[EM] Place Votes Table- Math 101

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A 5 by 5 place votes table for single winner elections--

Each letter-number is a number of votes

       1     2     3     4     5

A     A1    A2    A3    A4    A5
B     B1    B2    B3    B4    B5
C     C1    C2    C3    C4    C5
D     D1    D2    D3    D4    D5
E     E1    E2    E3    E4    E5

There may or may not be a first choice (or a last choice) majority.

There may or may not be a Condorcet winner or a Condorcet loser.

There ARE 1 or more majorities before or at the mid-point (going from the 
left 1 to 3 places) or going from the right (5 to 3 places)).

A divided majority or minority set may have up to all but 1 of the choices 
(i.e. 4 of the 5 choices in the example) (which may or may not be the same 
majority as in the preceding sentence).

There is (or should be, with truncated votes) a symmetry in the totals (e.g. 
all the row and column totals should be the same).

The above basics indicate, at least, that simple Borda is manifestly 
defective since it is not symmetrical.

Quare- What happens if the Borda points were 2, 1, 0, -1, -2 for the votes in 
the five places ???

What happens if the Borda points were 1.5, 0.5, -0.5, 1.5 for 4 choices ???

The table raises the question whether or not any partial removals (i.e. all 
but 1) are proper (other than perhaps removing majority last place and 
Condorcet losers).