody that I preferred over X, and no support for  
> anybody I liked
> less than X.
>
> But what about X ?  I could say that since X was the winner, X  
> probably didn't
> need my support, so I would wish that I had not supported X at all.   
> But if
> everybody took this attitude, then everybody would regret their  
> support for X,
> except those that preferred X over all of the other candidates.  And  
> most likely
> X could not have won with support only from those who considered X  
> as favorite.
>
> Suppose that due to some technicality the election had to be  
> repeated.  Would
> you give any support to X this time around (still not knowing  
> anything about how
> the other candidates fared) ?
>
> In my last message under this topic I suggested that perhaps the  
> thing to do in
> the case of a sure or almost sure winner (when you know nothing  
> about the
> chances of the other candidates) is to just give them your sincere  
> rating.
>
> Sincere ratings can be constructed by asking questions like this:   
> Would I
> prefer X to a lottery of 31%favorite+69%worst?  Suppose that the  
> answer is yes,
> but when the same question is put with the percentages changed to 29  
> and 71, my
> answer changes to no.  Then my natural rating for X would be about  
> 30 percent.
>
> What is the point of all of this?   I'm looking for a DSV (Declared  
> Strategy
> Voting) method that takes sincere natural ratings and converts them  
> into
> strategic range ballots in such a way that when the winner is  
> announced, the
> voters will be as satisfied as possible with the way the DSV handled  
> their ballots.

In some sense Condorcet is a DSV method for Range. If X is about to  
win then voters would like to cast a full one vote for all candidates  
that I prefer over X and cast a full vote for X against all candidates  
that I like less than X. In a Range ballot (and DSV) that could mean  
rating X at 0 or max depending on if the second strongest is liked  
less or more than X. If there is a Condorcet winner (X) then there is  
a "stable" strategy in the sense that no matter who the second  
strongest candidate is considered to be, X will win. Many voters (all  
but first preference X supporters) still have an interest to rate X at  
0 and all the more preferred candidates at max, but if that would make  
one of the more preferred candidates win then there would be more  
voters with (DSV) interest to reverse that change. Condorecet methods  
would do all this automatically.

We lost all the preference strength information in the Condorcet  
process but maybe this is unavoidable (in a highly competitive  
environment). Or could there be a declared strategy (or some other  
approach) where a voter would be happy to accept election of a  
slightly less liked candidate if other voters have clearly stronger  
preferences supporting some other outcome. Then we could make use of  
the Range ratings (or of indicated strengths of the rankings, e.g.  
A>B>>>C>D). Voters could voluntarily give up some of their voting  
strength. Maybe something like one indicated weak pairwise opinion to  
be canceled (tie) for each corresponding strong opinion in the reverse  
direction. (Such weak opinions could be used also to defend clones (or  
a grouping or a wing). There was some discussion on this on the EM  
list long time ago.)

Juho


>
> It turns out that it is impossible to do this in such a way that  
> everybody is
> perfectly satisfied with the handling of their ballot.  So what I am  
> trying to
> do is to minimize the number of disgruntled voters or minimize  
> something like
> the total or maximum disgruntlement of the voters.
>
> How do we define "disgruntlement" in this context?
>
> Here's another stab at this problem:
>
> Let  r  be the highest rating in the allowed range such that for some
> alternative X ...
>
> If
> the DSV approves all alternatives rated above X on all of the  
> ballots, none of
> the alternatives rated below X on any of the ballots, and all of the
> alternatives rated equal to X only at level r and above ...
>
> Then
> alternative X is the approval winner.
>
> At this level r there may be several alternatives that would qualify  
> as the
> alternative X in the above statement (just as in Bucklin there may  
> be several
> alternatives with the same median rank or rating).
>
> Of the alternatives X that fulfill the above condition for the level  
> of r
> defined above, which one should we choose?
>
> Should it be the one with the greatest approval total under the above
> conditions? Or how about the greatest approval margin?  Or should it  
> be the one
> that needed the fewest approvals at the level r to which we stooped  
> in order to
> satisfy the above condition?
>
> In other words, requiring some ballots to approve X when rated at  
> level r (below
> the topRating value) is the thing that is most likely to cause  
> disgruntlement.
> And that is what we want to minimize.
>
> Note that this does not mean that the level r alternatives will be  
> approved on
> every ballot (unless r happens to be the maxrange value).  When r is  
> below the
> toprange value, the only ballots that approve the alternatives at  
> level r are
> those that rate the winner X at level r or below.
>
> Suppose, for example, that for both alternatives X1 and X2 we have  
> to stoop to
> r=85% in order to get enough support to sustain a win, but in the  
> case of X1
> thirteen approvals are required at the 85% level, whereas for X2  
> only seven
> approvals are required at the 85% level.  Then X2 requires less  
> disgruntlement
> than X1 in order to be a range winner.  If all of the other  
> alternatives require
> stooping to approve X at a level strictly below 85%, then X2 is the  
> winner by
> this DSV method.
>
> More comments?
>
> Thanks,
>
> Forest
>
>
>
>
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