[EM] Clone-proof STAR (Score+Automatic Runoff)

Ted Stern dodecatheon at gmail.com
Tue Jul 25 11:46:19 PDT 2017

[Related to a topic that was discussed earlier on the Election-Methods list

STAR is described here:  http://www.equal.vote/

It is vulnerable to crowding -- too many clones could prevent the top-two
score winners from capturing the variance-minimizing candidate in the
pairwise runoff.

One relatively simple way to deal with clones is to reweight the ballots of
voters, and then choose one of the remaining candidates in some way.

Following that approach, let me propose the following, with no claims to
efficiency.  I'm just interested in whether it would be closer to Condorcet
in a Yee plot.

   - Find traditional STAR winner:  pick the top two scoring candidates,
   then take the pairwise-preferred of the two.  Call that candidate STAR1.
   - Assuming a score of 0 to 5, reweight ballots by a factor of (1 - score
   / 5).  In other words, if a voter scores STAR1 at a 4, their ballot is
   reweighted to (1 - 4/5) = 20%.  This is effectively a simplified form of
   multiwinner PR reweighting to find two representatives.
   - Tabulate the weighted scores on the remaining ballots, picking the top
   two weighted score winners for the second round.  Also tabulate the
   weighted pairwise preferences.  In other words, if a 60% ballot rates
   candidate Herbert over candidate Franklin, Herbert receives 0.6 preference
   against Franklin.
   - STAR2 is the winner using the sum of new pairwise preferences.
   - Finally, the winner would be the most preferred of STAR1 versus STAR2,
   using the original non-reweighted preferences.

In terms of efficiency, one could skip the SW2 round if there are no other
candidates preferred to SW1.  In other words, if regular STAR finds the
Condorcet winner, you're done.  But if not, ballots lose as much power as
they gave toward choosing STAR1, leaving behind the non-cloned candidates.
Choosing the second round finalist using STAR again would deal with cloning
at that level.

Is this method vulnerable to pushover?
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