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 Fair Election Criterion:
A FAIR election lets the voter vote for all of the candidates and alternatives he wants to vote for, and vote against all of the candidates and alternatives he wants to vote against, without being penalized or being forced to change one or more votes to obey the voting system.
Robinson's Independence Criterion:
Voting on each candidate or alternative in a race must be made on its own merit, independent of votes on the other candidates or alternatives in the race. There shall be no interlocking between candidates.
Robinson's Ranking Rejection:
Ranking is a very poor way to choose or decide anything. Ranking is stupid statistical garbage. A ranking system has no way to determine where a voter stops liking candidates (or alternatives) and starts disliking them. So rankings should never be used for elections. Systems that require a first choice, a second choice, etc. shall not be used.
Robinson's Plurality Rejection:
The Plurality Voting System is internally biased whenever more than two candidates or alternatives are in the race. The bias always unfairly favors the candidate or alternative most different from the others, and unfairly opposes candidates or alternatives that are similar to other candidates or alternatives.
Robinson's Election-Entry Conundrum:
How can a voter vote for his personal choice in an election when his personal choice is not on the ballot? Most election entry rules are based on the faulty Plurality system. Such election-entry barriers must be removed.
Robinson's Addition/Removal Criterion:
The entry of a candidate or alternative into the race or the exit of a candidate or alternative from the race must never be able to change the votes that other candidates or alternatives receive. It must not affect the outcome of the election unless this candidate wins when in the race. The resulting winner must be the Robinson Winner.
Removing an ineligible candidate or alternative from the ballot either before or after the election must not disrupt the rest of the election.
Robinson's Bias Prevention Criterion:
Voting NO on a choice must have exactly the same weight that voting YES on a choice has. The voter must be allowed to specifically vote NO on any choice and have that vote count.
Robinson's Bias Conundrum:
How can a voter vote to win if he has to know how others voted to know which choice to make? The voter must not be forced to change a vote to favor a less desirable choice in order for his viewpoint to win.
Robinson's Balance Criterion:
The voter must not have to work against a built-in bias toward extremists or centrists for his viewpoint to win.
Robinson's Fallacy:
"Every voter likes exactly one candidate or alternative, and dislikes all of the rest." Voting systems based on this false assumption disenfranchise voters.
Robinson's Disenfranchised Voter:
Any voter who is not allowed by the voting system to vote his preference is disenfranchised. This includes a voter who wants to vote against all of the candidates or alternatives, a voter who favors more than one candidate or alternative equally, a voter whose choice is not on the ballot, and a voter who wants an administrative office abolished. There shall be no such thing as an overvote or an undervote.
Robinson's Anti-Negative Campaigning Criterion:
Negative campaigning and news-produced scandals shall not increase the vote any other candidate receives by taking votes away from another candidate.
Robinson's Distinction Criterion:
The election result must be distinct, not a blurry result that could go either way with slight changes in voter preference.
The Robinson Winner:
The Robinson Winner is the candidate or alternative that pleases the largest number of voters.
The Robinson Loser:
The Robinson Loser is the candidate or alternative that displeases the largest number of voters.
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.
Changes:
Here are election criteria that were formed by others, along with the italicized evaluation of these criteria using Robinson's Criteria:
The Condorcet Criterion:
The winner of all votes on pairs of candidates or alternatives should be the winner.
This, of course, violates the Robinson Ranking Criterion. Ranking is a poor way of deciding an election because it cannot tell if a voter likes or dislikes any choice at a given ranking.
Condorcet Winner:
The winner of all votes on pairs of candidates or alternatives should be the winner, provided that the voters voted sincerely, and not attempting to increase odds of winning by voting for the poll leader in the party over their personal favorite choices.
Again, ranking is a poor way to choose. This violates the Robinson Ranking Criterion. The voter must be allowed to vote for or against all personal choices without penalty.
Condorcet Order-Reversal Resistance Criterion
The election system must not cause voters to try to increase odds of winning by voting for the poll leader in the party over their personal favorite choices.
This is a valid criterion. But the assumption that a voter must vote for only one candidate is false, as is the expectation of a ranking vote.
Condorcet Truncation Resistance Criterion:
The election system must work properly even if a lazy voter does not complete all of the ranking levels.
Again, ranking is a poor way to choose. But the system must work if a lazy voter leaves entries blank, and must not disqualify any voter choices, including leaving an entry blank.
