[EM] When Voters Strategize, Approval Voting Elects Condorcet

[Juho]

One more thought on the trend to reduce the level of strategic games  
with the votes. It may be possible to develop also automatic  
strategies for the votes. If there is a need to guarantee the  
termination of the strategy changes one could artificially force that  
by e.g. allowing the strategy changes only in one direction, e.g.  
from approving less towards approving more candidates.

Here's one example calculation (with "abc" loop and one extra not so  
popular "d" candidate). The strategy algorithm that I used is simply  
to move the approval cutoff one step forward if the currently leading  
candidate is worse than the next to be approved candidate in the  
ballot, until there are no more changes to the strategies. In some  
situations this algorithm can also provide protection against voter  
strategies.

35 a,bcd
33 b,cad
32 d,cab
=> leader is a

35 a,bcd
33 bc,ad
32 dc,ab
=> leader is c

35 ab,cd
33 bc,ad
32 dc,ab
=> leader is b

35 ab,cd
33 bc,ad
32 dca,b
=> leader is b
=> winner is b

Juho


On Jul 18, 2007, at 1:59 , Forest W Simmons wrote:

> Mr. Schudy's article reinforces the rationale behind DYN: that with
> reliable partial information, Approval does as well or better than
> Condorcet.
>
> Mr. Schudy treats the case in which there is a clear frontrunner and a
> clear runnerup.  In that case he shows that (what we usually call)
> "approval strategy A" is rational, and that it gets the Condorcet
> Winner elected, a result well known on this listserv.
>
> Of course, that requires reliable polling information.  I think that a
> version of DYN suggested by Juho is the simplest method to meet this
> requirement without requiring voters to return to the polls.
>
> DYN works well whether or not there are two leading candidates.
>
> Juho's version of DYN requires each candidate to publish their  
> rankings
> of the other candidates before the election, and allows only one proxy
> per voter.
>
> Voters approve (with Y for yes) some candidates and disapprove (with N
> for no) others.  If there are any left over, each voter designates (D)
> one candidate as proxy for making the remaining Y/N decisions.  After
> the statistics of the partial results are in, the candidates (as
> proxies) use their strategies to make the remaining Y/N decisions,
> which have to be consistent with their pre-election rankings.
>
> Consistency means that if the proxy ranked candidate A ahead of
> candidate B, and she gives a Y (for yes) to candidate B, then she must
> also give a Y to candidate A.
>
> It was Juho's suggestion that to simplify things we should allow only
> one proxy per voter. Also, Juho's suggestion of not giving too much
> leeway to the proxies inspired the idea of making their Y/N proxy  
> votes
> be consistent with their pre-published rankings.  That's why I call
> this "Juho's version of DYN."
>
> On another related topic.  How best to use sincere range ballots?
>
> I think maximizing the Gini score is the best (except in situations in
> which the spoils of the election are freely shared by the voters).
>
> For candidate X the Gini score is obtained by
>
> 1. (first) sorting the ballots in order of how they rate X from best
> rating to worst.
>
> 2. Then computing a weighted average of the ratings, where the rating
> on the j_th ballot in the sorted order is given a weight of (2*j-1),
> i.e. the consecutive odd numbers are the weights.
>
> For example,
>
> 50 A>B>C
> 50 C>B>A
>
> with B at midrange (50%) on all ballots, hence with an average of 50%,
> no matter the weights.
>
> It turns out that  A and C are tied for last with a common weighted
> average rating of
>
>    (1+3+...+99)/(1+3+...+ 199),
>
> which is exactly 25%.
>
> Of course, Gini optimal strategy is the same as ordinary Range optimal
> strategy, which is just Approval strategy, and in strategic voting the
> exact symmetry would have to be broken to determine a winner for this
> example.
>
> If exactly half of the voters approved B and the other half  
> disapproved
> B, then it would be a three way tie, whether measured by Approval,
> Gini, or Range.
>
> Forest
> ----
> election-methods mailing list - see http://electorama.com/em for  
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