[EM] TTR,MinMax, Losing Votes (TERW)

[Chris Benham]

Here is an example of  my suggested new FBC-complying method performing better than ICT 
("Improved Condorcet, Top", a name coined by Mike Ossipoff for a method I defined).

30: A=B
30: B
20: A
10: C>A
10: D>A

According to the TTR (Kevin Venzke's "Tied at the Top Tule"),
A>B 70-30 and B>A 60-40.    A> C 50-10, A>D 50-10,   B>C 60-10, B>D 60-10.

Only A and B are qualified by TTR, and ICT elects the qualified candidate with highest
Top ratings (we'll say these are Top-Middle-Bottom 3-slot ratings ballots, with default
rating being Bottom). 

TR scores:  B60,   A50,  C10,  D10.

So ICT elects B.

The first part of my new method is the same, so only A and B are qualified.

To determine the winner a different pairwise matrix is looked at to weigh defeats (while keeping
the same TTR "direction").

So A>B 70-60 and  "B>A" 60-70  (the 30 A=B ballots each give a whole vote to both A and B).

A and B have no other pairwise "defeats", so (weighing them by Losing Votes) A's MinMax score is
70 and B's is 60 so A wins.

A is rescued from the splitting of the  A>B "faction''s vote by C and D being on the ballot.

As it does here, the new method is much more likely than ICT to elect the real Condorcet winner.

Chris Benham


I wrote (Tues.20 Nov 2012):

I have an idea for a not-very-sinple FBC-complying method that behaves like ICT with 3 candidates, but better
handles more candidates and ballots with more than 3 ratings-slots or ballots that allow full ranking of the candidates.
 
*Voters rank from the top however many candidates they wish. Equal-top ranking and truncation must be allowed.
 
Use the "Tied-at-the-Top Rule" (invented by Kevin Venzke) to discover if any candidate/s pairwise beats (according
to that rule's special definition) all the others, and if so to disqualify all those that don't.
 
http://wiki.electorama.com/wiki/Tied_at_the_top_rule
 
Then construct a pairwise matrix that is "normal" except that ballots that equal-rank at the top any X and Y contribute
a whole vote (in the X versus Y pairwise comparison) to each of X and Y.  Ballots that equal-rank any X and Y in any
below-top position contribute (in that pairwise comparison) no vote to either.
 
The purpose of that matrix is just to determine Losing Votes scores. The directions of the defeats are determined by
the Tied-at-the-Top rule (according to which X and Y can pairwise "defeat" each other.
 
Elect the qualified candidate whose worse "defeat" (as identified by TTR and measured by Losing Votes with the above
equal top-ranking rule) is the weakest.*
 
I hope that inelegant waffle is at least clear.
 
Chris Benham
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