CRITERIA FOR FAIR ELECTIONS

What is a fair election? It is an election where every voter can vote the way he wants to vote. Here are some criteria for determining whether or not an election is fair:


ROBINSON'S CRITERIA

Out of these criteria and Finite Mathematics is born the Independent Voting System. It is able to separate the candidates and alternatives into separate independent votes, rather than pitting them against each other.


OTHER CRITERIA

Here are election criteria that were formed by others, along with the italicized evaluation of these criteria using Robinson's Criteria:

DEFINITE CRITERIA


INDEFINITE CRITERIA


APPLICATION OF THESE CRITERIA TO DIFFERENT ELECTION SYSTEMS

YES means the criterion is met, except where marked with *.

Voting
System


-----------


Criterion
P   
L
U
R
A
L
I
T
Y
P
L
U
R  R
A  U
L  N
I  O
T  F
Y  F
A   
P
P
R
O
V
A
L
A
P
P  R
R  U
O  N
V  O
A  F
L  F
R
A
N  B
K  O
I  R
N  D
G  A
2
N  C
D  O
   N
C  D
H  O
O  R
I  C
C  E
E  T
C
O
N  R
D  A
O  N
R  K
C  I
E  N
T  G
R
A
N
K
 
I
N  R
S  U
T  N
A  O
N  F
T  F
F
R
A
C
T  R
I  A
O  T
N  I
A  N
L  G
R
A  R
N  A
G  T
E  I
   N
9  G
R
A
N  R
G  A
E  T
   I
9  N
9  G
I
N
D
E
P
E  V
N  O
D  T
E  I
N  N
T  G
   P
   R
   O
   P
   O
   R
   T
   I
L  O
I  N
S  A
T  L
   P
I  R
N  O
D  P
E  O
P  R
E  T
N  I
D  O
E  N
N  A
T  L
R
A
N
K  T
   R
S  A
I  N
N  S
G  F
L  E
E  R
Condorcet Criterion
(win all pairs wins)
nono nonoYES noYESno YESYESYES YESnoYES YES
Condorcet Winner
(pairs win w/o strategy)
nono nonono YESYESno YESYESYES YESnoYES YES
Order-Reversal Resist
(needs no strategy)
nono YESYESYES nonono YESYESYES YESYESYES YES
Truncation Resistance
(Incomplete ballot OK)
nono YESYESno noYESno nonono YESnoYES no
Condorcet Protective
(Cond & Ord-Rev & Trunc)
nono nonono nonono nonono YESnoYES no
Condorcet Loser
(lose all pairs loses)
nono YESYESYES YESYESYES YESYESYES YESnono YES
Smith Criterion
(party w/ most wins)
nono YESnoYES noYESno YESYESYES YESYESYES no
Majority Criterion
(Over 50% wins)
YESYES YESYESYES noYESYES nonono YESnoYES YES
Above Criteria
Subtotal Met
11 545 262 555 8 (all)27 5
Voting
System


-----------


Criterion
P
L
U
R
A
L
I
T
Y
P
L
U
R  R
A  U
L  N
I  O
T  F
Y  F
A
P
P
R
O
V
A
L
A
P
P  R
R  U
O  N
V  O
A  F
L  F
R
A
N  B
K  O
I  R
N  D
G  A
2
N  C
D  O
   N
C  D
H  O
O  R
I  C
C  E
E  T
C
O
N  R
D  A
O  N
R  K
C  I
E  N
T  G
R
A
N
K
 
I
N  R
S  U
T  N
A  O
N  F
T  F
F
R
A
C
T  R
I  A
O  T
N  I
A  N
L  G
R
A  R
N  A
G  T
E  I
   N
9  G
R
A
N  R
G  A
E  T
   I
9  N
9  G
I
N
D
E
P
E  V
N  O
D  T
E  I
N  N
T  G
   P
   R
   O
   P
   O
   R
   T
   I
L  O
I  N
S  A
T  L
   P
I  R
N  O
D  P
E  O
P  R
E  T
N  I
D  O
E  N
N  A
T  L
R
A
N
K  T
   R
S  A
I  N
N  S
G  F
L  E
E  R
Participation Criterion
(honesty doesn't hurt)
YESYES YESYESYES nonono YESYESYES YESnoYES YES
Favorite-Safe Criterion
(no strategy needed)
nono YESYESno nonono YESYESYES YESnoYES no
Clone-Safe Criterion
(no result change)
nono YESYESno noYESno YESYESYES YESnoYES no
Remove-Loser-Safe
Criterion (no result change)
nono YESYESno nonono YESYESYES YESnoYES no
Monotonicity Criterion
(voting can't hurt)
YESYES YESYESYES noYESno YESYESYES YESnoYES no
Precinct
Countable
YESYES YESYESYES noYESno YESYESYES YESnono no
Dumb Machine
Compatible
YESYES YESYESno nonono nonono YESnoYES no
Extremist/Centrist
Nonbias Criterion
ExtExt CenCenCen CenCenExt YESYESYES YESExtYES Ext
Above Criteria
Subtotal Met
44 773 030 777 8 (all)07 1
Voting
System