Condorcet Protective Criterion:
The election must meet the Condorcet Criterion, it must be Order-Reversal Resistant, and it must be Truncation-Resistant.
Agreed, except that it must also not use ranking.
Condorcet Loser:
An alternative beaten in all paired votes must lose.
OK!
Smith Criterion:
If the most votes go to one party, faction, or belief, then the winner must be chosen from that party or belief.
Right. But it erroneously assumes that all votes are for an alternative.
Majority Criterion:
If an alternative is favored by over 50 percent of the voters, it must win.
What if over 50 percent of the voters favor two different alternatives? Robinson's fallacy is at work here, because the criterion assumes that each voter can favor only one alternative.
Participation Criterion:
Casting an honest vote must not lower the chance of the voter's viewpoint winning.
This is similar to Robinson's Bias Conundrum and the Condorcet Order-Reversal Resistance Criterion.
Favorite-Safe Criterion:
The voter must never need a strategy of voting for the poll leader instead of the personal favorite for the viewpoint of the voter to win.
This is similar to the Participation Criterion. It also assumes that the voter can vote for only one candidate or alternative.
Clone-Safe Criterion:
The entry or exit of a candidate or alternative similar to another candidate or alternative (a "clone" candidate) must not change the outcome of the election, unless the clone candidate or alternative wins when in the race.
This is similar to Robinson's Addition and Removal Criterion.
Remove-Loser-Safe Criterion:
The removal of an ineligible losing candidate or alternative from the election must not change the outcome of the election. The same ballots should be usable and should still elect the same winner.
This is similar to Robinson's Addition and Removal Criterion.
Monotonicity Criterion:
Increasing a vote for a candidate or alternative (with all else remaining the same) must not decrease that alternative's probability of winning the election. Decreasing a vote for a candidate or alternative (with all else remaining the same) must not increase that alternative's probability of winning the election.
No fair election violates this.
Precinct Countable Criterion:
Each precinct must be able to produce a summary vote subtotal. The precinct subtotals must be usable in determining the overall winner of each race.
This is essential to an open election system with no hidden components other than ballot secrecy.
Dumb Machine Criterion:
The voting system must be usable without requiring computerized voting machines.
It must also work with paper ballots.
Extremist/Centrist Unbiased Criterion:
The voting system must not produce biases. It must not favor either extremists or centrists.
This is essential to a fair election.
Expressiveness:
The more kinds of votes you can cast, the more expressiveness you have.
Only one problem: Too much expressiveness dilutes the vote, and may produce no clear winner.
Simplicity Criterion:
The election system must have simple rules, must be simple for the voter to use, and must be simple for the election officials to count and determine the winner.
Simplicity must not be used to justify the use of an unfair voting system.
Arrow's Theorem:
No voting system satisfies all fairness criteria.
As we will see, this is not true.
Gibbard-Satterthwaite Theorem:
No voting system is immune to strategic (insincere) voting.
As we shall see, this is not true.
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) |
no | no | no | no | YES | no | YES | no | YES | YES | YES | YES | no | YES | YES |
| Condorcet Winner (pairs win w/o strategy) |
no | no | no | no | no | YES | YES | no | YES | YES | YES | YES | no | YES | YES |
| Order-Reversal Resist (needs no strategy) |
no | no | YES | YES | no | no | no | no | YES | YES | YES | YES | YES | YES | YES |
| Truncation Resistance (Incomplete ballot OK) |
no | no | YES | YES | no | no | YES | no | no | no | no | YES | no | YES | no |
| Condorcet Protective (Cond & Ord-Rev & Trunc) |
no | no | no | no | no | no | no | no | no | no | no | YES | no | YES | no |
| Condorcet Loser (lose all pairs loses) |
no | no | YES | YES | YES | YES | YES | YES | YES | YES | YES | YES | no | no | YES |
