[EM] Range-Approval hybrid

[Chris Benham]

I  have an idea for a  FBC complying method  that  I think is clearly
better  than the version of   "Range Voting" (aka  Average Rating or
Cardinal Ratings)  defined and promoted by  CRV.

  http://rangevoting.org/

I suggest that voters use multi-slot ratings ballots that have the bottom
slots (at least 2 and not more than half) clearly labelled as expressing
"disapproval" and all others as expressing "Approval".  The default
rating is the bottom-most.

Compute each candidate X's  Approval score and also "Approval
Opposition" score  (the approval score of the most approved candidate
on ballots that don't approve X). 

All candidates whose approval score is exceeded by their approval
opposition (AO) score are disqualified.  Elect the undisqualified
candidate that is highest ordered by Average Rating.

I suggest many fewer slots than 99  and no  "no opinion" option, so I
think the resulting method is not more complex for voters.

This method would work much better than normal RV in avoiding a
split-vote problem in a  '2 sub-factions confront a big faction' scenario
(such as  Obama and  Clinton versus McCain).  In this method  if  Obama
and Clinton supporters all approve both candidates and not McCain,
then if there are more of them voting than McCain supporters McCain
must be disqualified, so  Obama and Clinton can compete with each
other more meaningfully and with much less risk of  a McCain win.

Minor party supporters can make approval distinction between the 
front-runners and then rate their sincere favourites exclusive-top with
very little added risk  (compared with rating their preferred front-runner
equal-top) of  allowing their "greater evil" candidate to win.

It meets a sort of   "Approval Strong Minimal Defense" that says that
if more voters approve  X and not Y than approve Y, Y can't win.

And a sort of  "Approval Majority for Solid Coalitions" that says that
if  more than half  the voters rank/rate a subset S of candidates above
all others, and approve all the members of  S and none of the non-members,
then the winner must come from S. 

(This of course is only worth mentioning because the voters supporting
the S candidates can still make meaningful preference distinctions among
them, unlike in plain Approval.) 

Like normal Range it clearly meets Favourite Betrayal, because if  X wins
with some voters insincerely down-rating Y, then if  Y is raised to the top
slot alongside X; X will still be qualified (because X's approval score will
not be reduced and X's AO score can only be reduced), no non-XY candidate
can have a reduced PO score so no previously disqualified non-XY candidate
will become undisqualified; and of course only Y's  Average Ratings score
will be changed so if there is a  new winner it can only be Y.

Like normal Range and unlike  methods such  as  Bucklin, it meets Independence
from Irrelevant Ballots (IIB). This wouldn't be the case if  the rule regarding the
approvals specified for example that candidates need to be disapproved by "a
majority" to be disqualified.

I can't see that this method fails any desirable criterion that normal Range meets.

Comments?

Chris  Benham


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