-----------


Criterion
P
L
U
R
A
L
I
T
Y
P
L
U
R  R
A  U
L  N
I  O
T  F
Y  F
A
P
P
R
O
V
A
L
A
P
P  R
R  U
O  N
V  O
A  F
L  F
R
A
N  B
K  O
I  R
N  D
G  A
2
N  C
D  O
   N
C  D
H  O
O  R
I  C
C  E
E  T
C
O
N  R
D  A
O  N
R  K
C  I
E  N
T  G
R
A
N
K
 
I
N  R
S  U
T  N
A  O
N  F
T  F
F
R
A
C
T  R
I  A
O  T
N  I
A  N
L  G
R
A  R
N  A
G  T
E  I
   N
9  G
R
A
N  R
G  A
E  T
   I
9  N
9  G
I
N
D
E
P
E  V
N  O
D  T
E  I
N  N
T  G
   P
   R
   O
   P
   O
   R
   T
   I
L  O
I  N
S  A
T  L
   P
I  R
N  O
D  P
E  O
P  R
E  T
N  I
D  O
E  N
N  A
T  L
R
A
N
K  T
   R
S  A
I  N
N  S
G  F
L  E
E  R
Robinson Fair Election
(vote for any, against any)
nono YESnono nonono YESYESYES YESnoYES no
Independence Criterion
(no interlock)
nono YESnono nonono YESYESYES YESnoYES no
Ranking Rejection
(ranking doesn't work)
nono YESnono nonono YESYESYES YESYESYES no
Plurality Rejection
(plurality doesn't work)
nono YESnoYES YESYESYES YESYESYES YESnoYES no
Robinson Election-Entry
(can get on ballot)
nono YESYESno nonono YESYESYES YESYESYES no
Robinson Anti-Bias I
(entry no result change)
nono nonono nonono YESYESYES YESYESYES no
Robinson Anti-Bias II
(NO & YES same power)
nono nonono nonono YESnono YESnoYES no
Robinson Bias
(no special info needed)
nono nonono nonono YESYESYES YESnoYES no
Robinson Balance
(no bias disadvantage)
nono nonono nonono YESnono YESnoYES no
Robinson Fallacy *
("voter wants only one")
yesyes NOyesyes yesyesyes NONONO NONONO yes
Disenfranchised Voter *
(can't vote preference)
yesyes yesyesyes yesyesyes yesyesyes NOyesNO yes
Robinson Removal
(no result change)
nono YESnono nonono YESYESYES YESnoYES no
Robinson Winner
(pleases most wins)
nono YESnono nonono YESnono YESYESYES no
Robinson Loser
(pleases least loses)
nono YESYESno nonono YESYESYES YESnono no
Robinson Criteria
Subtotal Met
00 921 111 131010 14 (all)513 0
All Criteria
Total Met
55 21139 3103 252222 30 (all)727 6
Voting
System


-----------


Criterion
P
L
U
R
A
L
I
T
Y
P
L
U
R  R
A  U
L  N
I  O
T  F
Y  F
A
P
P
R
O
V
A
L
A
P
P  R
R  U
O  N
V  O
A  F
L  F
R
A
N  B
K  O
I  R
N  D
G  A
2
N  C
D  O
   N
C  D
H  O
O  R
I  C
C  E
E  T
C
O
N  R
D  A
O  N
R  K
C  I
E  N
T  G
R
A
N
K
 
I
N  R
S  U
T  N
A  O
N  F
T  F
F
R
A
C
T  R
I  A
O  T
N  I
A  N
L  G
R
A  R
N  A
G  T
E  I
   N
9  G
R
A
N  R
G  A
E  T
   I
9  N
9  G
I
N
D
E
P
E  V
N  O
D  T
E  I
N  N
T  G
   P
   R
   O
   P
   O
   R
   T
   I
L  O
I  N
S  A
T  L
   P
I  R
N  O
D  P
E  O
P  R
E  T
N  I
D  O
E  N
N  A
T  L
R
A
N
K  T
   R
S  A
I  N
N  S
G  F
L  E
E  R
Expressiveness
(3-way race choices)
4 of
27
8 of
108
8 of
27
16 of
108
6 of
27
9 of
27
9 of
27
9 of
27
all of
1331
all of
1000
all of
10^6
all of
27
8 of
27
all of
1331
6 of
27
Simplicity
(subjective 0 to 10)
97 973 432 876 1068 1
Arrow's Theorem
(fairness violation)
yesyes yesyesyes yesyesyes yesyesyes Refutedyesyes yes
Gibbard-Satterthwaite
Theorem (strategy sensitive)
yesyes yesyesyes yesyesyes yesyesyes Refutedyesyes yes

* "NO" meets the criterion; "yes" does not.

For info on each of these election systems, click HERE.


The Refuted Theorems

Arrow's Theorem: No voting system satisfies all fairness criteria.

Gibbard-Satterthwaite Theorem: No voting system is immune to strategic (insincere) voting.

These theorems are faulty because they assume that the only fair systems must be ranking systems. But the system that does meet all of the fairness criteria is not a ranking system. The Independent Voting System is as far as it can be from a ranking system. The vote on each candidate is totally independent from the vote on any other candidate.


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