| Smith Criterion (party w/ most wins) |
no | no | YES | no | YES | no | YES | no | YES | YES | YES | YES | YES | YES | no |
| Majority Criterion (Over 50% wins) |
YES | YES | YES | YES | YES | no | YES | YES | no | no | no | YES | no | YES | YES |
| Above Criteria Subtotal (number met) |
1 | 1 | 5 | 4 | 4 | 2 | 6 | 2 | 5 | 5 | 5 | 8 ∀ | 2 | 7 | 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) |
YES | YES | YES | YES | YES | no | no | no | YES | YES | YES | YES | no | YES | YES |
| Favorite-Safe Criterion (needs no strategy) |
no | no | YES | YES | no | no | no | no | YES | YES | YES | YES | no | YES | no |
| Clone-Safe Criterion (no result change) |
no | no | YES | YES | no | no | YES | no | YES | YES | YES | YES | no | YES | no |
| Remove-Loser-Safe (no result change) |
no | no | YES | YES | no | no | no | no | YES | YES | YES | YES | no | YES | no |
| Monotonicity Criterion (voting can't hurt) |
YES | YES | YES | YES | no | no | no | no | YES | YES | YES | YES | no | YES | no |
| Precinct Countable (no special process) |
YES | YES | YES | YES | YES | no | YES | no | YES | YES | YES | YES | no | no | no |
| Dumb Machine Usable (no special machine) |
YES | YES | YES | YES | no | no | no | no | no | no | no | YES | no | YES | no |
| Extremist/Centrist Nonbias (neutral) |
Ext | Ext | Cen | Cen | Cen | Cen | Cen | Ext | YES | YES | YES | YES | Ext | YES | Ext |
| Above Criteria Subtotal (number met) |
4 | 4 | 7 | 7 | 2 | 0 | 2 | 0 | 7 | 7 | 7 | 8 ∀ | 0 | 7 | 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) |
no | no | YES | no | no | no | no | no | YES | YES | YES | YES | no | YES | no |
| Independence Criterion (no interlock) |
no | no | YES | no | no | no | no | no | YES | YES | YES | YES | no | YES | no |
| Ranking Rejection (ranking doesn't work) |
no | no | YES | no | no | no | no | no | YES | YES | YES | YES | YES | YES | no |
| Plurality Rejection (plurality doesn't work) |
no | no | YES | no | YES | YES | YES | YES | YES | YES | YES | YES | no | YES | no |
| Robinson Election-Entry (can get on ballot) |
no | no | YES | YES | no | no | no | no | YES | YES | YES | YES | YES | YES | no |
| Robinson Add/Removal (entry/exit no result change) |
no | no | no | no | no | no | no | no | YES | YES | YES | YES | no | YES | no |
| Robinson's Bias Prevent (NO & YES same power) |
no | no | no | no | no | no | no | no | YES | no | no | YES | no | YES | no |
| Robinson Bias (no special info needed) |
no | no | no | no | no | no | no | no | YES | YES | YES | YES | no | YES | no |
| Robinson Balance (no bias disadvantage) |
no | no | no | no | no | no | no | no | YES | no | no | YES | no | YES | no |
| Robinson Fallacy * (voter wants only one) |
yes | yes | NO | yes | yes | yes | yes | yes | NO | NO | NO | NO | NO | NO | yes |
| Disenfranchised Voter * (can't vote preference) |
yes | yes | yes | yes | yes | yes | yes | yes | yes | yes | yes | NO | yes | NO | yes |
| Anti-Negative Campaign (can't steal votes) |
no | no | YES | no | no | no | no | no | YES | YES | YES | YES | no | YES | no |
| Distinction Criterion (no vague result) |
YES | YES | YES | YES | no | no | no | no | no | no | no | YES | no | YES | no |
| Robinson Winner (pleases most wins) |
no | no | YES | no | no | no | no | no | YES | no | no | YES | YES | YES | no |
| Robinson Loser (pleases fewest loses) |
no | no | YES | YES | no | no | no | no | YES | YES | YES | YES | no | no | no |
| Robinson Criteria Subtotal (number met) |
1 | 1 | 10 | 3 | 1 | 1 | 1 | 1 | 13 | 10 | 10 | 15 ∀ | 4 | 14 | 0 |
| All Criteria (Total Met) |
6 | 6 | 22 | 14 | 7 | 3 | 9 | 3 | 25 | 22 | 22 | 31 ∀ | 6 | 28 | 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) |
9 | 7 | 9 | 7 | 3 | 4 | 3 | 2 | 8 | 7 | 6 | 10 | 6 | 8 | 1 |
| Arrow's Theorem (fairness violation) |
yes | yes | yes | yes | yes | yes | yes | yes | yes | yes | yes | Refuted | yes | yes | yes |
| Gibbard-Satterthwaite (strategy sensitive theorem) |
yes | yes | yes | yes | yes | yes | yes | yes | yes | yes | yes | Refuted | yes | yes | yes |
* "NO" meets the criterion; "yes" does not.
∀ works for all criteria.
For info on each of these election systems, click HERE.
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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