[EM] Election Goals & Methods - a review

[Dave Ketchum]

Seems clear that robert bristow-johnson wrote clear thoughts but,  
seems to me, we need a clearer review.

While electing from a district multiple members for such as a  
legislature (PR) is important, I skip that to concentrate on electing  
such as mayors and governors.

Candidate identification:
      Via petition - a wannabe who cannot demonstrate interest via  
petition is likely not worthy of election (though petition rules can  
be excessively demanding).
      Via primary - almost essential to agree on a single candidate  
for any party for FPTP, since multiple candidates for the party would  
have to share votes of party backers.  Questionable whether worth the  
expense for other election methods. Does not solve all of FPTP's  
problems since multiple parties can back competing candidates.
      Via write-in - should be permissible, though likely to win only  
with the special effort that backers may find worthwhile in special  
cases.

FPTP:  NO method, such as FPTP, that supports only bullet voting  
should be used for electing an officer.  While many elections may need  
nothing more to satisfy their voters, this cannot be predicted when  
deciding on a method.

Bullet voting:  Many voters, in many elections, may see bullet voting  
as satisfying their needs.  They should be permitted this and not  
penalized for doing it.  Still, they should know what is available  
from the method used, to be able to take advantage of this when they  
see need.

Non-bullet voting:  Some voters, in some elections, will want to show  
preference for more than one candidate over the less desirable -  
election methods offer:
      Rating - these candidates can be distributed from best liked to  
barely worth mentioning.  Choosing ratings can get tricky, for ratings  
too close to each other make it easier for the one rated lower to win  
because of what other voters have rated them.
      Ranking - equal ranking implies equal desirability while higher  
ranking asserts greater desirability for higher ranks - but says  
nothing about how much more desirable they may be.
           Note that if the higher ranked truly deserve it, more  
voters can be expected to join in the higher ranking.

Approval:  All approved share equal ranking or rating over those not  
approved - but voter cannot express unequal liking here.

IRV:  Voting is ranking.  Vote counting initially considers candidate  
most liked from each voter.  If this does not produce a winner,  
recount the ballots based on remainder after excluding the least liked  
candidates.
      Among its problems consider awarding to other than the one best  
liked.  In the example below for Condorcet IRV will see B as weakest  
among those it sees as best liked (45A, 29C, 26B), letting A win (45A,  
44C).

Range:  A major rating method.

Condorcet:  A major ranking method (or collection of methods, since  
there is debate as to how to respond to cycles).  Since all ranking by  
each voter gets counted, counters know for each pair of candidates  
which is voted as better liked, and by how many.  The candidate that  
is best liked in each of its pairs wins.  If there is no such  
candidate, we have a cycle such as A>B>C>A to analyze - knowing that  
each cycle candidate would win if compared only with non-cycle  
candidates.  Building the following with reference to Wikipedia  
(remembering that either margins or winning votes can be used in the  
deciding):

100 votes:
45A
11B
15B,C
29C,B

The pairwise defeats are as follows:
B beats A, 55 to 45 (55 winning votes, a margin of 10 votes)
A beats C, 45 to 44 (45 winning votes, a margin of 1 vote)
C beats B, 29 to 26 (29 winning votes, a margin of 3 votes)

Using the winning votes definition of defeat strength, the defeat of B  
by C is the weakest, and the defeat of A by B is the strongest. Using  
the margins definition of defeat strength, the defeat of C by A is the  
weakest, and the defeat of A by B is the strongest.
Using winning votes as the definition of defeat strength, candidate B  
would win under minimax, Ranked Pairs and the Schulze method, but,  
using margins as the definition of defeat strength, candidate C would  
win in the same methods.
If all voters give complete rankings of the candidates, then winning  
votes and margins will always produce the same result. The difference  
between them can only come into play when some voters declare equal  
preferences amongst candidates, as occurs implicitly if they do not  
rank all candidates, as in the example above.

Runoffs:  Essential with FPTP unless one candidate receives a majority  
vote, for there is too great a chance for best-liked to not receive  
the most votes.  Top-two runoff weakness is the chance for FPTP to  
have seen true best-liked as third.  Of less value for methods that  
let voters better express their desires.

General:  I have not tried for a full list of methods, though these  
deserve major consideration.
      Method needs to be simple and  properly earn trust of voters.
      Giving extra value to voter's first choice can hurt more than it  
helps - voter can want equal power in deciding among major candidates,  
AND to do best possible for a minor candidate.

Dave Ketchum

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