One more thing about "unknown middle"

[DEMOREP1 at aol.com]

Mr. Layton asked-

Incidentally, do you (and I would like to hear responses from other list

members as well) support optional preferential or compulsory preferential or

something in between (ie a minimum number of preferences be expressed for a

vote to be considered valid)?  While truncated votes cause significant

problems for pairwise comparisons, should a vote where the intention of the

voter is clear (ie a single number 1, or a single x) be declared invalid,

simply because it causes difficulties?
---
D- 1. No minimum.

2. In view of the place votes table, each truncated choice should have 1/N 
vote in each place involved, as I noted about 2 weeks ago.

Example

A voter votes

CB [A=D=E]

A, D and E should get a 1/3 vote each in the 3rd, 4th and 5th places of a 
place votes table from such ballot (computerized votes needed in large 
elections).

However, in each head to head pairing, there would be a majority of all votes 
(MOAV) winner (assuming no ties) if each choice involved has a 1/2 vote.

Example

45 G > H  ranked votes
 5 G > [H = other] truncated votes
33  H > G  ranked votes
 7 H > [G = other] truncated votes
10 Other > [G=H=other] truncated votes

100

G vs H head to head

G 45 + 5 + 10/2 = 55
H 33 + 7 + 10/2 = 45

100 = 100