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VFA Examples

FS
Forest Simmons
Fri, Feb 9, 2024 2:46 PM

Exemple 1.
40 A-B
10 C-A
10 C-B
40 B-A
Respective For And Against Totqls: x,x'

for x= a,b, c
40, 50.  40, 50.  20, 0

So

ab' =4050 = 2000 = ba'
ac' = bc' = 0
ca' = cb' = 20
50 = 1000

Strength of finish orders:
A>B>C and B>A>C have strength
ab' + ac' + bc' = 2000

C>B>A and C>A>B both have strength
cb' + ca' +ba' = 4000

A>C>B and B>C>A both have strength
ac' + ab' + cb' = 3000

So the two finish orders that place C in first place are tied for strongest.

Now suppose the A faction decides to bury C unilaterally ... by voting
40 A-C instead of  A-B

Then b' is reduced to 10, and c' is increased to 40.

The respective finish order strengths become ...
A>B>C: 40*(10 +40) + 40*40 = 3600
B>A>C:  also 3600
A>C>B: 2400
B>C>A: 5600
C>A>B: 1600
C>B>A: 3200

The strongest finish order is B>C>>A .... the bus B is the single winner
candidate.

This version of VFA seems to be burial resistant.

Check my work .... in my old age I am susceptible to both typos and thinkos.

-fws

Exemple 1. 40 A-B 10 C-A 10 C-B 40 B-A Respective For And Against Totqls: x,x' for x= a,b, c 40, 50. 40, 50. 20, 0 So ab' =40*50 = 2000 = ba' ac' = bc' = 0 ca' = cb' = 20*50 = 1000 Strength of finish orders: A>B>C and B>A>C have strength ab' + ac' + bc' = 2000 C>B>A and C>A>B both have strength cb' + ca' +ba' = 4000 A>C>B and B>C>A both have strength ac' + ab' + cb' = 3000 So the two finish orders that place C in first place are tied for strongest. Now suppose the A faction decides to bury C unilaterally ... by voting 40 A-C instead of A-B Then b' is reduced to 10, and c' is increased to 40. The respective finish order strengths become ... A>B>C: 40*(10 +40) + 40*40 = 3600 B>A>C: also 3600 A>C>B: 2400 B>C>A: 5600 C>A>B: 1600 C>B>A: 3200 The strongest finish order is B>C>>A .... the bus B is the single winner candidate. This version of VFA seems to be burial resistant. Check my work .... in my old age I am susceptible to both typos and thinkos. -fws